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EARTH WARMING: A SIMPLE, CHEAP AND FAST MECHANISM FOR REVERTING THE PROCESS - A PREPRINT

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Abstract

The warming of the Earth system, due to the large increase in the amount of greenhouse gases in the atmosphere and the climate consequences of this warming present an existential threat to the civilization that evolved with the fossil fuel-intensive industrialization of the last two centuries. Even if we manage to achieve a carbon-neutral economy in the next two or three decades, the effects of the accumulated gases in the atmosphere will cause an average increase in the Earth's surface temperature with catastrophic climate consequences for large parts of the population and Earth ecosystems. The economic costs alone in such a scenario run easily into the trillions of US dollars. Adding the losses of livelihood for hundreds of millions of people and unfavourable ecosystems for the fauna and flora on which we depend, points to the dire consequences and urgency of addressing the problem. This paper proposes a mechanism for controlling, monitoring, and even reverting the Earth warming that should be (I) technically feasible, (II) economically cheap, and, (III) that can be implemented in a relatively short period of time. The implementation of such a proposal may help us avoid a catastrophic situation and give us more time to reshape our economy and society in a more sustainable way. The mechanism consists of tweaking the Earth albedo in order to offset the radiation forcing effect of the greenhouse gases accumulated in the atmosphere and in this way slowing down or stopping the process and even reverting the heating that has already occurred. This can be achieved by coating surfaces (e.g. rooftops, pavements, and roads) in urban and rural occupied areas with materials with a high reflective index. It can also be applied to deserted areas or lakes and ocean. In Section 1 the qualitative description of the model is expanded and described with more details and in Section 4 a zeroth-order model is presented with a calculation that supports the proposal presented here. In Section 6 a tentative road-map for the implementation of the solution is laid out.
EARTH WARMING: A SIMPLE,CHEAP AND FAST MECHANISM
FOR REVERTING THE PROCESS
A PREPRINT
Jose Nivaldo Hinckel
National Institute for Space Research - INPE (retired)
São José dos Campos, SP (Brazil)
hinckeljn@gmail.com
June 16, 2020
ABS TRAC T
The warming of the Earth system, due to the large increase of the amount of greenhouse gases in
the atmosphere and the climate consequences of this warming present an existential threat to the
civilization that evolved with the fossil fuel-intensive industrialization of the last two centuries.
Even if we manage to achieve a carbon neutral economy in next two or three decades, the effects of the
accumulated gases in the atmosphere will cause an average increase in the Earth surface temperature
with catastrophic climate consequences for large parts of the population and Earth ecosystems.
The economic costs alone in such a scenario run easily into the trillions of US dollars. Adding the
losses of livelihood for hundreds of millions of people and unfavourable ecosystems for the fauna and
flora on which we depend, points to the dire consequences and urgency of addressing the problem.
This paper proposes a mechanism for controlling, monitoring and even reverting the Earth warming
that should be (I) technically feasible, (II) economically cheap, and, (III) that can be implemented
in a relatively short period of time. The implementation of such a proposal may help us avoid a
catastrophic situation and give us more time to reshape our economy and society in a more sustainable
way.
The mechanism consist in tweaking the Earth albedo in order to offset the radiation forcing effect of
the greenhouse gases accumulated in the atmosphere and in this way slowing down or stopping the
process and even reverting the heating that has already occurred. This can be achieved by coating
surfaces (e.g. rooftops, pavements and roads) in urban and rural occupied areas with materials with a
high reflective index. It can also be applied to deserted areas or lakes and ocean.
In Section 1 the qualitative description of the model is expanded and described with more details and
in Section 4 a zeroth order model is presented with calculation that support the proposal presented
here. In Section 6 a tentative road-map for the implementation of the solution is laid out.
Keywords Global Warming ·Climate Change ·Earth Albedo
1 Introduction
The warming of the Earth’s surface caused by the greenhouse effects due to the huge amount of man-made carbon
dioxide generated by the burning of fossil fuels for energy production and heating, and released into the atmosphere,
has the potential for forcing large scale climate changes and modifications to the environment.
The greenhouse effect on the temperature of the Earth is not a new phenomenon, and is well understood. It was first
formulated and studied more than a century ago. Several components of the Earth atmosphere have a significant
greenhouse effect and are responsible for an increase in the average temperature of the Earth by approximately
30 °C
as
compared to the situation if this effect did not exist.
Earth Warming: A simple, cheap and fast mechanism for reverting the process A PREPRINT
During the long history of the Earth, the amount of this naturally existing greenhouse gases in the atmosphere has
fluctuated and has been accompanied by significant climate consequences (I) large fluctuation of temperature, (II)
droughts and precipitation regime changes, (III) advancing and receding of glaciers, (IV) sea level changes and many
others.
Compared to the historical changes of the Earth temperature and climate, the changes expected from the man-made
increase of carbon dioxide in the atmosphere are small, yet, significant enough to endanger the civilization as we know
it with tragic consequences for a large fraction of the population and the ecosystem on which many species depend.
2 The nature of the problem and the proposed solution
The root cause of the problem is the massive increase in the greenhouse gases emissions into the atmosphere since the
beginning of the industrial age with an ever increasing usage of energy generated by the burning of fossil fuels. The
scientific approach of the warming effect is well established and understood.
The climate changes are driven by the warming and encompass a large number of complex phenomena that are difficult
to model because of the uncertainty on the data and the myriad of feedback mechanisms in play. Some of these
mechanisms have even a feedback loop with the warming.
2.1 The nature of the problem
Conceptually the greenhouse effect is well understood and can be modelled with great confidence with the scientific
knowledge established more than a century ago.
The warming is caused by an imbalance in the radiative exchange of energy of the Earth’s system with the Sun and the
deep cold space.
The incoming energy from the Sun, which is concentrated around the visible light spectrum wave length, reaches the
Earth where it is partly reflected or absorbed by the atmosphere and partly transported to the Earth surface. A small part
of the energy hitting the Earth surface is reflected back to space and the larger part is absorbed and thermalized.
The thermalized energy is also radiated back to space, but, at a different wave length, in the infrared band of the
electromagnetic spectrum.
The problem caused by the greenhouse gases is that they block partially the outgoing radiation of the Earth in the
infrared band (i.e. the thermalized energy). The greenhouse gases present in the atmosphere absorb part of the outgoing
radiation and radiate it back to the Earth surface. The net effect is that part of the outgoing energy gets trapped by
the Earth system resulting in a net storage of energy. Since the heat capacity of the Earth is finite it results that its
temperature starts to increase.
As the temperature of the Earth increases the intensity of infrared radiated energy also increases. The temperature of the
Earth increases until a new equilibrium between the incoming and outgoing energy fluxes balance out.
3 The proposed solution
To avoid the heat storage in the Earth system caused by the energy blockage to the Earth radiation in the infrared portion
of the spectrum we must decrease the amount of the Sun radiation that hits the surface and is available for absorption
and thermalization.
We may decrease the amount of energy absorption by reflecting it back to space instead of being absorbed. If it is
reflected in the visible (incoming) band of the spectrum it will not get absorbed/trapped by the greenhouse gases.
If the increase in the reflected energy flux equals the rate of energy store we restore the balance between the incoming
and outgoing radiation total without the accumulation of heat by the Earth system and no required temperature rise is
required for a new equilibrium situation.
In more technical terms this increase in the reflectivity is an increase in Earth albedo.
3.1 The means for increasing the Earth albedo
As shown in the Section 4, the average reflectivity of the Earth’s surface is approximately 0.1. The required increase of
the reflectivity to offset the rate of heat storage is approximately 4% to 0.104.
2
Earth Warming: A simple, cheap and fast mechanism for reverting the process A PREPRINT
It would be very difficult to increase the reflectivity of the Earth uniformly. We may instead promote a higher increase
of the reflectivity in a small fraction of the Earth surface.
As shown in the crude model of Section 4, if we increase the reflectivity of an area that is 1% of the total surface of the
Earth from 0.1 to 0.5 we obtain the required increase of 4% of the average reflectivity of the whole surface of the Earth.
Assuming that the fraction of the Earth that is occupied by human construction (houses, industrial buildings, streets,
highways, railroad, etc) is of the order of 1% we may cover these surfaces with reflective material. Since the reflectivity
need not be specular, the cover material may be a painting or a metallized thin sheet. For this, no expensive supporting
structure is required.
If this area is not enough we may use deserted areas or the surface of lakes and the ocean.
3.2 How to measure the effectiveness of the solution
To determine how well the solution is working it is necessary to measure the incoming and outgoing radiation flux
and balance them over the whole Earth during a long period of time. The measurements may be obtained with a
constellation of space platforms with global and continuous Earth coverage. The on board sensors must be accurate
enough to detect the variations in the third and fourth significant digits of the measurement. The measurements may be
complemented by aerial or balloon hosted sensors.
The measurement of the incoming radiation is simpler since it is highly uniform and with very minor fluctuations. The
measurement of the outgoing radiation is more complicated since it covers the spectrum from the infrared (thermal
radiation of the Earth) to the visible (albedo).
Given the large local and temporal variations of the radiative balance it is necessary to integrate the measurements over
a long period of time, at least one year.
3.2.1 Low-cost of implementation
A first cut at an estimation of the cost of the space platforms for measuring the energy balance is a number between 20
and 50 satellites. Considering a unitary cost (on station) from 100 million US dollars to 200 million of US dollars, we
have that the cost of the space part would be between 2 billion US dollars and 10 billion US dollars.
A first cut for the cost of covering of the rooftops with reflective paint or metallized this film is for cents of US dollars
per
m2
. A low number of hundreds of billions of US dollars would go a long way towards the offset of a large fraction
of the radiative imbalance.
A couple of hundreds of billions of US dollars for the implementation of system is certainly a large sum but still a
bargain against the estimated costs and losses if nothing is done.
The costs of most other proposal for correction or mitigation of the problem, that have floated around, are usually
upwards of 1 trillion US dollars.
3.2.2 Potential for other favourable externalities
Reduce extreme heat in urban areas and reduced energy consumption for air conditioning. The propose solution is more
effective if applied more vigorously in hot areas near the Equator.
4 The Model
In this section a simplified model is presented for the main concepts and parameters involved and sample calculation
are carried out to illustrate the relations between the parameters.
The approach draws heavily on the energy balance concept as discussed in a very elegant and illustrative way by
Rebecca Lindsey et al. in the NASA supported study [
1
] and on discussions in the thread Controlling the Earth warming
(on the cheap) of the forum Engage of the AIAA (American Institute of Aeronautics and Astronautics).
4.1 The amount of man-made greenhouse gases in the atmosphere
From historical data on the utilization of the fossil fuel since the beginning of the industrial era, the quantity of
man-made carbon dioxide added to the atmosphere is estimated to be approximately
2.0×1015 kg
. If condensed on a
layer at sea level pressure, the height of the layer would be approximate 2.1 m.
3
Earth Warming: A simple, cheap and fast mechanism for reverting the process A PREPRINT
4.2 The radiative forcing
The radiative forcing concept is a very rich and powerful parameter for the analysis of the balancing of incoming energy
(mainly radiative energy from the Sun) and outgoing energy (reflected solar radiation and thermal radiation emission by
the Earth’s surface and atmosphere).
In a situation of equilibrium, incoming and outgoing energy balance out, and the average temperature of the Earth
remains constant. In a situation of non-equilibrium, the average temperature of the Earth must change to accommodate
the imbalance until a new equilibrium is reached. Imbalances may be caused by natural phenomena as fluctuations of the
solar radiated energy, variations of the reflectivity of the Earth’s surface, due to particles suspended in the atmosphere
(e.g. due to volcanic eruptions), cloud or snow cover, or changes of thermal radiation transport through the atmosphere
due to variations of the contents of greenhouse gases, from natural sources or, man-made.
Due to the large heat capacity of the Earth, the path to the new equilibrium value of the surface temperature may last for
decades.
The main concern here is from the man-made increase of carbon dioxide gases resulting from an unprecedented large
scale burning of fossil fuels. But, the solution described here may also be used to address the non anthropogenic
imbalances.
The radiative forcing effect of the layer of antropogenic carbon dioxide is estimated to be
1.0 W/m2
. This means that
on the average over the year for each square meter of the Earth’s surface this is the rate of storage of energy due to the
imbalance between the incoming and outgoing energy fluxes.
For the value of the radiative forcing of
1.0 W/m2
the rate of energy storage by the Earth’s system is of the order of
5.0×1014 W.
By linearising the relation between the amount of carbon dioxide in the atmosphere and the radiative forcing we obtain
that the radiative forcing is of the order of 5.0×104W/Gt of carbon dioxide released into the atmosphere.
In more familiar terms we can say that for each kilogram carbon dioxide released into the atmosphere we are increasing
the rate of storage of power in the Earth’s system by
0.25 W
. Over the course of a decade, this amounts to
7.7×107J
,
or 20 times the energy released by burning the fossil fuel that produced this one kilogram of gas.
4.3 The radiative forcing and Earth warming
By linearising the Stefan-Boltzmann equation we get a very simple equation relating the radiative forcing and the
increase of the average temperature of the Earth required to offset this radiative forcing. The linearised equation is
given by:
T=T0
4
ρ
ρ0
where
T
is the temperature increase,
T0
is the temperature before the increase in
K
,
ρ
is the radiative forcing and
ρ0
is the emissive power at T0.
The average temperature of the Earth is
288 K
(
15 °C
). For a radiative forcing of
ρ= 1 W/m2
, the temperature increase
is approximately 1.25 °C.
The rate of temperature increase depends on the heat capacity of the Earth’s system (I) atmosphere plus the (II) layer of
the Earth crust and ocean cover that is heated up.
A crude estimation of the value for the heat capacity of the Earth,
CE
is
CE= 2 ×1023 J/kg
. With this value of
the heat capacity of the Earth’s system, and a value of the radiative forcing of
1.0 W/m2
the rate of increase of the
temperature of the Earth is 0.08 °Cper year.
As the Earth’s temperature increases towards the new equilibrium value, the radiative forcing decreases, and, absent
new sources of forcing, the rate of temperature rise tends to zero.
4.4 The reflectivity of the Earth’s surface and the radiative forcing
The average amount of solar radiation reaching the Earth’s surface is
184 W/m2
. Approximately
163 W/m2
of this
amount is absorbed and converted into heat, and 19 W/m2is radiated back to space; (the albedo) [1].
The average reflectivity of the Earth’s surface is therefore, %= 19/184 = 0.1033.
If we increase the albedo, the amount of radiation that is absorbed is decreased by the same amount and, therefore, the
rate of energy stored and the radiative forcing are also decreased. In order to offset the radiative forcing of
1 W/m2
4
Earth Warming: A simple, cheap and fast mechanism for reverting the process A PREPRINT
the amount of reflected radiation must be increased to
20 W/m2
. To achieve this, the average reflectivity must be
%0= 20/184 = 0.1087.
Instead of increasing the reflectivity of the Earth homogeneously we can increase the reflectivity of only a part of the
Earth surface.
Let
x
be the fraction of the area of the Earth over which we change the reflectivity from the average value,
%
, to a new
value, %. By combining the values of xand %we can obtain the desired average value, %0.
Let the relation between the original average reflectivity and the desired average reflectivity be
%0=α%
. The relation
between the variables is:
%= (α+x1) %
x
Ex.: In the present case, with
%= 0.1033
and
%0= 0.1087
. If we change the reflectivity of an area that is 1% (
x= 0.01
)
of the surface of the Earth the required value of the reflectivity in the small area is %= 0.46.
Since the data used in the calculations above use average values, the results are very conservative. In the regions near
the tropics and close to the equator the average incident solar radiation is higher. Additionally, since the reflectivity
of the atmosphere is lower in this region due to near normal incidence and lower cloud cover. As the result of the
combined effect of these characteristics, it is possible to obtain the same effect of increased albedo with a smaller
increase in the reflectivy and/or lower value of the affected area.
As an exercise we divide the Earth’s surface in two equal parts, A1, a belt around the equator and A2 the sum of the two
polar caps complement. Assuming that the solar incidence on surface A1 is 50% above the average we have the power
incidence on surface A1 is three times the solar incidence on surface A2.
Additionally let us assume that the reflectivity of the atmosphere above this this surface is 15% instead of the average
value of 23% (due to reduced cloud cover and shorter travel path across the atmosphere of the radiation).
Table 1 presents the results of calculations with different conditions of radiation intensity, reflectivity, area on which the
reflectivity is changed and the required change of reflectivity to offset the radiative forcing of
1 W/m2
. In the first 2
lines the average value of the solar radiation and reflectivity are used. In the last 3 lines it is assumed that the average
local radiation is 50% higher than the global average. Also the base reflectivity is higher because it is assumed that the
the ratio between absorptivity and reflectivity is independent of the incident radiation.
In a more accurate calculation the local conditions must be measured with more accuracy; the local average incident
radiation, the average local cloud coverage and atmosphere reflectivity and ratio between local absorptivity and
reflectivity.
P [W/m2]% %0x [%] %
340 0.1033 0.1088 1.0 0.64
340 0.1033 0.1088 1.5 0.46
510 0.1451 0.1487 0.5 0.86
510 0.1451 0.1487 1.0 0.5
510 0.1451 0.1487 1.5 0.38
Table 1: Required reflectivity change for different conditions
5 The advantages
The solution has several favourable points:
Effective immediately: The effects will start to be felt as soon as the actions are being taken. No need for a
long engineering planing and lengthy deployment.
Controllable and reversible: The effects of the actions can be monitored and can be used to increase or
decrease the amount of radiation being reflected back to space. And it can also take into account other natural
phenomena that may occur and interfere with the heating, as for example volcanic activity.
Distributed implementation: Each country or community can participate in the effort. No need to exchange
resource between countries.
No need for a large centralized bureaucracy: Negotiations for the implementation may be carried out within
current international agreement.
5
Earth Warming: A simple, cheap and fast mechanism for reverting the process A PREPRINT
Easily verifiable: A protocol for monitory of the implementation on the agreed upon action can be established.
All countries with access to space resource may measure the variations of the reflectivity implemented by every
other partner. Resources may be pooled together and shared with countries without access to space resources.
Meaningful missions for new entrants in the exploration of space resources: Countries may pool resources to
develop and launch the platforms for monitoring of their own efforts and compliance by other partners.
The technology involved is largely available and a large number of agents, public, NGO’s and private entities
may pool together to accelerate the implementation of the solution.
Another positive side effect is that by increasing the reflectivity in urban areas, and therefore decreasing the
amount of heat absorbed the local temperature will decrease, improving the thermal comfort in hot days and
reducing the energy requirements for air conditioning.
6 A Road-map for action
The course of action is not fully laid out. A number of steps are listed in order to implement the solution.
6.1 Mapping of areas with best potential
One of the first actions needed is the consolidation of data regarding geographical distribution of local radiation and
surface reflectivity at current conditions. A large part of these data is already available. The main task is to convert
the data to a format that is readily usable by applications that will determine the most favourable places to begin the
implementation of the albedo tweaking solution.
6.2 Improve the cost models
The numbers thrown in here for the cost of the measurement platforms are very crude. A more realistic cost model is
required for both the monitoring and the materials and manpower to apply the reflective cover.
6.3 The funding of program
Funding of the program may come from different sources. One obvious candidate is a clean-up cost surcharge to be
imposed on the use of fossil fuels.
As shown in the crude model on Section 4, for each
kg
of carbon dioxide released into the atmosphere a radiative power
of
0.25 W/m2
is added to the Earth’s system. It is only natural that the surcharge cover the installation and maintenance
cost of reflective surface to offset the added radiative power.
A market for trading of emissions of carbon dioxide and installation of sun light reflective capacity may be established.
With this market system it is possible to place the reflective capacity at the most favourable places.
6.4 The infrastructure monitoring
The infrastructure for monitoring is composed of a space based constellation of satellites that are capable of global and
continuous coverage of the Earth’s surface and equipped with sensors to measure radiation balance of the Earth with an
accuracy to determine the effective radiate forcing over a long period of time. The average radiative forcing is obtained
by integrating the instant and local radiative balance over a period of at least one year.
During the subsequent time the measure of the radiative balance will be used to determine if, and how well the correction
action is working.
Conceptually the constellation may be composed of LEO satellites, MEO satellites, our geosynchronous satellites (not
stationary to cover the whole Earth surface). A dedicated constellation may be designed or the sensors may be hosted in
some of the many constellations that serve other purposes.
Since this is a large scale geoengineering effort, it is important to be alert to possible unintended consequences.
Assuming the implementation of the solutions starts in a period of one or two year and runs along for decades there is
plenty of time to evaluate, first analytically and later practically any potentially harmful consequence. Mitigation or
corrective actions may be adopted.
6
Earth Warming: A simple, cheap and fast mechanism for reverting the process A PREPRINT
7 Acknowledgment
The author is fully aware that this is an active research field with a large number of publicatioarens available and
pertinent to the subject of the proposal. The absence of citations is mainly due to the difficulty and extensive effort
required to search and systematically evaluate such a rich literature.
The author is fully aware of the potential for contributions from individuals and institutions with the data and analytic
methods to improve the proposal.
The main claim of the proposal is for the jump from the richness of data and concepts to the daring proposal of a simple,
cheap and fast solution to a very complex problem and in full knowledge of the saying that goes as: For every complex
problem there is a solution that is simple and fast, and, wrong.
On a personal side I would like to thank my sons Bruno and Pedro for the encouragement in writing this piece and the
help in reviewing the text.
References
[1]
Rebecca Lindsey. Climate and earth’s energy budget. Available at
https://earthobservatory.nasa.gov/
features/EnergyBalance.
7
ResearchGate has not been able to resolve any citations for this publication.
Climate and earth's energy budget
  • Rebecca Lindsey
Rebecca Lindsey. Climate and earth's energy budget. Available at https://earthobservatory.nasa.gov/ features/EnergyBalance.