Albedo Modification

(Increasing the reflective power of the Earth's atmosphere)

©Ron Nielsen, 2006

Albedo — Albedo is the reflective power of a surface. In the case discussed in this article, it is the reflective power of the atmosphere, and it describes how much of the incoming solar radiation is reflected by the atmosphere.

IN PLAIN ENGLISH (For those who like it short and simple. This is the shortest and the simplest description I can make.)

Aerosols

We have two problems caused by burning of fossil fuels: (1) global warming caused by emitted greenhouse gases, mainly carbon dioxide, and (2) pollution by small particles (aerosols) mainly from exhaust pipes and coal power stations. Aerosols come also from natural sources such as volcanoes, dust storms, and grass or forest fires.

Aerosols are both beneficial and harmful. They are beneficial because they protect us from an excessive exposure to solar radiation. They do it in two ways: by reflecting solar radiation and by helping in the formation of clouds that also reflect solar radiation. This partial screening effect of aerosols is called global dimming. Without the beneficial protection of human-made aerosols, global warming would increase by about 60%.

However, aerosols are also harmful to humans and to the environment, particularly aerosols containing sulphur and nitrogen compounds, which come from burning fossil fuels. For instance, sulphur-containing aerosols cause acid rain. Aerosols also cause such health problems as chronic wheezing, coughing, prolonged respiratory illness, sore throat, hay fever, eye irritation, phlegm, shortness of breath, chronic bronchitis, chest pain, and cardiovascular disease.

So the question is: Should we reduce the atmospheric pollution or not? If we reduce pollution, we shall remove the protective screening by aerosols and increase global warming. If we keep the atmosphere polluted, global warming will be less severe but we shall have to deal with ecological and health problems caused by the presence of air pollutants.

Catch 22

To decide whether to keep the atmosphere polluted or not is even more complicated because aerosols remain in the atmosphere for a short time. Typically, they are removed after just a few days. On the other hand, greenhouse gases stay in the atmosphere for hundreds of years.

So now we have Catch 22. To protect ourselves from global warming we have to keep aerosols in the atmosphere. To replace the aerosols that are quickly removed from the atmosphere we have to keep on burning fossil fuels. However, by burning fossil fuels we increase concentration of the long-living greenhouse gases in the atmosphere and increase global warming. Thus to protect ourselves from global warming we have to increase global warming. To make the matter worse, we also increase health and environmental risks. This is what I call a trap of global dimming. Is there a way out of this trap?

A possible way out

One possible way to escape the Catch 22 paradox would be to stop using fossil fuels. The atmosphere would then clean itself from the human-made aerosols, global warming would increase but maybe we could still cope with the resulting undesirable climate change. However, we cannot use this way out because fossil fuels account for close to 90% of our global energy consumption.

Another possible solution would be to develop a clean fossil fuels technology, that is, a technology that would minimise the emissions of aerosols and carbon dioxide. Related to this solution, would be to develop faster alternative sources of energy.

A third solution would be to improve the reflective power (albedo) of the Earth's atmosphere. If we could do it in an environmentally safe way, we could clean the atmosphere of the harmful pollutants without the danger of increasing global warming.

Albedo modification

One way to try to enhance albedo of the Earth's atmosphere is to deposit reflective material in the stratosphere, that is, in that part of the atmosphere which is between 11 and 50 km above the ground. The advantage of depositing aerosols in the stratosphere is that they remain there for much longer time than in the lower parts of the atmosphere (the troposphere). The typical lifetime of aerosols in the stratosphere is 1-2 years, rather than just a few days as it is in the troposphere.

Albedo modification of the Earth's atmosphere is a massive undertaking. It is an engineering project on a global scale. The name for such a massive engineering project is geoengineering.

In a sense, we are already involved in geoengineering activities. For instance, through the use of fossil fuels we change the composition of the Earth's atmosphere and cause global warming, which already has far-reaching global consequences. We also change the Earth's environment in many other ways.

Albedo enhancement would be a controlled geoengineering project. It is not suggested to do it immediately but rather to study it carefully in order to assess not only its technical and financial feasibility but more importantly its possible effect on the environment. The current critical global trends associated with human activities already shape the future of our planet in a negative way and it would be irresponsible to undertake a geoengineering project, however well intended it might be, if it would make it all even worse. On the other hand, in order to change the already advanced progression of the threatening trends we probably have no choice but take radical remedial steps.

How to do it

How to construct the protective shield in the stratosphere? How much of reflective material we would have to deposit? How long would it take to construct the shield? The material deposited in the stratosphere has a limited lifetime of 1-2 years. How much we would have to add to compensate for the natural loss? How much would it cost to construct and maintain the required stratospheric shield?

To understand this geoengineering project and to answer all these questions I have derived some mathematical formulae and used them to carry out some essential calculations. To deploy an albedo enhancing material in the stratosphere we could use rockets or balloons. I concentrate on the delivery by rockets. I present formulae that can be used to calculate the cost of the project. All these calculations illustrate also the complexity of such a geoengineering project.

To compensate for the removal of human-made aerosols from the lower parts of the Earth's atmosphere (the troposphere) we would have to construct a protective shield in the stratosphere containing 2 million tonnes of reflective aerosols. I have found that the simplest and cost-effective way of constructing and maintaining the protective shield would be to deposit 1 million tonnes per year if the residence time of reflective material is 2 years or 2 million tonnes per year if the residence time is 1 year. We would have to do it virtually indefinitely, or at least for as long as human-made greenhouse gases remain in the atmosphere.

If we decided to do it by rockets, we would have to use 67-133 rocket launchers (the lower number is for the residence time of 2 years and the higher number for 1 year) working round the clock, 250 days per year. (I exclude weekends and public holidays). We would have to launch 2-4 million rockets per yeas (8,000-16,000 shots per working day). The estimated cost, using 1992 prices, would be US$23-45 billion per year.

If in addition we would also like to protect ourselves from the continuing increase in global warming between now and say 2050 caused by our continuing use of fossil fuels and the resulting continuing increase in the concentration of carbon dioxide, we would have to increase the thickness of the protective shield to between 4 and 6 million tonnes. The uncertainty is dictated by the uncertainty of predicting the increase of global warming between now and 2050.

To construct and maintain such a shield, we would have to deploy 2-6 million tonnes of reflective material per year, using 133-400 rocket launchers working round the clock, 250 days per year. The number of launched rockets would be 4-12 million per year (16,000-48,000 per working day) and the ongoing cost would be US$45-135 billion per year.

Of course, if we go beyond 2050 and if our emissions of greenhouse gases increase, our efforts to protect ourselves from the increased global worming would be even more complex and costly.

Is it safe?

Is such a geoengineering project environmentally safe? The short answer to this question is that we do not know. We have to study and assess the possible environmental risks. We can do it both theoretically and by experimentation. The risks will depend not only on the amount of the reflective material we would have to deposit in the stratosphere but also on the type of the material. If the material is chemically neutral the risk might be small. However, even chemically neutral material might provide an environment for harmful chemical reactions between atoms and molecules, which are already present in the stratosphere.

If the deposited material is chemically active, the risk might be greater. For instance, if we deposit sulphur, we would have to explore its possible chemistry in the stratosphere. For instance, we would have to make sure that it would not contribute substantially to the destruction of the ozone layer. Furthermore, we would have to understand how sulphur compounds interact with the atmospheric components when they are being removed from the stratosphere by natural processes and what environmental and health problems they might be causing.

Volcanic eruptions that deposit large quantities of sulphur into the stratosphere seem to indicate that there are no environmental risks. However, we do not know what might happen if we maintain large quantities of sulphur in the stratosphere for a long time.

A safety factor is in the relatively short residence time of reflective materials in the stratosphere. The first step is to assess as carefully as possible that the proposed geoengineering project is safe. If we then decide to go ahead with the project but discover later that it causes environmental problems, we could stop the project without causing much damage to the environment. In 1-2 years, the deployed material would be removed from the stratosphere by natural processes and the stratosphere would be restored to its original condition.

Not a permanent solution

It should be stressed that albedo enhancement of the Earth's atmosphere is not a solution to global warming. It is only a temporary solution designed to give us a breathing space while we work on such issues as developing clean fossil fuel technology, alternative sources of energy to replace fossil fuels, and more efficient methods of energy consumption.

We have made many mistakes in the past. We have been using planet's resources carelessly but now we slowly realise that we should be more prudent. It takes time to build a better future. We are as it were on a bridge now, between the past and the future, and any proposals that could help us to cross over to the other side should be welcome, and they should be carefully considered and assessed.

Abstract: This article describes my calculations related to the albedo enhancement of the Earth's atmosphere. I have found that if we wanted to compensate for the increase in global warming caused by cleaning the atmosphere of human-made pollution, we would have to deposit 1-2 Tg of reflective material in the stratosphere per year at the annual cost of US$23-45 (using 1992 prices). The range of values depend on the residence time of the reflective material. If in addition we would like to protect ourselves from the increased global warming between now and 2050, caused by our continuing use of fossil fuels, we would have to deposit a total of 2-6 Tg of reflective material per year at the estimated annual cost of US$45-135 billion. I have derived a simple mathematical formula, which describes the mechanism of construction of the albedo enhancing shield. I also give formulae, which can be used to calculate the cost of construction using rockets. The cost of construction using hydrogen-filled balloons is approximately the same as for rockets, but cost of the construction using helium filled balloons is about 4 times higher.

Introduction

As if we did not have enough trouble with global warming, we have now created a problem of global dimming. Through our interference with nature we have placed ourselves in a trap without an easy way to escape.

The use of fossil fuels creates two forms of atmospheric pollution: pollution with greenhouse gasses, mainly carbon dioxide, and pollution with aerosols (small particles). Greenhouse gases reside in the atmosphere for a long time. Their residence time is unknown but is estimated at hundreds of years. Aerosols, on the other hand, stay in the atmosphere for a short time. Their residence time depends on their size, chemistry, and location in the atmosphere, but typically they are removed from the lower part of the atmosphere within days. For instance, much of human-made atmospheric pollution contains sulphur. The residence time of sulphur dioxide is 0.6-2 days and of sulphates 2.7-7.2 days. Various natural processes contribute to the production of aerosols but human activities have now a significant contribution.

Aerosols have a beneficial cooling effect on the Earth's surface. The effect is either direct or indirect. The direct effect occurs when aerosols scatter solar radiation, which otherwise would have reached the Earth's surface. The indirect effect is through the formation of clouds. Droplets of water are formed around aerosols and the created clouds reflect the solar radiation. The cooling effect of human-made aerosols is called global dimming.

The problem with aerosols is not only because they are quickly removed from the atmosphere and thus have to be replaced by new aerosols, but also because they cause a variety of ecological and health problems. When aerosols containing sulphur or nitrogen are incorporated in the clouds they return to the Earth's surface in the form of acid rain. Aerosols can be carried by the air currents and deposited in places far removed from places of their production. Harmful effects of aerosols are discussed in my book, The Little Green Handbook.

So here we have Catch 22: we need aerosols to keep us cool but we don't need them because they cause ecological and health problems. To reduce the effects of global warming we have to keep on polluting the atmosphere because aerosols do not stay there long, but by polluting the atmosphere we are also increasing the concentration of greenhouse gases, which stay in the atmosphere much longer and cause global warming. Thus to protect ourselves from global warming we have to increase global warming. This is what I call the trap of global dimming.

Maybe we could escape the trap by abandoning the use of fossil fuels. Without replacing the aerosols, the surface temperature would increase but we might hope that it would not increase too high. However, we cannot try this solution because we depend almost entirely on fossil fuels.

It has been suggested that we might solve the problem, at least temporarily, by creating a protective shield made of aerosols deposited in the stratosphere. The advantage of having aerosols in the stratosphere is that they remain there over much longer time than in the troposphere, for about 1-2 years. Also, we would not be in an immediate contact with them, so hopefully we would not suffer health problems. It would also appear, that depending on the type of aerosols they would probably be environmentally harmless. However, all these issues would have to be carefully discussed and assessed. Aerosols would provide a reflective shield for the sunrays and would compensate for the increased global warming caused by the cleaning the lower part of the atmosphere of the human-made pollution.

The apparent need for geoengineering illustrates the immensity of the problem we have created. There is no simple solution. We are already involved in uncontrolled geoengineering in the form of changing the composition of the Earth's atmosphere through the use of fossil fuels. Maybe there is no other way out but to fight fire with fire and use a well-designed and well-controlled geoengineering project.

I have carried out the presented here calculations in connection with the proposed albedo enhancement by injecting sulphur into the stratosphere. I was fascinated by this idea and I wanted to understand how such a massive geoengineering project would work. Part of my calculations involved an estimation of the costs, which interested Professor Dr Paul Crutzen and which he used in his publication, "Albedo Enhancement by Stratospheric Sulfur Injections: A Contribution to Resolve a Policy Dilemma?", Climate Change 77(2006)211-220.

THE DYNAMICS OF ALBEDO MODIFICATION

Preliminary considerations

To understand the process of construction of an albedo enhancing shield in the stratosphere we have to include in our calculations not only the amount of the reflective material we can deploy in a given span of time but also the gradual deterioration of the shield because of the limited residence time of the deposited material. The amount of material removed by natural processes from the atmosphere is proportional to the amount of material present at any given time:

where N is the amount of material, t is the time and λ is a constant characterising the considered material.

Solution of this simple equation gives:

which gives:

The residence time is defined by N/N0=1/e, i.e. it is the time when the original amount of material is reduced to 1/e, which is approximately 37%. Thus, the residence time T is given by:

The residence time of aerosols in the stratosphere is estimated at between 1 and 2 years, which corresponds to λ = 1 and 0.5, respectively.

Gradual deployment

The amount of albedo enhancing material is so large that it is impossible to deposit it in one shot. We have to do it gradually. But this creates the problem because while we are depositing new material, the material we have already deposited decays. It is like filling in a leaking container with water.

So now the questions are, how long and how fast do we have to keep on deploying the albedo enhancing material into the stratosphere to create a protective shield of required concentration? Once we have created it, how much shall we have to keep on adding to compensate for its continuing deterioration? The remaining calculations are aimed at answering these questions.

Let us assume that we measure time in years. Let the total injection period be t years. To calculate how much material we have to deploy we can divide the total injection period t into small sections and calculate how much of the injected material during this small section of time will remain in the atmosphere at the end of the total injection period t.

Let m be the number of assumed small injection periods per year and M the total number of injection periods during the total injection time t. The length of time τ0 of each assumed small injection period is of course:

and the total length of injection period is:

Let W be the total amount of material deployed during the time t. This time could be one year or more. The amount of material deployed during each small period τ0 is:



and the amount of material deployed per year is:

Let us label each consecutive small section of time τ0 using index i. Let Li be the amount of material that will remain in the atmosphere at the end of time t from the material injected in the section i. Using the basic equation for the decay, we can see that this amount is given by:

The total amount of the material that will remain in the atmosphere at the end of time t is given by:

Therefore

 

which can be reduced to:

After integration we get the following simple formula:

 

which can be rewritten more conveniently as:

 

where

— the thickness of the protective albedo enhancement layer after the total injection time t.
— The amount of albedo-modifying material injected per year.
λ  — The decay constant (e.g.1 if residence time is 1 year or 0.5 if residence time is 2 years)

We have derived a simple but interesting formula. It shows that if we continue injecting a fixed amount of albedo-modifying material, the thickness of the protective layer will be at first increasing rapidly but after a certain time it will gradually level off and continue approaching an asymptotic value of . This asymptotic value is the maximum level of protective layer we can construct by annual injections of a fixed amount of the albedo-modifying material.

The figure below illustrates this time-dependent behaviour. (Tg =1012 grams, that is, trillion grams.)

Albedo modification
The dynamics of albedo modification of the Earth's atmosphere

So for instance, by regularly injecting 5 Tg per year, we can construct a 10 Tg protective layer if the residence time is 2 years (λ = 0.5) or 5 Tg if the residence time is 1 year (λ = 1). To construct a 10 Tg layer for the residence time of one year we would have to increase the regular annual injections to 10 Tg.

We can also calculate how much time we need to have to construct a shield of a required concentration. Here we have to consider the ratio


The number of years t’ required to reach a satisfactory level of construction is given by:

Thus for instance, the construction will reach 99% of the saturation level in 4.6 years if the residence time is 1 year or 9.2 years if the residence time is 2 years. This might sound counterintuitive but we should remember, that with fixed injections and longer residence time we shall be contracting a thicker protective layer (see the enclosed figure).

We could deposit larger amounts of material to build the protective shield faster but this approach would be unadvisable. Depending on the delivery system, fast deployment could create environmental, technical, and financial problems.

We can also see that in order to maintain a protective layer at a required concentration we would have to continue injecting large quantities of the albedo enhancing material forever. Clearly, this is not a solution to global warming but only a temporary solution while we try to clean up the atmosphere and to reduce emissions of greenhouse gases.

 

ESTIMATION OF THE COSTS

Approximate calculations

Carbon concentration in the atmosphere increases. If we want to protect ourselves from the expected increase in global warming, we have to consider not only the increase caused by removing human-made aerosols from the atmosphere but also the additional increase caused by our continuing use of fossil fuels.

Let us first calculate the thickness of the protective shield we would have to construct to compensate for the increase in global warming caused by cleaning the atmosphere of the human-made pollution. The protective power of aerosols is labeled in scientific literature as negative radiative forcing or negative climate forcing, and is measured in Watts per square metre (W/m2). We can change "negative radiative forcing" to a more convenient label radiative cooling, which is then represented by positive numbers.

Estimations of the radiative cooling of atmospheric aerosols vary typically between 1.4 and 2.2 W/m2 , which give the mean value of 1.8 W/m2. Crutzen (private communication) used 1.4 W/m2 and estimated that to compensate for the removal of human-made aerosols we would need to construct a 1.9 Tg sulphur shield.

I used a different approach to estimate the thickness of the protective shield. My estimation, which does not depend on the type of the reflective material, were made in the following steps.

First, I have analysed carbon dioxide concentrations dating back to 1765 and the corresponding increase in radiative forcing of carbon dioxide. I have found that at the beginning of the past century, for each 46 ppmv increase of carbon dioxide concentration, radiative forcing increased by 1W/m2. At the end of the last century, this value increased to 60 ppmv. Using a conservative linear approximation gives me a value of 55 ppmv. Thus at present, for each 55 ppmv increase of carbon dioxide concentration in the atmosphere, radiative forcing increases by 1 W/m2.

If the radiative cooling by human-made aerosols is indeed 1.4 W/m2, as assumed by Crutzen, then by removing them from the atmosphere we would increase the effective radiative forcing of greenhouse gases by 1.4 W/m2, which is like increasing carbon dioxide concentration by 77 ppmv.

Next, to calculate the thickness of the protective shield we also need to know the relationship between carbon dioxide concentration expressed in ppmv and the concentration and the weight of carbon. This relationship can be calculated using the mass of the troposphere. The calculations give the following prescription:

1ppmv =2.13 GtC

The equivalent increase in carbon dioxide concentration by 77 ppmv is like adding an extra 164 GtC to the atmosphere .Finally before we take the final step, we need to know what thickness of the albedo enhancing shield can mitigate this amount of carbon.

In 1992, National Academy of Science published a voluminous book entitled Policy Implications of Greenhouse Warming: Mitigation, Adaptation, and the Science Base. Let's abbreviate it as NAS-1992. The book contains many small errors (as one could expect in such a big volume) but with proper care it's possible to navigate around them. The authors claim that a 10 Tg (Tg stands for teragram or trillion grams) albedo enhancing shield can mitigate 1 TtC (TtC stands for trillion tonnes of carbon) in the atmosphere, which means that 1 Tg albedo enhancing shield mitigates 100 GtC (GtC stands for gigatonne of carbon or billion tonnes of carbon).Thus to compensate for the increase in surface warming caused by the removal of human-made aerosols we would need to construct a 1.6 Tg protective shield. This value is close to the value of 1.9 Tg of sulphur estimated by Crutzen.

If we assume that radiative cooling of aerosols is 1.8 W/m2, then to compensate for the increased radiative forcing caused by cleaning the atmosphere of aerosols we would have to construct a 2.1 Tg protective shield. For the sake of cost estimates we can assume that we need a 2 Tg shield.

To construct and maintain such a shield we would have to deposit 1 Tg of reflecting material per year (indefinitely) if its residence time is 2 years or 2 Tg per year if its residence time is 1 year.

Now we can also calculate the additional thickness of the protective shield if we also wanted to protect ourselves from an increase in global warming between now and say 2050 caused by our continuing use of fossil fuels. We have to understand that while we continue burning fossil fuels, our problems increase. The longer we wait the more difficult it will be to solve them.

At present, the estimated carbon dioxide concentration is 375 ppmv (parts per million per volume). The projected concentrations vary over a large range of values (see my book, The Little Green Handbook). My calculations indicate that by 2050 we shall have 450-500 ppmv. IPCC estimations give 480-580 ppmv and UNEP gives 450-500 ppmv. Thus, by 2050, we can expect an extra 75-205 ppmv of carbon in the atmosphere.

The Earth is already too warm and the increasing concentration of carbon dioxide will make it even warmer. Indeed, IPCC estimates that by 2050, the average surface temperature of our planet will increase by 1.1-3.70C. This should be compared with the average increase of only 0.60C in the last century, which is already not only uncomfortable but also dangerous. Thus, by 2050, the temperature increase will at least double as compared with the increase in the last century.

Thus, the additional 75-205 ppmv of carbon concentration in the atmosphere by 2050 would mean an additional 160-437 GtC. To mitigate it we would need 1.6-4.4 Tg albedo enhancing shield, which gives the combined thickness of 3.6-6.4 Tg (approximately 4-6 Tg).

Using the1992 prices given in NAS 1992 we can calculate that the approximate cost of deploying albedo enhancing material in the stratosphere is $25 billion per Tg. To construct and maintain a 4-6 Tg shield we would have to deploy 2-6 Tg of albedo enhancing material (depending on the residence time) per year (indefinitely) at the annual cost of $50-$150 billion.

If our emissions of greenhouse gases are going to continue to increase after 2050, we will have to increase the thickness of the protective shield. However, maybe by then we shall manage to reduce the use of fossil fuels.

Formulae for the exact calculations of the costs.

Two ways have been suggested to deploy albedo modifying material in the stratosphere: rockets and or balloons. According to NAS-1992, the cost of delivery for both is the same as long as balloons are filled in with hydrogen. If they are filled in with helium, the cost is about four times higher. As an example of exact cost calculations I shall consider here the rockets. I base my formulae and calculations on the data supplied in NAS -1992.

The number of rocket launches (naval rifles or guns) N needed to deliver a total weight of the required material per year can be calculated using the following simple formula:

where
w – weight of deployed material per shot (per rocket)
f – number of shots per hour for each rocket launcher
t – number of hours of shooting per day
d – number of shooting days per year

Calculations of the costs have to include a number of components as listed below:

The cost P1 of rockets:


where p1 the cost of a rocket and the albedo enhancing material it will carry to the stratosphere.

The cost P2 of barrel replacement:

 

where

p2 the cost of a gun barrel
n1 – the number of shots per gun before the barrel needs to be replaced.

The rockets are arranged is stations so we have to calculate the cost P3 of running the stations.

 

where

q – a factor accounting for extra guns that will be out of action for maintenance (1<q<2).
N – as before, the number of working guns at any given time.
n2 – the number of guns per station
p3 – the cost running a single station. This cost includes overheads, electricity, etc. We can also include here the capital cost for constructing a station and spread it over the number of years of expected operation.

In the calculations, the total number of guns, qN, is rounded up to an the nearest higher integer number. In my calculations, I round it up to the higher 10 (see below).

The salary P4 for the personnel working at the stations:

 

where
n3 – the number of people per rocket launcher per shift
s – the number of shifts
S – the annual salary per person
D – number of working days per year excluding weekends and holidays.

As an example I use input data as suggested in NAS-1992. They are summarised in the table below.

The weight of the albedo enhancing material per rocket
500 kg
Number of rocket launches per hour per rocket launcher
5
The number of shooting hours per day
24
The number of shooting days per year (excludes weekends and holidays)
250
Cost of a rocket and the albedo enhancing material
$10,000
The number of launches before a barrel will have to be replaced
1500
The cost of barrel replacement
$1,000,000
Running costs of a station (overheads, electricity, etc)
$130,000,000*
The number of working rocket launchers per station
10
Factor accounting for rocket launchers shut down for maintenance
1.15
Number of shifts
3
Number of people per rocket launcher per shift
10
Annual salary per person
$100,000
The number of working days per year
250
* This figure includes the capital cost invested in a station spread over 40 years of estimated operation.


Results of the calculations are presented in the table below:

Thickness of the albedo enhancing shield (in Tg)*
1
2
3
4
5
6
Number of working rocket launchers
67
133
200
267
333
400
Total number of rocket launchers**
80
160
230
310
390
460
Number of rocket launching stations
8
16
23
31
39
46
Ongoing cost per year (in billion dollars)
23
45
68
90
113
135
Number of rocket launches per year (in millions)
2
4
6
8
10
12
* 1Tg = 1Mt (one million tonnes)
** Includes the number of rocket launchers shut down for maintenance at any given time. I assume that there are 10 rocket launchers per station.The total number of rocket launchers, qN, is therefore rounded up to the higher 10.

 

Environmental implications of atmospheric geoengineering

To be continued