Global Warming and Ice Ages:

I. Prospects for Physics-Based Modulation of Global Change


E. Teller

I. Wood

R. Hyde


This paper was prepared for submittal to the 22nd International Seminar

on Planetary Emergencies

Erice (Sicily), Italy

August 20-23, 1997


August 15, 1997


Lawrence Livermore National Laboratory


This is a preprint of a paper intended for publication in a journal or

proceedings. Since changes may be made before publication, this preprint

is made available with the understanding that it will not be cited or

reproduced without the permission of the author.


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GLOBAL WARMING AND ICE AGES:


I. Prospects for Physics-Based Modulation of Global Change


Edward Teller & and Lowell Wood#

Hoover Institution, Stanford University, Stanford, CA 94305-6010

and

Roderick Hyde

University of California Lawrence Livermore National Laboratory,

Livermore, CA 94551-0808


ABSTRACT


It has been suggested that large-scale climate changes, mostly due to

atmospheric injection of “greenhouse gases” connected with fossil-

fired energy production, should be forestalled by internationally-

agreed reductions in, e.g., electricity generation. The potential

economic impacts of such limitations are obviously large: greater than

than ten/11 dollars per year. We propose that for far smaller

-- <1% -- costs, the mean thermal effects of “greenhouse gases” may be

obviated in any of several distinct ways, some of them novel. These

suggestions are all based on scatterers that prevent a small fraction

of solar radiation from reaching all or part of the Earth. We propose

research directed to quite near-term realization of more or more of

these inexpensive approaches to cancel the effects of the “greenhouse

gas” injection.


While the magnitude of the climatic impact of “greenhouse gases” is

currently uncertain, the prospect of severe failure of the climate,

for instance at the onset of the next Ice Age, is undeniable. The

proposals in this paper may lead to quite practical methods to reduce

or eliminate all climate failures.


_____________________

* Prepared for invited presentation at the 22nd International Seminar on

Planetary Emergencies, Erice (Sicily), Italy, 20-23 August 1997.

Aspects of this work were performed under the auspices of the U.S.

Department of Energy, in the course of Contract W-7405-Eng-48 with the

University of California. Opinions expressed herein are those of the

authors only, and are not necessarily those of Stanford University,

the University of California, or the Department of Energy.


& Research Fellow. Also Director Emeritus and Consultant, University

of California Lawrence Livermore National Laboratory, Livermore CA 94550.


# Visiting Fellow. Permanent address: University of California Lawrence

Livermore National Laboratory, Livermore CA 94550.

______________________


Introduction. In recent years, consideration of the possible warming

of the climate due to the injection into the atmosphere of “greenhouse

gases,” particularly carbon dioxide, CO2,(1) has motivated proposals

to impose international limitations of the burning of fossil fuels,

particularly ones yielding less heating-value per gram of CO2 released,

such as coal. The starting point of the present paper is the widely-

appreciated fact(2) that increases in average world-wide temperature of

the magnitude currently predicted can be canceled(3) by preventing

about 1% of incoming solar radiation - insolation - from reaching the

Earth.(4,5) This could be done by scattering into space from the

vicinity of the Earth an appropriately small fraction of total insolation.

If performed near-optimally,(6) we believe that the total cost of such

an enhanced scattering operation would probably be at most $1 billion

per year, an expenditure that is two orders of magnitude smaller in

economic terms than those underlying currently proposed limitations on

fossil-fired energy production.(7,8,9) Some of these insolation-

modulating scattering systems may be re-configured to effectively increase

insolation by an amount -- perhaps 3% -- sufficient to prevent another

Ice Age.(10)


We first survey various physical processes to accomplish this scattering.

We then compare the various ways in which these scatterers may be deployed.

Next, we propose that particular attention be given to three possible

realizations of this technology-based program. We note geographical

variability aspects of insolation modulation. We conclude by suggesting

that the problem of possible changes in climate may be better solved by

cooperative application of modern technologies rather than by international

measures focused on prohibitions.


Scattering Fundamentals. In general, three basic types of scatterers exist,

for scattering any type of electromagnetic radiation, including sunlight.

The simplest type is based on any material in which the electric fields of

light cause a displacement of electric charges; thus, any material at all

can be used. The magnitude of the displacement of charges by an electric

field of unit strength is measured by the dielectric constant e, where e=1

means there is no displacement. The scattering is proportional to (e-1)2,

that is, highly polarizable materials generally will be more useful. This

class of scatterer requires the near-optimal deployment(11) of an

estimated several million tons of scattering material in order to prevent

an estimated (global-and time-) average temperature increase of 3±1.5° C

associated with a doubling of atmospheric CO2 during the coming century;(12)

the corresponding cost of ~$0.5 billion/year.


More effective scatterers can be realized by employing that subset of

materials which exhibit high electrical conductivity. In this special case,

electrons may be separated from their original locations by any distance,

and it is the magnitude of the optical-frequency current carried by these

electrons that characterize the effectiveness of such scattering materials

-- which are generally metals. Employed near-optimally, tens of thousands of

tons of high-conductivity metal -- roughly 1% of the required mass of

dielectric materials -- are required to scatter 1% of the Earth’s total

insolation; the corresponding costs are $0.07-0.14 billion/year.


In principle, the most effective of all possible scatterers are atoms or

molecules that scatter light in resonance. Such extremely strong scattering

can be obtained for light of a frequency adapted to a specific atom or

molecule. The simplest example would be scattering of a narrow band of red

light by lithium atoms or of yellow light by sodium atoms. Unfortunately,

such exceptionally strong scatterings occur only in the immediate neighbor-

hood of an atomic transition-frequency, and the atom will selectively interact

with light of frequencies which deviates from the resonant one by about one

part in ten million (for visible light). This difficulty can be overcome

by broadening the resonance (accompanied by a proportionate weakening of the

scattering-strength) or by using scatterers that have many separate resonances

-- or, most effectively, by a combination of these two approaches. Of the

order of 1 million tons of such resonant-type scattering material are

estimated to suffice to remove 1% of the total insolation of the Earth; the

corresponding cost may be $0.3-$0.75 billion/year.


The intrinsic scattering strengths of dielectrics, electrical conductors, and

resonant scatterers are in the approximate ratio of 1 to 10/4 to 10/6,

respectively,(13) for visible light; in practical implementations(14) useful

for insolation modulation, however, these ratios may be much different.

______________________________

Also, it is necessary to select scattering materials which scatter only with

quite small losses, in order to minimize possibility undesirable heating of

the portion of the atmosphere in which the scatterer is deployed.

______________________________


How Should Scatterers Be Deployed? There are three obvious choices for

deployment-sites for scatterers on scales of interest for insolation

modulation.(15) One is the terrestrial stratosphere, the second is in a

low-Earth orbit (i.e., an orbit whose radius may be as much as twice the

radius of the Earth), and the third is a position along the line between the

centers of the Earth and the Sun (approximately one hundred times the Earth’s

radius distant from the Earth).


Of the three deployments, the stratospheric location is by far the least

expensive on a pound-for-pound basis; positioning mass in the stratosphere

currently is at least 104 times less costly than putting it into low Earth

orbit.(16) Moreover, the mid-stratospheric residence time of sub-microscopic

scattering particles of anthropogenic(17) and natural(18) origins is

comparable to the half-decade residence time of its molecular components,(19)

so that appropriately fine-scale particulate loadings of the middle

stratosphere will persist for five-year intervals. However, the stratosphere

is a chemically uncongenial location due to the high flux of ultraviolet

radiation from the Sun and the presence of oxygen, particularly in the more

reactive form of ozone.


Ideally, we would prefer to deploy scattering systems -- or their principal

components -- that would remain in place and retain their performance-

pertinent properties for a century, which is of the order of the interval(20)

required for a CO2 emission pulse to be effectively sunk into the deep ocean.

However, we consider the half-decade mid-stratosphere residence time to be

sufficiently long for practical deployments. We may re-constitute the

deployment of a scattering system twice per decade (or 20% per year), and we

even consider such a short duration to constitute a relatively rapid,

naturally-operating means of disposing of possible unwanted side-effects of

insolation modulation. Chemical stability in the stratosphere, even for

material with readily available electrons on its surface, is a tractable

issue for present purposes.


Deployment in low-Earth orbit is an obvious alternative,(21) one which

offers potentially very long-term positional stability combined with

excellent durability of many materials. Technologies that could greatly

decrease the cost of space-launch could make a telling difference in the

practicality of all types of space-deployed scattering systems of scales

appropriate to insolation modulation.(22) Light pressure arising from the

momentum imparted to the scatterer by sunlight may significantly perturb the

orbital elements of the scatterer, and managing this momentum poses an

additional technical challenge to LEO-deployed scatterers.


An interesting though not necessarily a practical case comprises the third

alternative.(23) Terrestrial insolation has an angular definition of one

part in 120. Thus, if the scattering system is deployed ~10/2 times the

Earth’s diameter distant from the Earth, small-angle (less than 1°) scattering

will suffice for an appropriate deflection of the Earth-directed sunlight

(either toward the Earth, if warming is desired, or away from it, if cooling

is sought). This small angle permits the use of relatively very modest

quantities of either conductors or dielectrics to comprise the scattering

system -- approximately 102-fold smaller than those needed to effect

insolation modulation of the same magnitude when deployed near the Earth.(24)

The management of the radial and angular momenta of the sunlight scattered

poses basic, albeit quite tractable issues with respect to position

maintenance.(25)


Some Specific Proposals. There are obviously numerous ways in which the

potentialities and difficulties mentioned above can give rise to a workable

scattering system, one of a scale adequate to modulate the total insolation

of the Earth by 1%. In the following, we shall provide some details

regarding specific possibilities, ones selected to illustrate basic features

of each of the major classes of scattering systems.


Sub-Microscopic Oxide Particulates. During the present decade, the eruption

of Mt. Pinatubo in the Philippines induced a transient drop in the global

mean temperature of ~0.5° K, apparently due to insolation modulation by

volcanic particulates.(26) It is believed that this cooling was induced

predominantly by scattering of sunlight by SO2-based particulates of sub-

micron scale, ones which may have grown into more effective scatterers by

scavenging residual stratospheric water and cations, resulting in myriad

still-sub-micron droplets of high-concentration sulfur acids and salts.

Indeed, it has been suggested that the advent of marked greenhouse effects

due to CO2 emissions has been delayed through the present time by the

simultaneous emission of large quantities of sulfate particulates

(primarily arising from the ~2±1% sulfur content by weight of typical

fuel-grade coal), resulting in significant tropospheric scattering of

sunlight.(27) To these extents, the case of dielectric scattering-based

insolation modulation already has some empirical basis.


It may well be feasible to transport and disperse enough SO2 (or SO3 or H2SO4)

into the stratosphere to produce the desired insolation modulation effect

(28,29) -- and even to do so partly on the basis of existing experience,

as well as much prior analysis. It has also been suggested that alumina

injected into the stratosphere by the exhaust of solid-rocket motors might

scatter non-negligible amounts of sunlight.(30) We expect that introduction

of scattering-optimized alumina particles into the stratosphere may well be

overall competitive with use of sulfur oxides;(31) alumina particles offer

a distinctly different environmental impact profile.


Conducting Sheets. The reference 1% reduction in insolation might be

obtained by deploying electrically-conducting sheeting, either in the

stratosphere or in low Earth orbit. Three quite different physical

mechanisms comprise the foundations of the three distinct approaches which

we consider. In the first, mixture of suitable metals are deposited in

ultra-thin layers and convenient area, and are then protectively coated.(32) Platelets of such material are then deployed in the stratosphere -- or

perhaps in low Earth orbit -- and act to absorb sunlight by the photoelectric

effect; the absorbed energy is then thermally re-radiated, with ~half

escaping into space. In the second, metallic “nets” of ultra-fine

mesh-spacing are employed to reflect solar photons of optical wavelengths

into space.(33) In the third, optimized metallic-walled balloons --

similar in concepts to ones with which children play -- are self-deployed

into the stratosphere from ground level, where they serve to scatter

insolation.(34) Each of these approaches involves total masses of the

order of 10/5 tons, although the detailed mass budgets are quite different.

The total cost-to-own any one of these three metallic systems at full-scale

appears to lie in the range of $0.07-0.14 billion/year.


Quasi-Resonant Scatterers. A third approach involves the use of resonant

-- actually quasi-resonant scatterers, also deployed in the stratosphere.(35)

While the potential mass efficiency of this class of scatterers is singularly

high, practical considerations centered on photochemical durability in the

stratosphere indicate that total masses of 10/6 tons of material may have to

be deployed(36) -- still modest-scale systems(37) which moreover may have to

be replaced only twice per decade. For near-term, relatively low-risk

insolation modulation studies, we propose the use of sub-microscopic

particulates composed of frozen perfluorohydrocarbon “nano-droplets” loaded

with embedded molecules of selected organic dyes.(38) The total cost-to-own

such a full-scale insolation modulation system may be quite competitive --

of the order of $0.3-0.75 billion/year.


Fine-Grained Insolation Modulation. We note technical possibilities of

modulating insolation in a latitude-dependent manner. Consistent with the

slow latitudinal mixing-time of the stratosphere well above the tropopause,

different amounts of scattering material might be deployed (e.g., at middle

stratospheric altitudes, ~25 km) at different latitudes, so as to vary the

magnitude of insolation modulation for relatively narrow latitudinal bands

around the Earth, e.g., to reduce heating of the tropics by preferential

loading of the mid-stratospheric tropical reservoir with insolation scatterer.


Indeed, scatterers of sunlight could be deployed at some latitudes to

decrement insolation, while scatterers of Earth-emitted long-wavelength

infrared radiation (which effectively increment insolation) could be deployed

at other latitudes.(39) Differential cooling and heating, respectively,

of underlying land-and-ocean latitudinal bands could thereby be accomplished.

Furthermore, use of scatterers of varying stratospheric residence times to

simultaneously modulate insolation and I.WIR radiative losses in a specified

latitude band might be employed to fine-tune, e.g., diurnal or seasonal

temperature variability.(40)


Conclusions. We have reviewed all the approaches known to us which appear

to be of practical significance with respect to addressing the large-scale

thermal effects of climate failure -- both global warming and Ice Ages --

from the perspective of insolation modulation. In the course of this review,

we have applied fundamental physical design principles to mass-optimize

several previous proposals in order to enhance their practicality, and we

have been able to remove more than an order-of-magnitude of superfluous mass

from some earlier conceptual designs. Two insolation modulation systems

which we have considered -- quasi-resonant scatterers for intra-atmospheric

applications and the small-angle-scattering system for deep space use --

are apparently novel. These involve total system masses of the order of

10/3-10/6 tons -- which is 2-5 orders of magnitude less mass than that of

the most interesting previous proposals. We conclude that the insolation

modulation approach to prevention of climate failure is certainly

technically feasible-in-principle, and that the total costs-to-own its best

examples may be de minimis.


We believe that research along several lines to study the deployment and

operation in sub-scale -- perhaps 10-3 of a full-scale, 1% insolation-

equivalent system -- of appropriate scatterers of sunlight is justified

immediately by considerations of basic technical feasibility and possible

cost-to-benefit. Summary discussions such as those sketched here can only

outline the directions to consider. However, even very preliminary estimates

of performance and practicality suffice to make us optimistic about ultimate

workability and utility.


Success can be expected to be more significant than merely counteracting the

global climate modifications arising from large-scale injection of greenhouse

gases. Straightforward modifications of what we have discussed including

the scattering not of incoming sunlight but of the long-wavelength infrared

radiation emitted by the Earth could be effective in preventing onset of

both “little” and full-sized Ice Ages.(41) These may occur with little

warning, seemingly at any time, and could severely impact human affairs on

notably brief time-scales.(42) Indeed, the Earth’s climate system may

manifest finite-amplitude instability along several axes, with small

perturbations occasionally resulting in large shifts, some swiftly executed.(43)


Greenhouse warming of the Earth due to human activities is a possibility,(44)

moreover one for which mitigative/remedial actions of the types proposed here

can be at once deliberate and effective.(45) In contrast, Ice-Age-severity

cooling, another in the series of events that have occurred quasi-periodically

many times during the last 1.2 million years,(46) is a practical certainty.

Moreover, a several-decade duration “cold snap” of Ice Age Maximum

temperature-drop is known to have occurred in the Northern Hemisphere with

essentially no warning during the last interglacial period, under precursor

climatic conditions only slightly warmer than the present-day one.(47)


Today, our scientific knowledge and our technological capability already are

likely sufficient to provide solutions to these problems; both knowledge and

capability in time-to-come will certainly be greater. Whether exercising of

present capability can be done in an internationally acceptable way is an

undeniably difficult issue, but one seemingly far simpler than securing

international consensus on near-term, large-scale reductions in fossil

fuel-based energy production(48) -- especially in a world exhibiting very

large geographical and cultural differences in per capita energy use, past,

present and future.


We believe that, prior to any actual deployment of any scattering system

aimed at full-scale 1% insolation modulation, completely transparent and

fully international research in sub-scale could result in public opinion

conducive to a reasonable technology-based approach to prevention of

large-scale climatic failures of all types. International cooperation in

the research phase, based on complete openness, is necessary and may be

sufficient to secure the understanding and support without which any of these

approaches will fail.


The purpose of this paper is not to advocate definite solutions. It is only

to augment the scientific effort to find solutions of general acceptability

and benefit.


The blame for “bad weather” may be too heavy for any human to bear. But we

hope, thinking before acting might be acceptable.


FOOTNOTES:


(1) Intergovernmental Panel on Climate Change, Climate Change 1995: The

Science of Climate Change, JT Houghton et al., eds., (Cambridge Univ. Press,

Cambridge, 1996).


(2) E.g., Hansen JE and Lacis AA, Sun and dust versus greenhouse gases: An

assessment of their relative roles in global climate change, Nature 346,

713-9 (1990).


(3) See, e.g., MacCracken M, Geoengineering the Climate, Proceedings of the

Workshop on the Engineering Response to Global Climate Change, Palm Coast FL,

June 1-6, 1991, and UCRL-JC-108014 (1991), Lawrence Livermore National

Laboratory, Livermore, CA 1991.


(4) Ref. I, ibid. Also, Wigley, TML, “The Contribution From Emissions of

Different Gases to the Enhanced Greehouse Effect” in Climate Change and the

Agenda for Research, T. Hanisch, ed. (Westview, Boulder, CO 1994) estimates

the present-day excess positive radiative forcing to be -2 W/m2, roughly

three-fourths of which is due to CO2 and one-quarter to CH4.


(5) While it may be argued that uncertainties in the accuracy and fidelity

of modeling tools are sufficiently great that they should not be relied upon

to forecast reliably the effects of enhanced sunlight scattering on the

climate [or as does, e.g., Lindzen RS, Ann. Rev. Fluid Mech. 26, 353 (1994),

that they are fundamentally unverified predictive tools], it is these same

modeling tools -- not the presently quite ambiguous observations of the actual

climate -- that are considered sufficiently robust to motivate the present

level of concern about man-made climate change.


(6) One basic point-of-departure of the present paper from the large body of

excellent previous work in similar directions [see, e.g., work surveyed in

Panel on Policy Implications of Greenhouse Warming, Policy Implications of

Greenhouse Warming: Mitigation, Adaptation and the Science Base, U.S. National

Academy of Sciences (National Academy Press, Washington, DC 1992), and in

Working Group II, Climate Change 1995 Impacts, Adaptations and Mitigation of

Climate Change: Scientific-Technical Analysis, Second Assessment Report of the

Intergovernmental Panel on Climate Change, RT Watson, et al., eds. (Cambridge

University Press, 1995)] is the emphasis which we have placed on reducing

deployed scatterings system masses down to rather fundamental physical limits,

consistent with contemporary engineering realities, in order to realize

conceptual designs which may be the most practical to study in sub-scale and

then to deploy in full-scale. We expect that all cost-effective mitigation

efforts may require such optimization-focused design work. With respect to

the fundamental utility of such efforts, we note that the section of the cited

NAS report addressing “mitigation” options of the general type which we now

consider concluded with the statement (on p. 460) “Perhaps one of the

surprises of this analysis is the relatively low costs at which some of the

geoengineering options [aimed at offsetting global warming] might be implemented.”


(7) See, e.g., testimony by Janet Yellen (Chair, Council of Economic Advisers to

the President of the U.S.), before the House Commerce Subcommittee on Energy

and Power, July 15, 1997, and press reports thereof (e.g., Fialka JJ, “Effort

to Curb Global Warming Is Tied To Higher Energy Prices In Two Studies,”

Wall Street Journal, 16 July 1997, p. A2), in which estimates of ~40%

increases in bulk fossil-energy prices in order to attain price-rationing of

fossil fuel-derived energy sufficient to suppress greenhouse emissions below

“dangerous levels” were characterized as mid-level ones.” Those fractional price

increases translate to ~$4x1011/year world-wide, or ~$10/11 per year in the U.S.


(8) All cost estimates in this paper should be regarded as scoping in character.


(9) We note that efforts directed to cost minimization of mitigation technologies

is specifically supportive of the UN Framework Convention on Climate Change,

whose Article 3 states that “policies and measures to deal with climate change

should be cost-effective so as to ensure global benefits at the lowest possible

cost.”


(10) A doubling of atmospheric CO2 during the coming century is IGCC-estimated to

result in a 2.5± 1.5° C change in mean temperature, while the mean temperature

decrease from the present level which prevailed at the middle of the last Ice Age

is estimated to be -10° C.


(11) The large variance in previous estimates of the amount of dielectric scatterer

required for full-scale insolation modulation appears to arise primarily from

references to dimensionally non-optimized scattering materials, which can be

quite mass-wasteful. (The optimal choice is to match the size of the scatterer

to the reduced wavelength of the peak of the solar spectral radiance, and to

maximize the squared difference from unity of the scatterer’s dielectric constant

divided by its specific gravity.)


(12) Intergovernmental Panel on Climate Change, Climate Change 1995: The Science

of Climate Change, JT Houghton, et al., eds. (Cambridge Univ. Press, Cambridge, 1996).


(13) In evaluating the mass efficiency of any scattering unit or a scattering system,

consideration of the space- and time-averaged optical-frequency current density in

the matter comprising the system gives a general-purpose figure-of-merit for the

mass budget of the system. When multiplied by the “optical leverage” figure-of-

merit, it generates an index of effectiveness of mass utilization in creating a

sunlight-deflecting system. Note that this average (optical frequency) current

density-per-gram metric permits the comparison of metallic, dielectric and

atomic-resonant scattering materials, moreover in a manner independent of

particular scattering system geometry. It merely looks at the quantity which

scatters the sunlight’s optical field: the space- and time-averaged current

density driven up by the electric fields of the solar photons in the matter

constituting the scattering unit, and the outgoing wave optical-frequency fields

which this density generates.


Most dielectric materials of interest have optical dielectric coefficients e less

than 2, and we generally must consider (e-1)less than 9x10/-13 farads/cm.

Available metals (e.g., Al) have electrical resistivities greater than 3x10/-6

ohm-cm (taking some degradation from best bulk properties for very thin layers), i.e.,

conductivities ? less than 3x10/5 mho/cm. Optical frequencies of resonant

transitions are -10/15 Hz, and these transitions correspond to electron ravel

over orbital distances -3 Å, i.e., across atoms of -3 Å diameter. Take a

reference mid-visible optical angular frequency of -4x10/15 sec-1. Then the

optical current density I in a unit volume (whose greatest dimension is assumed

to be less than ?/2p) of such a dielectric at unit electric field strength is

I-E/Z--wC, or 4x10/15 x 9x10/-13, or 3.6x10/3 amp/cm2. The current density in the same circumstances

in a good metal is just I-sE-s, or 3x10/5 amps/cm2. Unit optical electric field strength

of 1 V/cm corresponds to an optical flux of 10/-4 W/cm2, so that sunlight’s

intensity at 1 AU of 0.1 W/cm2 implies a mean frequency-averaged optical electric

field of -30 V/cm. This optical field strength will drive -30 transitions/sec

in a typical full-strength-dipole atomic oscillator, as noted above; unit optical

electric field strength thus will drive -3x10-2 transitions/second in such an atom.

Each atom is assumed to occupy a volume of -3x10/-23 cm3, so that -10/21

transitions/sec are driven by a unit-strength solar-spectral optical field in a

cm3 volume of such material. Each such transition corresponds to a optical-

frequency current of a single electron’s charge -1.6x10-19 coulombs - moving

through a distance -3x10/-8 cm every -10/-15 sec. This corresponds to a optical

frequency current density of -5x10/9 amp/cm2 (!).


For constituting scattering units, then the relative figures-of-merit of best-

available dielectrics, metals and resonant-scatterers are roughly 1:10/2:10/6.


(14) The “packaging mass overhead” for quasi-resonant scatterers typically is much

larger than that for metallic and dilectric scatterers, so that much of the

former’s huge intrinsic mass advantage is lost in scattering systems prepared for

multi-year durability-in-service.


(15) The Earth’s surface is not considered for reasons of land-use and local

microclimate impacts, while the ocean surface poses stability / durability /

navigation compatibility concerns, and tropospheric residence times are not

usefully long for the types of scattering systems which we consider.


(16) We estimate a total cost of lifting mass into the stratosphere on wide-body

commercial aircraft to be ~$0.3/pound, whereas the current cost of putting a

pound-mass of payload into low Earth orbit by contract with commercial space-

launch services is ~$5,000 for 5-15 ton payloads. Indeed some types of

stratospheric deployment of oxide particulates -- e.g., SO2 or Al2O3 -- might

be accomplished simply by operating one or more well-engineered combustors

-- e.g., of elemental S or Al -- at high-altitude, near-equatorial ground-

sites, from which stratospheric injection of warm gas is intrinsically

advantaged. (Combustor engineering would focus on mass-efficient,

optimal-sized scatterer particle generation in the vertically-directed exhaust,

which likely would have a rocket nozzle character in order to facilitate

swift manipulation of the temperature and density of combustion products

across usefully large ranges.)


(17) Feely HW and Spar J, Tungsten-185 From Nuclear Bomb Tests As a Tracer

For Stratospheric Meteorology, Nature 188, 1062-4 (1960); Telegadas K and

List RJ, Atmospheric Radioactivity along the HASL Ground-LEvel Sampling

Network, 1968 to mid-70, as an Indicator of Tropospheric and Stratospheric

Sources, J. Geophys. Res. 74, 1339 (1969); Telegadas K, Report 243 (U.S.

Atomic Energy Commission, Washington, DC, 1971).


(18) Trepte CR and Hitchman MH, Tropical stratospheric circulation deduced

from satellite aerosol data, Nature 355, 626-8 (1992); Trepte CR, Veiga RE,

and McCormick MP, The Poleward Dispersal of Mount Pinatubo Volcanic Aerosol,

J. Geophys. Res. 98, 18563-73 (1993); Grant WB, et al., Use of volcanic

aerosols to study the tropical stratospheric reservoir, J. Geophys. Res.

101, 3973-88 (1996).


(19) Boering KA, Wofsy SC, Daube BC, et al., Stratospheric Mean Ages and

Transport Rates from Observations of Carbon Dioxide and Nitrous Oxide,

Science 274, 1340-3 (1996).


(20) See, e.g., Manabe S and Stouffer RJ, Century-scale effects of increased

atmospheric CO2 on the ocean-atmosphere system, Nature 364, 215-7 (1993).


(21) National Academy of Sciences, National Academy of Engineering and

Institute of Medicine, Policy Implication of Greenhouse Warming: Mitigation,

Adaptation, and the Science Base (National Academy Press, Washington, D.C. 1992).


(22) Since space-deployed scatters could in principle last indefinitely,

they have a several dozen-fold advantage in time-integrated mass budget

relative to stratospherically-deployed ones, which must be re-constituted

twice per decade. This durability-in-service saving trades of interestingly,

albeit not compellingly, against the present ~104-fold disadvantage in cost of

transportation to deployment-site. Space-launch service costs will have to

decrease to a few dozen dollars per pound in order to become competitive for

present purposes. High-acceleration payload launchers are potentially of interest,

as scatterer payloads are likely to be very acceleration-tolerant -- and perhaps

can be segmented into quite modest sizes and masses, as well.


(23) Positioning a sunlight-shade or Snell’s Law-refractor (i.e., a 1-D Fresnel

phase plate) composed of 1014 gms of lunar glass near the Earth-Sun interior

Lagrange point (LI) has been suggested in Early JT, Space-Based Solar Shield

To Offset Greenhouse Effect, J. Brit. Interplanet. Soc. 42, 567-9 (1989).

The present proposal positions a metallic small-angle-scatterer of sunlight of

comparable area but ~105-fold smaller mass Sunward of LI. A system of this type

likely would be assembled quite close to the Earth, e.g., in LEO, and then

rapidly “flown” into its deployment location as a solar sail, exploiting its

very small mass-to-optical cross-section and its active radiation momentum

management capabilities.


(24) The total area size of such a scattering system must remain the same as

scattering systems deployed in close proximity to the Earth, but its total mass

potentially may be much more modest, as it must scatter sunlight only through

~10/2-fold smaller angles. In particular, the conducting elements of the

scattering units need carry only ~10/2-fold smaller currents, so that they can

be of 10/2-fold smaller cross-sectional area (for a given optical electric

field strength, which is effectively constant for all scattering system

deployments in ~1 AU sunlight) and thus can have 10/2-fold smaller mass.

The mass of such a scattering system can be estimated by noting that the

total area must be ~1% of the Earth’s disc, while it must have good metallic

conductors of -3x10/-11 cm2 cross-sectional area (-600 Å thick by -1000 Å in

transverse width) spaced every 100l/2~3x10/-3 cm in both transverse dimensions.

If the density of the conductor is taken to be 3 gm/cm3 (e.g., Al), then the

mass density is - 1.2x10/-7 gm/cm2, and the total mass is just this density

times the 1% of the Earth’s disc area of -1.2x10/18 cm2 which is to be

sun-shaded, or -1.2x10/16 cm2: -1.4x10/9 gms. The total mass of the ideal

scattering system thus is -1.5x10/9 gm or 1,500 ton - plus whatever overhead

mass is required to deploy and operate these (literally) diaphanous scattering

screens; the actual scattering system has about twice this mass -- 3,400 tons

-- for reasons which are discussed below.


The possibilities of incrementing or decrementing terrestrial insolation in

manners which are both geographically and spectrally selective by use of such a

distant scattering system seem obvious.


(25) The momentum carried by sunlight, while very small, is assuredly not

negligible: at 1 AU, it amounts to -4x10/-5 dynes/cm2. Over a day, this

accumulates to -3 dyne-sec/cm2 and, over a year, to -10/3 dyne-sec/cm2 of

impulse fluence. If exactly backscattered (toward the sun), only radial

momentum is gained by the scattering unit; however, if deflected at any angle it will also impart angular momentum to the scatterer: the Poynting-Robertson

effect. Since scattering units typically have an areal mass <<10/-3 gm/cm2,

they can undergo many gee-sec of acceleration even during a day, and thousands

of gee-second annually (i.e., can see Dv of >>10 km/sec). Such velocity changes

in essentially all orbits of interest are almost invariably intolerable, and

either deployment or operational means must be devised to avoid them.


Unwanted angular momentum may be readily jettisoned by time-varying the

orientation of a relatively very small reflector capable of scattering sunlight

through a high mean angle. However, the radial momentum imparted by sunlight

must be sustained for intervals as long as a half-year, until the Earth’s

orbital motion about the sun will dissipate it; in most cases-of-interest, this

is a very long time-interval over which to tolerate radial momentum absorption.

However, if the scattering unit is deployed upward of the Earth’s orbit but

quasi-orbits the sun at the same angular rate as does the Earth (so as to

continually shadow-shield the designated fraction of the Earth), then it may

in principle sink as large fraction as may be desired of the incident sunlight’s

radial momentum into the solar gravitational field, i.e., it may position itself

closer to the Sun that the L1 point so as to sink the scattered radiation’s

radial momentum into the solar gravitational field, i.e., it may position

itself closer to the Sun that the L1 point so as to sink the scattered

radiation’s radial momentum into the solar gravitational field; the smaller

its areal mass density, the more Sunward of L1 it must position itself. Now

the radial radiation momentum flux is -4x10/-5 dynes/cm2, only 5x10/5 of which

is deposited on the scatterer as it deflects the incident sunlight by 10/2 rad,

so that the mass density corresponding to deposited radiation radial momentum

balancing the gravitational deficiency is -1.5x10/-7 gm/cm2. This is only

a few times greater than the areal mass density of the ideal scattering system

positioned at L1. Thus, by moving -1% inward from L1 - and increasing the

total area of the scattering system by -2-fold, in order to continue to

shadow the Earth while moving further Sunward from it -- we can simultaneously

sink the residual radial momentum of the scattered sunlight into the solar

gravitational field and maintain the desired shading of the Earth.


Residuals in both radial and angular momentum flux from solar gravitation

and from the Poynting-Robertson effect, respectively, are probably best sunk

by sunlight retroreflection action performed by a relatively small area

(i.e., 0.3%) of high-angle reflector. However, this necessarily will have a

-50X greater areal mass-density than does the small angle-scattering screens of

greatest interest, so that a -15% overhead cost is thereby incurred by the

scattering system.


(26) Trepte CR and Hitchman MH, Tropical stratospheric circulation deduced

from satellite aerosol data, Nature 355, 626-8 (1992); Trepte CR, Veiga RE,

and McCormick MP, The Poleward Dispersal of Mount Pinatubo Volcanic Aerosol,

J. Geophys. Res. 98, 18563-73 (1993); Grant WB, et al., Use of volcanic

aerosols to study the tropical stratospheric reservoir, J. Geophys. Res. 101,

3973-88 (1996).


(27) See, e.g., Taylor KE and Penner JE, Response of the climate system to

atmospheric aerosols and greenhouse gases, Nature 369, 734-7 (1994); Chuange CC,

et al., An Assessment of the Radiative Effects of Anthropogenic Sulfate, J.

Geophys. Res. 102, 3761-78 (1997); and Intergovernmental Panel on Climate Change,

Climate Change 1995: The Science of Climate Change, JT Houghton, et al., eds.

(Cambridge Univ. Press, Cambridge, 1996).


(28) See, e.g., Dyson FJ and Marland G, Technical fixes for the climatic

effects of CO2. Workshop on the Global Effects of Carbon Dioxide from Fossil Fuels.

USDoE Report CONF-770385 (USDoE, Washington DC, 1979); Budyko MI, The Earth’s

Climate: Past and Future (Academic Press, New York, 1982); Broecker WS, How to

Build a Habitable Planet (Eldigio Press, Palisades, NY, 1985).


(29) In this approach, advantage is taken of the stronger Rayleigh scattering of

the shorter wavelengths of optical sunlight as compared to those of terrestrial

thermal emissions. A performance-optimized scattering system of present interest

consists of a world-wide, ultra-thin cloud of dielectric particles, each of 0.05-0.1mm

diameter, deployed in the Earth’s stratosphere. The Rayleigh scattering cross-

second å= (8p/3)(w/c)4a2V2. [See, e.g., Landau LD and Lifshitz EM, Electrodynamics

of Continuous Media (Pergamon, Oxford, 1984).] For such a spherical particle

whose diameter is equal to a quarter-wavelength of 0.5 mm radiation which has

a dielectric coefficient e-1.7 (e.g., a water-rich microdrop of refractive

index -1.3), å may be estimated to be -5x10/-12 cm2. Thus -10/28 of these particles,

uniformly distributed in the stratosphere, would be required to scatter-shield the

5x10/18 cm2 of terrestrial surface with optical density 10/-2 at the sub-solar point.

(While only the bluer portion of the visible spectrum, ? less than 0.5 mm, would be

scattered with this cross-section, the effective scattering in the earlier half

of local morning and the latter half of local afternoon in the tropics and all

day at higher latitudes is considerably greater than this value, due to the greater

atmospheric path traversed by incident sunlight, so that the net required energetic

effect of panchromatic scattering is attained, in first approximation). Each of

these scattering particles may be estimated to have an average mass of -10/-15 gm

(i.e., be -0.12 mm in diameter and of unit density), so that the required quantity

of them would imply a total mass of the scattering system of -10/13 gms, or

10,000,000 tons. A mean stratospheric lifetime of each scattering particle of

5 years would imply a required injection rate of 2x10/6 tons annually, or a

time-averaged injection rate of 60 kg/second, which is feasible to maintain, e.g.,

with highly parallel exercising of existing fine-aerosol-dispersion technology.


(30) E.g., Brady BB, Fournier EW, Martin LR and Cohen RB, Stratospheric Ozone

Reactive Chemicals Generated by Space Launches Worldwide. Aerospace Report No.

TS-94(4231)-6. (The Aerospace Corporation, El Segundo, CA 1994).


(31) Because of the strong dependence of the Rayleigh scattering cross-section

on e, [(e-1)/(e+2)]2, when e is not much greater than unity, it would be more

somewhat mass-efficient to deploy alumina microspheres, instead of SO2/SO3/H2SO4

ones: the significantly greater density of alumina (-3.5 gm/cm3) is more than

compensated by its greater dielectric coefficient 3.10. (Alumina, like sulfate,

is ubiquitous in the terrestrial biosphere, and its stratospheric injection

seemingly pose no significant environment issues. However, its refractory

character makes it more challenging to deploy, at least in some modes. A notable

exception might be a high-average-power combustor of aluminum powder deployed

at a high-altitude, near-equatorial ground-site, one whose carefully-engineered

exhaust-stream could hydrodynamically penetrate the overlying tropopause and

inject less than 0.1 mm-diameter alumina particles into the mid-stratosphere

with high mass-efficiency.) Worth noting in passing is the fact that the annual

tonnages of either sulfur or aluminum oxides presently proposed for stratospheric

deployment are tiny compared to the quantities of these materials which are

either naturally lofted into the atmosphere (e.g., by dust storms) or are already

injected by human activities (i.e., burning of fossil fuels of all types).


(32) Absorption of solar photons with thermal (quasi-isotropic) re-radiation of

the absorbed energy may be reasonably mass-efficient in some circumstances, e.g.,

when using photoelectric-effect (bound-free) absorbers. For instance, the

photoelectric cross-section of good metals just above the work-function-edge

for near-optical radiation is -3x10/-17 cm2, and is -3x10/-18 cm2 at three times

this photon energy (i.e., a 10/7- and 10/8-fold reduction below the line-center

bound-bound resonant cross-section, corresponding to the relative final-state

phase-space volumes of the two types of transitions). For scattering unit design

purposes, an effective photoelectric cross-section of 10/-17 cm2 is a reasonable

estimate (taking into account finite solar spectral width requirements and

considering that the solar spectral intensity falls rapidly above even the

lowest-energy single-element photo-edge, that of Cs metal at a photon wavelength

-0.37 mm), and assuming that all photons with energies above the photo-edge

interact with this cross-section. Likewise, note that a multiple alkali-metal

alloy system can lower this photo edge to an effective 2eV threshold (e.g., as

the tri-and quad-alkali metal alloy photo cathodes of commercial photo

detection devices routinely do). A sheet of this material of a few dozen

atoms thicknesses -- -100 Å-- would then represent an extinction length

for blue-green photons, and would have a mass-density of less than 3x10-6 gm/cm2.

Then assuming that scattering units comprised of such 10/-6 cm-thick sheeting

would absorb half the incident solar spectrum and that the corresponding

scattering system would sun-shield 0.01 of the Earth’s disc continuously, the

minimum mass-budget of an efficiently implemented scattering system comprised

of such ultra-thin sheets of photoelectric absorber/thermal re-radiator would

be (2)(10/-2)(1.2x10/18 cm2)(3x10/-6 gm/cm2)-7x10/10 gms - 70,000 tons. If

deployed either in the atmosphere or in LEO, individual scattering units could

be effective only less than 50% of the time, so that greater than 140,000 tons

would be required to fully implement such a scattering system.


The constituent materials of every efficient photoelectric absorber for solar-

spectrum radiation inherently are readily oxidizable, particularly in the highly

(photo) reactive upper atmosphere, so that only LEO deployment of such systems

appears feasible -- unless ³ two-fold mass penalties are paid for protective

jacketing, e.g., SiO2. In addition to having a relatively large mass budget

for a space-deployed system, such an absorption/re-radiation module in space

would have the active momentum management requirements characteristic of any

space-based scattering system; this additional complexity would trade off

against the multi-decade lifetimes (and thus far lower annualized costs)

implicit in LEO deployment.


(33) The scattering system of this approach is comprised of a set of single

-layer screens which scatter incident sunlight through -p/2 rad, and whose

conducting elements must be -1 skin-depth in longitudinal extent, or greater than

200 Å, by -300 Å in transverse width, spaced at less than 3x10/-5 cm distances

in both dimensions; packing mass for protection against stratospheric oxidation

would be comparatively small, if metal having a thin protective oxide,

such a Al, is used. Such a high-angle scattering system would have

electrically conducting “wire” elements massing a total of -15,000 tons;

averaging random orientation and diurnal availabilities drives this up by

-2x to -90,000 tons. (Overhead mass for deployment and operation would, of

course, be additional, although, in fractional terms, it would be smaller, as

the scattering screens would be much stronger, due to their thicker conducting

members).


(34) Thin-walled helium-filled balloons are routinely employed to lift multi-ton

payloads to 30/-5 km altitudes, and maintain them there for multi-day intervals

(limited mostly by the durability-against-photo oxidation of the balloon’s plastic

wall). It thus seems entirely reasonable to consider ultra-thin metallic-walled

balloons, partially inflated with a suitable lifting-gas, e.g., H2, as sunlight

-backscattering “stratostats,” for they can be expected to have very long

stratosphere residence times (probably limited by micrometeoritic puncture-rates).

A wall thickness of -0.02 mm of e.g., Al, is -1 skin-depth at the 8x10/14 Hz

frequencies characteristic of mid-visible solar radiation and thus suffices to

(predominantly) backscatter the blue end of the incident solar spectrum; however,

it is less than 0.2 skin-depth at 2/-3x10/13 Hz and thus is nearly transparent

to Earth thermal emissions in the 8/-14 mm wavelength atmospheric pass-band.

Each of these balloons thus constitutes a “micro anti-greenhouse”: it passes

space-directed low-frequency photons emitted by the Earth but reflectively

backscatters into space the high-frequency ones incoming from the Sun.


Since the thickness of the balloon’s metallic wall is determined by electro-

dynamic skin-depth considerations, the balloon diameter is selected so as to

position it at the desired stratospheric altitude when it is fully expanded,

subject to the constraint that it must be buoyant at the launch-site altitude.

An Al wall thickness of 0.02 mm, a balloon radium of 44 mm, a fully-inflated

volume of 0.25 cm3, a mass of 10/-5 grams, and an optical scattering cross-

section (between -0.25 and -1 mm wavelength) of 0.5 cm2 correspond to a balloon

deployment altitude of 25 km. (Likely different choices of deployment altitude

involved less than 2-fold adjustment of the balloon diameter while keeping

its wall thickness invariant). Since it is required to scatter-shield -5x10/16

cm2 (recalling that 1% of the Earth’s total area is to be so sun-shielded),

-10/17 of these “self-lofting blue-UV chaff” objects will be required, with

an associated mass of -10/12 grams, or 1,000,000 tons. If they are deployed

uniformly over a 50 year interval (i.e., quickly compared to a doubling-time

of atmospheric CO2), then -2x10/10 grams/year -- -6x10/7 balloons/sec, or 10/8

cm2/sec, or 1hectare/sec of these scatterers -- must be created and deployed.

(Newspaper printing-press technology seems a particularly likely basis for

“printing” these balloons on a H2-loaded bilayer-sandwich substrate. High-

circulation major newspapers print -10/6 copies of a -10/-2 hectare-area

newspaper daily, for a round-the-clock mean rate of -0.1 hectare printed

per second; the peak printing rate is -0.3 hectare/sec. Thus, the time

-averaged balloon creation-and-deployment rate is comparable to the peak

output rate of a large newspaper printing facility.) This deployment rate

will require 4.5x10/7 lbs./year of Al-as-foil (at a current annual cost of

less than $40 M for ingot, likely a few times this for mass-produced ultra-thin

foil), and a -15-fold lower mass of several-fold cheaper H2 gas: -1,500 tons.


These self-lofting blue-UV chaff” balloons constitute one of the lowest-

technology approaches, in that, once created and released at ground-level,

they self-deploy and automatically-operate. The feedstream requirement is

only -1% of the current total annual production of aluminum metal. Since 6%

(by mass) of the Earth’s crust is Al, the quantity of ultra-thin Al foil

drifting down from the skies during the mid-21st century wouldn’t discernibly

impact the environment, the more so as such very thin foils would photo

oxidize to the hydrated oxide quite rapidly in the wet troposphere: at

-290° K, Al exposed to dry oxygen forms a stable oxide layer of 10/-30 Å thick-

ness, but wet oxidizing atmospheres can form >1 mm hydrated oxide layers on

bulk Al in a matter of hours -- an hydrated AlOx films crumble to powder very

rapidly. (It therefore should be feasible to deploy such “self-lofting

blue-UV chaff” from desert sited-factories -- or from high-latitude

ground-sites -- and have them quickly rise into the stratosphere intact,

while they would invariably be wet-oxidized into invisibly-fine hydrated

alumina dust during their slow, end-of-life descent through the troposphere,

obviating “littering” concerns raised in connection with return-to-Earth

of far larger, non-optimized balloons). It is obviously feasible to employ

a metallic overcoating of the required thickness applied to an appropriate

thickness of a stronger dielectric, e.g., a modern plastic film such as

polyaramid or polybenzoxazole, in order to gain durability. (The metallic

overcoating would then serve its sunlight-scattering function and would also

protect the super-strength plastic film from stratospheric photochemical

damage.)


This particular insolation-scattering solution has a much less pronounced

dispersion than does the Rayleigh scattering one: it only scatters more

strongly with the half-power of the photon frequency (rather than the fourth).

Its two distinctive features are that it’s an approach which manifestly

can be implemented without any human machinery leaving the surface of the

Earth and it’s a scattering system which quickly assumes and thereafter

maintains a designed-in altitude in the stratosphere, e.g., so that its

meridional transport features will be known a priori. Moreover, its

effectiveness could be nearly doubled by applying a somewhat heavier

coating of I.WIR-reflecting material (e.g., a small band-gap semiconductor)

to one of the two sheets of film used in balloon manufacture, so that the

upper metal-coated hemisphere of each balloon would scatter sunlight back

into space, while its lower semiconductor-coated hemisphere would scatter

Earth-emitted I.WIR radiation back Earth-ward.


(35) Resonant absorption and (quasi-isotropic) fluorescent re-radiation of

solar (near-)optical photons is an incompletely-compelling candidate

mechanism for scattering units primarily because even atoms with full-dipole-

transition oscillator strengths in the (near)visible spectrum absorb with

maximum radiative strength only over relatively very small wavelength

intervals (Dw/w ~ 10/-7) and secondarily because such strong absorption is

typically seen only in metallic gases (and similarly low-density,

effectively-collisionless circumstances, in which the natural width of the

transition is a regrettably large fraction of its full width). However, the

intrinsic mass efficiency of scattering units comprised of a set of resonant

absorbers could be expected to be extremely high, and it likely is worth

considerable applied photophysics experimental effort to spectrally broaden

such resonant transitions to cover -2% of the solar spectrum. Normal matter

never works harder in sustainable electromagnetic terms than when it’s

scattering radiation on a full electric-dipole-strength transition at the

maximum rate given by that transition’s Einstein A coefficient (-10/8 sec-1,

for the full-dipole-strength optical transitions of present interest): i.e.,

an alkali-metal atom (e.g., Li) will process -3x10/-11 W of resonant radiation

(less than 10/8 photons/sec. each of 1.8 eV or 3x10/-12 ergs energy) for a

mass-cost of 10/-23 grams (e.g., an Li6 atom, scattering on its 6708 Å resonant

transition) -- which corresponds to a specific scattering power of

3x10/12 W/gm(!). If it were feasible to exercise matter this vigorously in

scattering units, then the working-mass of an entire scattering system would

be only -1 kg. However, the less than 10/18 photons/cm2-sec of (near-)optical

solar flux at 1 AU only present -10/11 photons/cm2-sec within the -30 MHz

absorption-line of a typical full electric-dipole-strength optical resonant

transition, which has a characteristic peak absorption cross-section section ??3x10/-10 cm2

(i.e., ? ~ l2/4p, with l ~ 6x10/-5 cm. Thus, such an atom only processes -30 photons/sec when

hung-in-space in 1 AU sunlight, i.e., it works at only 3x10/-7 of its maximum

feasible scattering rate. Instead of 1 kg of scattering unit-mass, 3x10/9 grams,

or 3,000 tons, would have to be employed -- moreover, as a scattering-disc of

free atoms positioned on the Sun-Earth line. Nonetheless, this is a small

mass for the “active” component of a full-scale insolation modulation system;

it motivates serious consideration of options based on resonant scattering physics.


(36) Intercalation-loading any of the new nanometer-scale poly-carbon structures

with fully-enclosed interiors (e.g., C60 buckyballs, graphitic nanotubes, etc.)

with alkali metal atoms (e.g., as has already been done, using K and Rb, in order

to generate moderately high-temperature superconductors) might constitute a useful

[packaging+spectral broadening] means which would simultaneously protect the

contained species from oxidation and would appropriately broaden its resonant

transition. At least some of these structures, e.g., nanotubes, can be sized to

“semi-snugly fit” the atom being so caged, so that its outer-electronic-shell-

based resonant transition could be broadened to the required extent by either a

RMS environmental variation from one caged atom to another of -4x10/-3 Ry or an

equivalent variability-in-time of the caged atom’s environment.


If the scattering system so constituted were to be made of -unity optical

thickness on these broadened resonant transitions, then this unit-optical-depth

system would effectively reflect -50% of the incident in-band solar radiation

back into space: thus, there is a requirement for an effective width of 2% of

the solar spectrum near the Planck peak for a full-scale insolation modulation

system. These scattering units might be positioned in the stratosphere;

however, atmospheric positioning imposes a diurnal efficiency penalty,

relative to positioning in a scattering-disc on the Earth-Sun line. Also,

since a cage for a Li6 atom may have a mass -120 times that of the caged

atom itself, the 3,000 tons of full electric dipole-strength optical scatterer-

in-a-disc intrinsically required to scatter 2% of the solar spectral radiance

at 1 AU might be increased to -750,000 tons with the concatenated diurnal

efficiency penalty and the [packaging+spectral broadening] “mass overhead”

of a C60 buckyball.


A distinctly different alternative route to realizing such high-strength,

broadband quasi-resonant scattering of (near-)optical radiation is based

upon organic dye molecules which, in solution, exhibit rather ideally the

high oscillator strengths and broadband absorption desired in the present

application. While isolated dye molecules exhibit fine structure-rich

absorption/fluorescence on their electronic transitions in the (near-)

visible spectrum due to concatenated effects of myriad rotational and

vibrational splittings, solvent-broadening effects smear the spectrum of dye

molecules-in-solution into a featureless continuum -- without significantly

diminishing the frequency-integrated radiative strengths of the principal

interband electronic transitions. Highly concentrated gels of such dyes

-- e.g., ones derived from low vapor pressure solvents which are “glasses”

at stratospheric temperatures, such as the higher molecular weight

perfluoroalkanes, may be expected to serve aptly as scattering units of

still quite high mass-efficiency, ones for which the corresponding scattering

system mass may be not much greater than that whose scattering units are

caged alkali/alkaline-earth metal atoms: -106 tons. Materials such as Al

or Si, which auto-coat with durable, oxygen-impervious, high-integrity

oxide-skins of only a few monolayers thickness, might be aptly employed in

lieu of graphitic nanotubes for transparently jacketing such dye-loaded-

glasses against stratospheric conditions. Alternatively, use of

perfluorohydrocarbons as the dye-bearing material may obviate the need for

any protective jacketing, as well as simplify the mass-production of such

scattering units. The corresponding scattering systems may be the ones of

choice within this preferred class of quasi-resonant scattering units,

simply because the dye-bearing fluid could be stratospherically dispersed

from an airplane tank as a suitably fine aerosol, the individual

nano-particles of which would quick-freeze at stratospheric temperatures

and thereupon become photo chemically inert over multi-year time-scales.

While significantly greater total mass might have to be deployed to

constitute such a scattering system, the simplicity and relatively low

technical risk with which the system could be created and deployed might

be an overriding consideration.


How much total mass would be required for each of these alternatives can be

reliably estimated from spectroscopic measurements of such metal atom --

or dye molecule-loaded nano-containers, i.e., what the absorption spectra

and oscillator strengths of the as-packaged materials actually are. After

such scoping-level measurements, it will likely be productive to prepare

ton-quantities of such quasi-resonant scattering material, disperse it

into the stratosphere and then measure the residence time and global

distribution of the scattering units, e.g., with ground-based range-gated,

spectrally-resolved lidar systems. Such modest quantities should be very

readily prepared and dispersed, and can be argued from first principles

to not have any discernible global effects. Such measurements, in turn,

should provide a reliable basis for predicting the effects of 10/3-10/4

greater quantities of such scattering units, i.e., their utility as a

full-scale insolation modulation system. It’s also worth noting-in-passing

that the resonant transitions chosen to be intercalation-broadened -- or

those glassed-in dyes chosen to absorb and fluoresce -- likely could be

selected to lie exclusively in the near-UV or IR portions of the solar

spectral radiance on the Earth’s atmosphere, so that the resulting

“spectral notching” of sunlight as seen at or near the Earth’s surface

would be invisible to people, just as the near-IR solar spectral notchings

due to absorption by atmospheric H2O already are. The as-perceived

“environmental impact” of such spectrally-notched insolation subtraction

would thereby be essentially zero.


(37) We estimate that an as-deployed caged metal atom-based full-scale

scattering system may have a total mass of 7.5x10/5 tons. Due both to

higher molecular weight and lower unit radiative strength of dye molecules

relative to Li atoms -- offset somewhat by proportionately lower “mass

overhead” -- an organic dye-based system may have a total system mass of

~10/6 tons. (In spite of its greater mass, a dye-based system may be

preferred because its spectrally broadened features are readily attained

and maintained.) The less than $500 million deployment cost of such a

dye-based system would likely be considerably less than its materials

cost, which we estimate as ~$1 billion.


(38) We term this approach “quasi-resonant” because it involves spreading

out the exceedingly intense, pure hue arising from resonant absorption

and fluorescent emission of light by selected organic molecules into broad

bands of still quite intense absorption-fluorescence by these molecules

when intimately mixed with other materials. We provisionally choose the

perfluorohydrocarbons as the “other materials,” because their durability

in the even more demanding solar UV/EUV and atomic oxygen environments of

low Earth orbit has been demonstrated on the Long-Duration Exposure Facility.

We proposed to load one or more of these dyes, selected for high radiative

strength in either the near-UV or near-IR spectral bands, in a high-boiling

fluorocarbon liquid and then to disperse ultra-small droplets of this

liquid in the stratosphere, where they will freeze and thereafter provide

effective protection against oxidation of the dye molecules which they carry

-- in addition to not perturbing stratospheric photochemistry.


(39) Such a system might have to be comprised of scatterers designed to have

stratospheric residence times significantly less than five years, so that

they would e.g., vertically, exit the stratosphere before they had migrated

in latitude to unacceptable extents. It appears feasible-in-principle to

exploit the stiffly altitude-dependent meridional transport in the lower-to-

middle stratosphere to move scattering material poleward from equatorial

deployments at most any desire mean rate between greater than 10 yr/-1 and

less than 0.2 yr/-1.


(40) The significance of design optimization to minimize deployed system

masses becomes more apparent when considering deployment options featuring

post-deployment operational intervals, much less than the greatest attainable

(~5 years). Deployment mass-rates and costs may become quite burdensome for,

e.g., single-month residence times just above the tropopause, unless near-

optimally designed scatterers are employed.


(41) Both types of space-based scattering systems -- high angle-scattering

ones in LEO and small-angle-scattering ones on the Earth-Sun line -- may be

used to scatter sunlight onto the Earth that otherwise would have passed

nearby it. “Self-lofting blue-UV chaff” could be transformed into

“self-lofting LWIR chaff” by replacing its metal shell with a semiconductor

one chosen to have a direct (for reasons of mass efficiency) band-gap of

a few tenths of an eV -- energetic enough to reflect LWIR radiation

coming up from the Earth’s surface and lower atmosphere but of sufficient

low energy to pass virtually all incoming solar photons without significant

attenuation (e.g., InSb). The very low mass small-angle-scattering system

in deep space can be readily converted to direct additional sunlight onto

the Earth from a position slightly offset from the Earth-Sun axis, rather

than scatter it away from an on-axis location.


(42) See, e.g., Greenland Ice Core Project (GRIP) Members, Climate

instability during the last interglacial period recorded in the GRIP

ice core, Nature 364, 203-7 (1993), for a discussion of observed “few

decade to centuries” large-amplitude temperature variability of the Northern

Hemisphere during the interglacial period immediately preceding the present

one. A repetition of the 7-decade “cold snap” of the ~14° C peak magnitude

inferred from examination of the Greenland cores might reduce arable land

world-wide by -- at the very least -- 1% per year following its abrupt onset,

a rate which would result in large-scale famine on single-decade time-frames,

as planetary food reserves become exhausted. (The inferred time-scale of

the associated shifts in atmospheric circulation occurring during these

“fast” events is 1-3 decades, which is comparable with that inferred to

have occurred during termination of the most recent Ice Age.


(43) E.g., Broecker WS, Cooling the tropics, Nature 376, 213-4 (1996),

concludes “The palaeoclimate record shouts out to us that, far from being

self-stabilizing, the Earth’s climate system is an ornery beast which

overreacts even to small nudges.”


(44) Hasselmann, K, Are We Seeing Greenhouse Warming?, Science 276, 914 (1997).


(45) See, e.g., Wigley TML, Richels R and Edmonds J, Economic and

environmental choices in the stabilization of atmospheric CO2 concentrations,

Nature 379, 240-3 (1996), where it is demonstrated that “business as usual”

in fossil fuel-based energy production for the next three decades does not

doom the Earth to global warming in excess of 2° C, if reasonable measures

are taken thereafter. We note that insolation modulation systems can be

studied-in-subscale and then deployed on single-decade time-scales, short

compared to the onset of any global warming (or cooling) currently considered.


(46) Imbrie J, et al., On the Structure and Origin of Major Glaciation Cycles

2. The 100,000-Year Cycle, Paleoceanography 8, 699-735 (1993).


(47) Greenland Ice Core Project (GRIP) Members, Climate instability during

the last interglacial period recorded in the GRIP ice core, Nature 364, 203-7 (1993).


(48) While we claim no particular expertise in policy matters, we note

expert opinion to the effect that “... stabilization [of atmospheric CO2 levels]

requires an eventual and sustained reduction of emissions to substantially below

current levels” [Wigley TML, Richels R and Edmonds J, Economic and environmental

choices in the stabilization of atmospheric CO2 concentrations, Nature 379, 240-3

(1996)], and we estimate that “substantial” worldwide reduction in fossil fuel

usage over the next several decades will not occur without substantial

likelihood of inducing major conflict.