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
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.
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
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 production48
– especially in a world exhibiting very large geographical and cultural
differences in per capita energy use, past, present and future.
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
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.
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.
for ''bad weather'' may be too heavy for any human to bear. But, we hope, thinking
before acting might be acceptable. 48
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.
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. 1, ibid. Also, Wigley, TML, ''The Contribution
From Emissions of Different Gases to the Enhanced Greenhouse 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 scattering 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,'' W a l l 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.'' These fractional price increases translate
to ~$4x1011/year world-wide, or ~$1011/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
10 'A doubling of atmospheric CO2 during the
coming century is IGCC-estimated to result in a 2.5± 1.5o 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 ~10o 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.)
Also, it is necessary to select scattering materials which scatter only with quite small
losses, in order to minimize possibly undesirable heating of the portion of the
atmosphere in which the scatterer is deployed.
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 spaceand time-averaged optical-frequency current density in the matter comprising the system gives a generalpurpose figure-of-merit for the mass budget of the system. When multiplied by the ‘optical
leverage’ figure-ofmerit, 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 £2, and we generally must consider (e-1)£9x10-13
farads/cm. Available metals (e.g., Al) have electrical resistivities ³3x10-6 ohm-c (taking some degradation from best bulk
properties for very thin layers), i.e., conductivities s£3x105 mho/cm. Optical frequencies of resonant transitions are ~1015
Hz, and these transitions correspond t electron travel over orbital distances ~3 Å, i.e., across atoms of ~3 Å diameter. Take
a reference midvisible optical angular frequency of ~4x1015 sec-1. Then the optical current density I in a unit volume (whose
greatest dimension is assumed to be £l/2p) of such a dielectric at unit electric field strength is I~E/Z~wC, or 4x1015 x 9x10-13,
or 3.6x103 amp/cm2. The current density in the same circumstances in good
metal is just I~sE~s, or 3x105 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 ~1021 transitions/sec are driven by a unit-strength solar-spectral
optical electric 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 ~5x109 amp/cm2 (!). For constituting scattering units, then, the relative figures-of-merit of best-available
dielectrics, metals and resonant-scatterers are roughly 1:102:106.
14 The ''packaging mass overhead'' for quasi-resonant
scatterers typically is much larger than that for metallic and dielectric 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, nearequatorial 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 oceanatmosphere 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 scatterers 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 off 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 (L1) 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 L1. 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 areal 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 ~102-fold smaller angles. In particular, the conducting elements of the scattering units need carry
only ~102-fold smaller currents, so that they can be of 102-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 102-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 ~3 x10-11 cm2 cross-sectional area (~600 Å thick by ~1000 Å in transverse width) spaced every 100l/2~3 x 10-3 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 ~1.2x1018 cm2
which is to be sun-shaded, or ~1.2x1016 cm2: ~1.4x109 gms. The total mass of the ideal scattering system thus is ~1.5x109 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 – ~3400 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 ~103 dynesec/ 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 <p, 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 sunward 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 than 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); Chuang 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,
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 0.05-0.1 mm diameter, deployed in the Earth’s stratosphere. The Rayleigh
scattering cross-section S of a particle of volume V whose polarizability a=3(e-1)/4p(e+2)
for photons of angular frequency w is S = (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), S may be estimated to be ~5x10-12 cm2. Thus, ~1028 of these particles, uniformly distributed in the stratosphere, would be required to scattershield the 5x1018 cm2 of terrestrial surface with optical density 10-2 at the sub-solar point.
(While only the bluer portion of the visible spectrum, l£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 ~1013 gms, or 10,000,000 tons. A mean
stratospheric lifetime of each scattering particle of 5 years would imply a required injection rate of 2x106 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 poses 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 groundsite, one
whose carefully-engineered exhaust-stream could hydrodynamically penetrate the overlying tropopause and inject £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 (e.g., burning of fossil fuels
of all types).
32Absorption 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 107- and 108-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 alkalimetal alloy system can lower this photoedge to an effective
2 eV threshold (e.g., as the tri- and quad-alkalimetal- alloy photocathodes of commercial photodetection 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 £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)(1.2x1018 cm2)(3x10-6 gm/cm2)~7x1010 gms ~ 70,000 tons. If
deployed either in the atmosphere or in LEO, individual scattering units could
be effective only £50% of the time, so that ³140,000 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 ³two-fold mass penalties are paid for protective jacketing, e.g., SiO. In addition to having a relatively large
mass budget for a space-deployed system, such an absorption/reradiation 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 ³200 Å, by ~300 Å in transverse width, spaced at £3x10-5 cm distances in both dimensions; packaging mass
for protection against stratospheric oxidation would be comparatively small, if metal having a thin protective oxide, such as 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 ~2p, 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 30-50 km altitudes, and maintain
them there for multi-day intervals (limited mostly by the durability-against-photooxidation 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 8x1014 Hz frequencies characteristic of midvisible solar radiation and thus
suffices to (predominantly) backscatter the blue end of the incident solar spectrum; however, it is £0.2 skin-depth at 2-3x1013
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 electrodynamic 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 radius of 4 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 involve £2-fold adjustment of the balloon diameter while
keeping its wall thickness invariant.) Since it is required to scatter-shield ~5x1016
cm2 (recalling that 1% of the Earth’s total area is to be so sun-shielded), ~1017 of these ‘‘selflofting blue-UV chaff’’ objects will be required, with an associated mass of ~1012
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 ~2x1010 grams/year
– ~6x107 balloons/sec, or 108 cm2/sec, or 1 hectare/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 Al bilayer-sandwich substrate. High-circulation major newspapers print ~106 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 4.5x107 lbs/year of Al-as-foil (at a current annual cost
of £$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 photooxidize to the hydrated oxide quite rapidly in the
wet troposphere: at ~290oK, Al exposed to dry oxygen forms a stable oxide layer
of 10-30 Å thickness, but wet oxidizing atmospheres can form >1 mm hydrated oxide layers on bulk Al in a matter of hours
– and 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 invisiblyfine 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's 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 LWIR-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 LWIR 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 fulldipole- 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 (~108 sec-1, for the full-dipolestrength optical
transitions of present interest): i.e., an alkali-metal atom (e.g., Li) will process ~3x10-11 W of resonant radiation (£108 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 3x1012 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 £1018 photons/cm2-sec of (near-)optical
solar flux at 1 AU only present ~1011 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 s ~ 3x10-10 cm2 (i.e., s ~ 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, 3x109 grams, or 3000 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 3000 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 nanoparticles of which would quick-freeze at stratospheric
temperatures and thereupon become photochemically 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 103-104 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-&-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 7.5x105 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 ~106 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 £$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 propose 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
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 desired mean rate between ³10 yr-1 and £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-anglescattering 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 sufficiently 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
~14o 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
43 E.g., Broecker WS, Cooling the tropics, Nature 376, 213-4 (1995) 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 2oC, if reasonable measures are taken thereafter. We note that insolation
modulation systems can be studied-in-subscale and then deployed on single-decade timescales,
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.
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MI Hoffert, K Caldeira, G Benford, DR Criswell, C … - Science, 2002 - nrel.gov
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the decarbonization of fuels alone will not mitigate global warming. ...
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The cumulative effects of climate warming and other human stresses on Canadian freshwaters in the
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... grasses embedded in lake sediments (Teller and Last ... are generically referred to as
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SH Schneider - nature.com
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GEOENGINEERING AND CARBON MANAGEMENT: IS THERE A MEANINGFUL DISTINCTION?
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IAF-02-U. 1.01 Earth Rings for Planetary Environment Control
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... Not all
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Annual Review of Energy and the Environment
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... a cooling to counter the climatic warming caused by ... in the troposphere currently
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Systems-Level Considerations for Mitigating the NEO Impact Hazard
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GGRREEEENNHHOOUUSSEE GGAASS AABBAATTEEMMEENNTT CCOOSSTTSS
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Earth systems engineering and management
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... people are so oblivious to the predicted consequences of global warming. ... Mitigation
Remediation Policies ... It was the computer that Dr Teller was said to be ...
Cited by 2 - Web Search - ingentaconnect.com - ingenta.com - ingenta.com
DEVELOPMENT OF ENVIRONMENTAL MODELING METHODOLOGIES FOR THE MANAGEMENT OF REGIONAL AND INDUSTRIAL …
A Thesis, L Liu, S Regina - env.uregina.ca
... 1992 & 1994).
These methods have been extensively applied for the planning of
environmental pollution control systems (Teller
1968; Werczberger 1974; ...
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