OPTIMAL SUNSHADE CONFIGURATIONS FOR SPACE-BASED GEOENGINEERING NEAR THE SUN-EARTH L1 POINT

Joan-Pau Sánchez & Colin McInnes

Climate Engineering ConferenceBerlin, Germany

August 18-21, 2014

• All space-based methods for geoengineering aim at diverting incoming solar radiation before it reaches the Earth.

• The estimated mass of the deployed structure is in the order of 107-108 tonnes (Seifritz 1989; Early 1989; McInnes 2002; Angel 2006).

Space-based Geoengineering

Optimal Sunshade Configurations

Reflectors Dust

Sunshades

Optimal Sunshade Configurations for Space-based Geoengineering near the Sun-Earth L1 point

Optimal Sunshade Configurations

• Revisiting the concept of deploying a large sunshade at L1.– Most of the previous work aims at a uniform reduction of the solar

insolation by 1.7%.

• Problem: a uniform insolation reduction of 1.7% would drive important changes to regional climates (Lunt et al. 2008).– Warming at high latitudes and cooling at the tropics.

• Goal: optimal configurations of sunshades that offset regional differences such as latitudinal and seasonal difference of temperature.

S=1367 W/m2

ΔS=23.24 W/m2Disk

Diskd S

R Rd S

1,489 DiskR km

*at the SRP-displaced equilibrium point

Table of Contents

GREB

Optimization

Results

Understanding of regional effects of climate change, while performing a numerically intensive search.

GREB model (Dommenget and Floter 2011)

• Globally Resolved Energy Balance model (GREB) provides an insight of the effects of altering the incoming solar insolation into the Earth’s climate system.

– GREB captures only the main physical processes by means of simplified models. It assumes fixed atmospheric circulation, cloud cover and soil moisture, which are given as boundary conditions.

• Simple and fast

2xCO2 Scenario2xCO2+Sunshade Scenario

• 2xCO2 (680 ppm) + static sunshade at L1

– An iterative secant approach is used to find the size of the disk that yields a global mean temperature of 14 Co.

Classical In-line Scenario

3D Energy Kick Function

1,434 DiskR km

Sun

EarthL1

L2

z

y

x

ˆω z

*ΔT difference with respect the control scenario (1xCO2 world)

Shade Patterns

• A static sunshade at L1 casts an almost uniform shade onto the Earth.

• By displacing the occulting disk, different shade patterns are achieved.

Sun

EarthL1L2

z

y

x

ˆω z

Sun

EarthL1

L2

z

y

x

ˆω z

7,000 kmz

Are there perhaps more suitable disk configurations that can reduce the impact of climate change further than what the Sun-Earth in-line configuration achieved?

A Multiple-Objective Optimization• More suitable disk configurations that reduce the impact of climate at

regional and seasonal scale?

Sun

EarthL1

L2

z

y

x

ˆω z

– 2 Mirrors of Shading areas A1 and A2

– 2 sinusoidal and displaced out-of-plane motions.

1 1 1 1sinz t a t c b

2 2 2 2sinz t a t c b

1 1 1 1 2 2 2 2A a b c A a b cxDesign Variables

1 2A A J f

Criteria Vector

Total Shading AreaGeoengineering

Performance Index

A Multiple-Objective Optimization• More suitable disk configurations that reduce the impact of climate at

regional and seasonal scale?– 2 Mirrors of Shading areas A1 and A2

– 2 sinusoidal and displaced out-of-plane motions.

1 1 1 1 2 2 2 2A a b c A a b cxDesign Variables

1 2A A J f

Criteria Vector

Total Shading AreaGeoengineering

Performance Index

Pareto Optimal Set

Geoengineering Performance Index

• Optimal sunshade configurations were sought that minimize J

– J is the root-mean-square difference of temperature with respect to the control scenario, averaged over the entire Earth’s surface.

– Return the largest fraction of Earth’s surface to a climate within ±0.1 Co

difference of the surface temperatures of that of the 1xCO2 world.

1:48

1:48

cos

cos

i f ii

ii

ii

J w T

w

if 0.1

0 if 0.1

AnnualRMS AnnualRMS oLat i Lat i

f i AnnualRMS oLat i

T T CT

T C

2 2 2

50 50 50

1, t , t ... , t

12th th th

AnnualRMSscenario

Jan Feb Dec

year year year

T

T T T

2 2:2 1, , ,GeoEng xCO xCOT t T t T t

1:96

, ,

,96

scenario jj

scenario

T t

T t

Multiple-objective Optimization Problem

• Pareto optimal design solutions that minimize both J and the total shading area At required for 2 sunshades.

1 2A A J f

1 1 1 1 2 2 2 2A a b c A a b cx

sinz t a t c b

J0 =0.325 Co Classical inline Sc.

½J0

Case I

Case II

Classical In-line Scenario

CASE I• A solution with At as in the

classical in-line geoengineering solution. – J = 0,275 Co

– Improvement of 0.05oC.– Case I returns nearly 40% of the

Earth surface to pre-global warming temperatures, while the classical geoengineering scenario achieves less than 10%.

1 1,200 mR k

2 790 mR k

CASE I• The motion required cannot be

generated with the natural periodic motion that exist near L1. – Specific control law are thus

required.

CASE II• Minimum At to achieve ½·J0

– 1.5 times the At of the classical inline geoengineering solution.

– J = 0,162 Co

– Environmental risk is reduced to a quarter.

1 1,522 mR k

2 880 mR k

Conclusions

• This work provides new insights into the possibilities offered by space-based geoengineering using orbiting solar reflectors.

• Optimal configurations of orbiting sunshades were investigated that not only offset a global temperature increase, but also mitigate regional differences such as latitudinal and seasonal difference of monthly mean surface temperature.

• Two configurations of two orbiting occulting disks were presented that achieve clear gains with respect to a static disk near the Sun-Earth L1 point.

3D Energy Kick Function

THANKS FOR YOUR ATTENTION

Optimal Sunshade Configurations for Space-based Geoengineering near the Sun-Earth L1 pointJoan-Pau Sánchez – jpau.sanchez@upc.edu

APPENDIX

Optimal Sunshade Configurations

Space-based Geoengineering

Optimal Sunshade Configurations

Fig. The effectiveness, affordability, safety and timeliness ratings of geoengineering methods analysed in a Royal Society report

Shepherd at al. Geoengineering the climate , Report of Royal Society working group on geoengineering, 2009

Optimal Configuration for Sun-Earth L1 Occulting Disk

Sun

EarthL1

L2

z

y

x

ˆω z

7,000 kmz (McInnes et al. 1994)

Libration Point Orbits

Shade Patterns

Sun

EarthL1

L2

z

y

x

ˆω z

7,000 kmz

Libration Point Orbits

• A static sunshade at L1 casts an almost uniform shade onto the Earth.

Sun

EarthL1

L2

z

y

x

ˆω z

• By displacing the occulting disk, different shade patterns are achieved.