Fig 1.
Occulting disk near the Sun-Earth Lagrange L1 point.
The L1 point rotates around the Sun with the same angular speed as the Earth, thus allowing an occulting disk to remain in a position where it casts continuous shade on the Earth.
Fig 2.
Circular restricted Three Body Problem frame of reference, vectors and occulting disk attitude definition (i.e. cone α and clock δ control angles).
Fig 3.
System mass required to geoengineer Earth.
Classical L1 position≈1.5x106km.
Fig 4.
Climate response of 2xCO2 world scenario as computed by GREB model in a 50 year simulation.
The initial CO2 concentration is set to 340 ppm (a level similar to that of 1980s), thus the doubled concentration is 680 ppm. a) Mean differences of monthly mean surface temperatures between the 2xCO2 scenario and 1xCO2 control scenario at the last year of simulation in GREB’s 3.75°x3.75° horizontal grid. b) Latitudinal and seasonal increase of temperature computed by averaging longitudinal data. c) Evolution of the global mean surface temperature Tsurf of the two scenarios considered (1xCO2 and 2xCO2) as a function of the length of the simulation. d) Mean surface temperatures during the last year of simulation (50th year) for the 2xCO2 scenario.
Fig 5.
Daily-averaged latitudinal incoming solar radiation over one complete year.
Note that the Earth’s orbital eccentricity is assumed zero. a) Natural isolation as a function of latitude and time of year. b) Shade cast by a 1,434 km radius occulting disk at the optimal SRP displaced L1 point (i.e. decrease of insolation with respect to the natural insolation). The shade is represented as daily-averaged decrease in solar insolation.
Fig 6.
Schematic of the occulting disk shade as seen from the Earth as a function of distance to the Sun-Earth line.
Fig 7.
2xCO2 geoengineered world scenario as computed by GREB model in a 50 year simulation.
The scenario assumes a circular disk of 1,434 km radius placed on the Sun-Earth line at a distance from Earth of 2.44x106 km. a) Root-mean-square1 (rms) differences of monthly mean surface temperatures between the geoengineering and control scenarios for the year 50 of the simulation. b) Latitudinal and seasonal variations of temperature between the geoengineering and control scenarios (averaged in longitude).
Fig 8.
Shade pattern and climate response for displaced occulting disks.
a) Daily-averaged latitudinal shade over a complete year. Shade cast by a 1,434 km radius occulting disk located at a distance from the Earth of 2.44x106km and displaced by 6,000 km below the plane of the Sun-Earth system. b) Climate response for the shade pattern. Climate response to shade as in a) in a 2xCO2 scenario as computed by GREB model in year 50 of the simulation.
Fig 9.
Pareto sets for differently sized occulting disk configurations.
Fig 10.
a) Out-of-plane motion of the configuration of two mobile occulting disks. The size of each disk is also represented and scaled with the z-axis. b) Daily-averaged latitudinal shade over a complete year cast by Case I solution. c & d) Geoengineered climate response as computed by GREB. c) rms differences of monthly mean surface temperatures between the geoengineering and control scenarios for year 50 of the simulation. d) Latitudinal and seasonal variations of temperature between the geoengineering and control scenarios (averaged in longitude).
Fig 11.
a) Out-of-plane motion of the configuration of two mobile occulting disks. The size of each disk is also represented and scaled with the z-axis. b) Daily-averaged latitudinal shade over a complete year cast by Case II solution. c & d) Geoengineered climate response as computed by GREB. c) rms differences of monthly mean surface temperatures between the geoengineering and control scenarios for year 50 of the simulation. d) Latitudinal and seasonal variations of temperature between the geoengineering and control scenarios.
Fig 12.
Case I geoengineering periodic orbit.
Artificial geoengineering configuration of two occulting disks with out-of-plane motion that satisfy z(t) = 3,850·sin(t-0.423π)+840 [km] (blue orbit) and z(t) = 11,100·sin(t-0.4π)+17 [km] (red orbit). a) 1 year period motion in the Earth rotating reference frame, centred on the SRP displaced L1 point. b) Cone and clock angle (α, δ) control law required to generate the required orbit.
Fig 13.
Case II geoengineering periodic orbit.
Artificial geoengineering configuration of two occulting disks with out-of-plane motion that satisfy z(t) = 7,856·sin(t-0.72π)+3,908 [km] (blue orbit) and z(t) = 13,272·sin(t-0.36π)-526 [km] (red orbit). a) 1 year period motion in the Earth rotating reference frame, centred on the SRP displaced L1 point. b) Cone and clock angle (α, δ) control law required to generate the required orbit.