Advertisement

Atmospheric and Oceanic Optics

, Volume 32, Issue 1, pp 55–63 | Cite as

Optimal Control for the Process of Using Artificial Sulfate Aerosols for Mitigating Global Warming

  • S. A. SoldatenkoEmail author
  • R. M. YusupovEmail author
ATMOSPHERIC RADIATION, OPTICAL WEATHER, AND CLIMATE
  • 27 Downloads

Abstract

The optimal control problem for deliberate intervention in the Earth’s climate system with the aim of stabilizing the global surface temperature is considered. The deliberate action on the climate system is implemented via the controlled radiative disturbance created by artificial aerosols injected into the stratosphere. The controlled object is described by a two-component energy-balance model subject to radiative action caused by an increase in the concentration of greenhouse gases in the atmosphere. The human impact on the climate system is specified in accordance with Representative Concentration Pathway (RCP) scenarios, as well as with the scenario corresponding to a 1% increase in atmospheric carbon dioxide per year. The albedo of the artificial aerosol global layer represents the control variable. The optimal control and the corresponding phase trajectory of the climate system are obtained analytically using Pontryagin’s maximum principle. The approach discussed in this paper can be considered as a basis for developing scenarios for deliberate intervention in the climate system using various geoengineering methods.

Keywords:

optimal control geophysical cybernetics climate engineering weather modification global warming 

Notes

REFERENCES

  1. 1.
    Climate Change 2013: The physical science basis. Contribution of working group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (University Press, New York, Cambridge, 2013)Google Scholar
  2. 2.
    Statement on the State of the Global Climate in 2017, Report N 1212 (WMO, Geneva, Switzeland, 2018).Google Scholar
  3. 3.
    www.unfccc.int/sites/default/files/paris_agreement_english_.pdf (Cited June 1, 2018).Google Scholar
  4. 4.
    J. Rodelj, M. Elzen, N. Hohne, T. Fransen, H. Fekete, H. Winkler, R. Schaeffer, F. Sha, K. Riahi, and M. Meinshausen, “Paris Agreement climate proposals need a boost to keep warming well below 2°C,” Nature 534, 631–639. (2016).ADSCrossRefGoogle Scholar
  5. 5.
    P. Brown and K. Caldeira, “Greater future global warming inferred from Earth’s recent energy budget,” Nature 552, 45–50 (2017).ADSCrossRefGoogle Scholar
  6. 6.
    A. E. Raftery, A. Zimmer, D. M. W. Frierson, R. Startz, and P. Liu, “Less than 2°C warming by 2100 unlikely,” Nat. Clim. Change 7, 637–641 (2017).ADSCrossRefGoogle Scholar
  7. 7.
    D. Jacob, L. Kotova, C. Teichmann, S. P. Sobolowski, R. Vautard, C. Donnelly, A. G. Koutroulis, M. G. Grillakis, I. K. Tsanis, A. Damm, A. Sakalli, and M. T. H. van Vliet, “Climate impacts in Europe under +1.5 °C global warming,” Earth’s Future 6, 264–285 (2018).ADSCrossRefGoogle Scholar
  8. 8.
    K. Tanaka and B. C. O’Neill, “The Paris Agreement zero-emissions goal is not always consistent with the 1.5°C and 2°C temperature targets,” Nat. Clim. Change 8, 319–324 (2018).ADSCrossRefGoogle Scholar
  9. 9.
    B. Henley and A. King, “Trajectories toward the 1.5 °C Paris target: Modulation by the Interdecadal Pacific Oscillation,” Geophys. Res. Lett. 44, 4256–4262 (2017).ADSCrossRefGoogle Scholar
  10. 10.
    K. L. Ricke and D. W. Keith, “Solar geoengineering as part of an overall strategy for meeting the 1.5°C Paris target,” Phil. Trans. Roy. Soc., A 376, ID 20 160 454 (2018).Google Scholar
  11. 11.
    Climate Intervention Requires Enhanced Research, Consideration of Societal and Environmental Impacts, and Policy Development. https://sciencepolicy. agu.org/files/2018/01/Climate-Intervention-Position-Statement-Final-2018-1.pdf (Cited June 1, 2018).Google Scholar
  12. 12.
    AGU White Paper 2017: Climate Intervention Requires Enhanced Research, Consideration of Societal Impacts, and Policy Development. https://www.sciencepolicy. agu.org/files/2017/11/AGU-White-Paper-on-Geoengineeging.pdf (Cited June 1, 2018).Google Scholar
  13. 13.
    M. I. Budyko, “Technique for climate impact,” Meteorol. Gidrol., No. 2, 91–97 (1974).Google Scholar
  14. 14.
    Izrael' Yu.A., “An efficient way to regulate the global climate is the main objective of the solution of the climate problem,” Rus. Meteorol. Hydrol., No. 10, 1–4 (2005).Google Scholar
  15. 15.
    P. J. Crutzen, “Albedo enhancement by stratospheric sulfur injections: A contribution to resolve a policy dilemma?,” Clim. Change 77, 211–220 (2006).ADSCrossRefGoogle Scholar
  16. 16.
    A. S. Ginzburg, D. P. Gubanova, and V. M. Minashkin, “Impact of natural and anthropogenic aerosols on the global and regional climates,” Ros. Khim. Zh. LII (5), 112–119 (2008).Google Scholar
  17. 17.
    D. W. Keith, :Geoengineering the climate: History and prospect,” Annu. Rev. Energy Environ. 25, 245–284 (2000).CrossRefGoogle Scholar
  18. 18.
    Yu. A. Izrael’, A. G. Ryaboshapko, and N. N. Petrov, “Comparative analysis of geo-engineering approaches to climate stabilization,” Rus. Meteorol. Hydrol., No. 6, 5–24 (2009).Google Scholar
  19. 19.
    A. Robock, A. Marquardt, B. Kravitz, and G. Stenchikov, “Benefits, risks, and costs of stratospheric geoengineering,” Geophys. Res. Lett. 36, L19703 (2009).ADSCrossRefGoogle Scholar
  20. 20.
    J. G. Shepherd, “Geoengineering the climate: An overview and update,” Phil. Trans. R. Soc. A 370, 4166–4175 (2009).ADSCrossRefGoogle Scholar
  21. 21.
    A. V. Chernokul’skii, A. V. Eliseev, and I. I. Mokhov, “Analytical estimations of the efficiency of climate warming prevention by controlled aerosol emissions into the stratosphere,” Rus. Meteorol. Hydrol., No. 5, 301–309 (2010).Google Scholar
  22. 22.
    Yu. A. Izrael’ and A. G. Ryaboshapko, “Climate geoengineering: the feasibility of implementation,” Problemy Ekol. Monitoringa Modelirovaniya Ekosistem 24, 11–24 (2011).Google Scholar
  23. 23.
    R. Bellamy, J. Chilvers, N. E. Vaughan, and T. M. Lenton, “A review of climate geoengineering appraisals,” WIREs Clim. Change 3, 597–615 (2012).CrossRefGoogle Scholar
  24. 24.
    P. J. Irvine, B. Kravitz, M. G. Lawrence, and H. Muri, “An overview of the Earth system science of solar geoengineering,” WIREs Clim. Change 7, 815–833 (2016).CrossRefGoogle Scholar
  25. 25.
    K. Caldeira and G. Bala, “Reflecting on 50 years of geoen-gineering research,” Earth’s Future 5 (1), 1–17 (2017).ADSCrossRefGoogle Scholar
  26. 26.
    B. Kravitz, A. Robock, O. Boucher, H. Schmidt, K. E. Taylor, G. Stenchikov, and M. Schulz, “The Geoengineering Model Intercomparison Project (GeoMIP),” Atmos. Sci. Lett. 12, 162–167 (2011).CrossRefGoogle Scholar
  27. 27.
    H. Schmidt, K. Alterskjær, B. D. Karam, O. Boucher, A. Jones, J. E. Kristjansson, U. Niemeier, M. Schulz, A. Aaheim, F. Benduhn, M. Lawrence, and C. Timmreck, “Solar irradiance reduction to counteract radiative forcing from a quadrupling CO2: Climate responses simulated by four earth system models,” Earth Syst. Dynam. 3, 63–78 (2012).ADSCrossRefGoogle Scholar
  28. 28.
    B. Kravitz, K. Caldeira, O. Boucher, A. Robock, P. J. Rasch, K. Alterskjær, Karam D. Bou, J. N. S. Cole, C. L. Curry, J. M. Haywood, P. J. Irvine, D. Ji, A. Jones, J. E. Kristjansson, D. J. Lunt, J. C. Moore, U. Niemeier, H. Schmidt, M. Schulz, B. Singh, S. Tilmes, S. Watanabe, S. Yang, and J.‑H. Yoon, “Climate model response from the Geoengineering Model Intercomparison Project (GeoMIP),” J. Geophys. Res. 118, 8320–8332 (2013).Google Scholar
  29. 29.
    D. W. Keith, B. Kravitz, and K. Caldeira, “Management of trade-offs in geoengineering through optimal choice of non-uniform radiative forcing,” Nat. Clim. Change 3, 365–368 (2013).ADSCrossRefGoogle Scholar
  30. 30.
    Yu. A. Izrael, E. M. Volodin, S. V. Kostrykin, A. P. Revokatova, and A. G. Ryaboshapko, “The ability of stratospheric climate engineering in stabilizing global mean temperatures and an assessment of possible side effects,” Atmos. Sci. Lett. 15, 140–148 (2014).CrossRefGoogle Scholar
  31. 31.
    V. P. Parkhomenko, “Simulation of stabilization of the global climate via controllable emissions of stratospheric aserosols,” Matem. Model. Chislennye Metody, No. 2, 115–126 (2014).Google Scholar
  32. 32.
    H. Muri, J. C. Moore, U. Niemeier, S. J. Phipps, J. Sillmann, T. Storelvmo, H. Wang, and S. Watanabe, “The Geoengineering Model Intercomparison Project Phase 6 (GeoMIP6): Simulation design and preliminary results,” Geosci. Model Dev. 8, 2279–2292 (2015).Google Scholar
  33. 33.
    M. Meinshausen, S. J. Smith, K. Calvin, J. S. Daniel, M. L. T. Kainuma, J.-F. Lamarque, K. Matsumoto, S. A. Montzka, S. C. B. Raper, K. Riahi, A. Thomson, G. J. M. Velders, and D. P. P. van Vuuren, “The RCP green-house gas concentrations and their extensions from 1765 to 2300,” Clim. Change 109, 213–241 (2011).CrossRefGoogle Scholar
  34. 34.
    A. J. Jarvis, P. C. Young, D. T. Leedal, and A. Chotai, “A robust sequential CO2 emissions strategy based on optimal control of atmospheric CO2 concentrations,” Clim. Change 86, 357–373 (2008).ADSCrossRefGoogle Scholar
  35. 35.
    A. J. Jarvis, D. T. Leedal, C. J. Taylor, and P. C. Young, “Stabilizing global mean surface temperature: A feedback control perspective,” Environ. Model. Software 24, 665–674 (2009).CrossRefGoogle Scholar
  36. 36.
    G. A. Ban-Weiss and K. Caldeira, “Geoengineering as an optimization problem,” Environ. Res. Lett. 5, 034009 (2010).ADSCrossRefGoogle Scholar
  37. 37.
    B. Kravitz, D. W. Keith, and A. Jarvis, “Dynamics of the coupled human-climate system resulting from closed-loop control of solar geoengineering,” Clim. Dynam. 43, 243–258 (2014).ADSCrossRefGoogle Scholar
  38. 38.
    B. Kravitz, D. G. MacMartin, D. T. Leedal, P. J. Rasch, and A. J. Jarvis, “Explicit feedback and the management of uncertainty in meeting climate objectives with solar geoengineering,” Environ. Res. Lett. 9, 044006 (2014).ADSCrossRefGoogle Scholar
  39. 39.
    D. V. Gaskarov, V. B. Kiselev, S. A. Soldatenko, and R. M. Yusupov, Introduction in Geophysical Cybernetics (SPbGUVK, St. Petersburg, 1998) [in Russian].Google Scholar
  40. 40.
    S. Soldatenko, “Weather and climate manipulation as an optimal control for adaptive dynamical systems,” Complexity 2017, ID 4615072 (2017).Google Scholar
  41. 41.
    J. M. Gregory and J. F. B. Mitchell, “The climate response to CO2 of the Hadley Centre coupled AOGCM with and without flux adjustment,” Geophys. Res. Lett. 24, 1943–1964 (1997).ADSCrossRefGoogle Scholar
  42. 42.
    J. M. Gregory, “Vertical heat transports in the ocean and their effect on time-dependent climate change,” Clim. Dynam. 16, 501–515 (2000).ADSCrossRefGoogle Scholar
  43. 43.
    I. M. Held, M. Winton, K. Takahashi, T. Delworth, F. Zeng, and G. K. Vallis, “Probing the fast and slow compo-nents of global warming by returning abruptly to preindustrial forcing,” J. Clim. 23, 2418–2427 (2010).ADSCrossRefGoogle Scholar
  44. 44.
    O. Geoffroy, D. Saint-Martin, D. J. L. Olivie, A. Voldoire, G. Bellon, and S. Tyteca, “Transient climate response in a two-layer energy-balance model. Part I: Analytical solution and parameter calibration using CMIP5 AOGCM experiments,” J. Clim. 26, 1841–1857 (2012).ADSCrossRefGoogle Scholar
  45. 45.
    K. E. Taylor, R. J. Stouffer, and G. A. Meehl, An overview of CMIP5 and the experiment design,” Bull. Am. Meteor. Soc. 93, 485–498 (2011).CrossRefGoogle Scholar
  46. 46.
    A. V. Eliseev, I. I. Mokhov, and A. A. Karpenko, “Global warming mitigation by means of controlled aerosol emissions into stratosphere: Global and regional of temperature response as estimated in IAP RAS CM simulations,” Atmos. Ocean. Opt. 22 (4), 388–395 (2009).CrossRefGoogle Scholar
  47. 47.
    J. Hansen, A. Lacis, R. Ruedly, and M. Sato, “Potential climate impact of Mount Pinatubo eruption,” Geophys. Res. Lett. 19, 215–218 (1992).ADSCrossRefGoogle Scholar
  48. 48.
    S. A. Soldatenko and R. M. Yusupov, “Sensitivity of zero-dimension climate model and its feedback in the context of the problem of the weather and climate control,” Tr. SPIIRAN, No. 3, 5–31 (2017).Google Scholar
  49. 49.
    P. J. Rasch, S. Tilmes, R. Turco, A. Robock, L. Oman, C.-C. Chen, G. L. Stenchikov, and R. R. Garcia, “An overview of geoengineering of climate using stratospheric sulphate aerosols,” Phil. Trans. R. Soc., A 366, 4007–4037 (2008).Google Scholar
  50. 50.
    J. Hansen, M. Sato, R. Ruedy, L. Nazarenko, A. Lacis, G. A. Schmidt, G. Russell, I. Aleinov, M. Bauer, S. Bauer, N. Bell, B. Cairns, V. Canuto, M. Chandler, Y. Cheng, A. Del Genio, G. Faluvegi, E. Fleming, A. Friend, T. Hall, C. Jackman, M. Kelley, N. Kiang, D. Koch, J. Lean, J. Lerner, K. Lo, S. Menon, R. Miller, P. Minnis, T. Novakov, V. Oinas, Ja. Perlwitz, Ju. Perlwitz, D. Rind, A. Romanou, D. Shindell, P. Stone, S. Sun, N. Tausnev, D. Thresher, B. Wielicki, T. Wong, M. Yao, and S. Zhang, “Efficacy of climate forcing,” J. Geophys. Res. 110, D18104 (2005).ADSCrossRefGoogle Scholar
  51. 51.
    T. M. Lenton and N. E. Vaughan, “The radiative forcing potential of different climate geoengineering options,” Atmos. Chem. Phys. 9, 5539–5561 (2009).ADSCrossRefGoogle Scholar
  52. 52.
    L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes (Nauka, Moscow, 1969) [in Russian].zbMATHGoogle Scholar
  53. 53.
    A. E. Bryson and Y.-C. Ho, Applied Optimal Control: Optimization, Estimation, and Control (John Wiley & Sons, New York, 1975).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.St. Petersburg Institute for Informatics and Automation, Russian Academy of SciencesSt. PetersburgRussia

Personalised recommendations