Vol. 32, issue 04, article # 9

Soldatenko S.A., Yusupov R.M. Model for estimating the transient response of the global mean surface temperature to changes in the concentrations of atmospheric aerosols and radiatively-active gases. // Optika Atmosfery i Okeana. 2019. V. 32. No. 04. P. 309–316 [in Russian].
Copy the reference to clipboard

A two-component energy-balance climate model (EBM) is considered, which allows estimating the transient response of the global mean surface temperature (i.e. the Earth climate system response) to radiative forcing due to atmospheric aerosols and radiatively-active gases in accordance with the specified scenarios of their atmospheric content. An expression for the impulse response function of EBM is analytically derived. The response of the climate system to arbitrary external radiative forcing is calculated as a convolution of two functions – an impulse response function and a function describing the radiative forcing. The comparative analysis of the results of numerical calculations performed for two idealized scenarios of radiative forcing (step-function and linearly increasing radiative perturbation) and the exact solution obtained analytically demonstrates a fairly high accuracy of the method. Using the impulse response function, the response of the global mean surface temperature was estimated to radiation forcing given in accordance with several scenarios of an increase in the concentrations of atmospheric greenhouse gases (four scenarios of the RCP family) and volcanic aerosol (eruption of the Pinatubo volcano in 1991). Since the method for estimating the transient climate response to radiative forcing, considered in this work, is quite accurate and computationally inexpensive, it can be used as an express analysis tool for estimating the climate system response to arbitrary radiation perturbation caused by natural and anthropogenic aerosols as well as radiatively-active gases including greenhouse gases.


climate change, global warming, impulse response function, transient climate response, stratospheric aerosols


   1.  Kabanov M.V., Zuev V.E. Optika atmosfernogo aerozolya. L.: Gidrometeoizdat, 1987. 256 p.
   2. Ginzburg A.S., Gubanova D.P., Minashkin V.M. Vliyanie estestvennyh i antropogennyh aerozolej na global'nyj i regional'nyj klimat // Ros. him. zhurn. 2008. V. LII, N 5. P. 112–119.
   3. Ivlev L.S. Aerozoli i global'nye izmeneniya klimata // Region. ekol. 2011. N 3–4(32). PС. 83–93.
   4. Myhre G., Myhre C.E.L., Samset B.H., Storelvmo T. Aerosols and their relation to global climate and climate sensitivity // Nature Education Knowledge. 2013. V. 4(5), N 7. URL: https://www.nature.com/scitable/ knowledge / library / aerosols-and-their-relation-to-global-climate-102215345 (last access: 19.12.2018).
   5. Boucher O. Atmospheric aerosols: Properties and climate impacts. Dordrecht: Springer-Verlag, 2015. 311 p.
   6. Smith S.J., Bond T.C. Two hundred fifty years of aerosols and climate: The end of the age of aerosols // Atmos. Chem. Phys. 2014. V. 14, N 2. P. 537–549.
   7. Perevedentsev Yu.P. Teoriya klimata. Kazan': Kazan. gos. un-t, 2009. 504 p.
   8. Loginov V.F. Radiatsionnye faktory i dokazatel'naya baza sovremennyh izmenenij klimata. Minsk: Belorusskaya Nauka, 2012. 266 p.
   9. Dymnikov V.P., Lykosov V.N., Volodin E.M. Modelirovanie klimata i ego izmenenij // Vestn. RAN. 2012. V. 82, N 3. P. 227–236.
10. Ritchie H., Roser M. CO2 and other Greenhouse Gas Emissions [Electronic resource]. URL: https://ourworldindata.org / co2-and-other-greenhouse-gas-emissions (last access: 29.12.2018).
11. Isaksen I.S.A., Granier C., Myhre G., Berntsen T.K., Dalsoren S.B., Gauss M., Klimont Z., Benestad R., Bousquet P., Collins W., Cox T., Eyring V., Fowler D., Fuzzi S., Jockel P., Laj P., Lohmann U., Maione M., Monks P., Prevot A.S.H., Raes F., Richter A., Rognerud B., Schulz M., Shindell D., Stevenson D., Storelvmo T., Wang W.C., van Weele M., Wild M., Wuebbles D. Atmospheric composition change: Climate-chemistry interactions // Atmos. Environ. 2009. V. 43, N 33. P. 5138–5192.
12. IPCC 2013: Climate Change 2013: The Physical Science Basis. Contribution of working group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change / T.F. Stocker, D. Qin, G.-K. Plattner, M. Tignot, S.K. Allen, J. Boschung, A. Nauels A. Xia, V. Bex, P.M. Midgley (eds.). Cambridge, New York: Cambridge University Press, 2013. 1535 p.
13. Yoshimori M., Watanabe M., Shiogama H., Oka A., Abe-Ouchi, Ohgaito R., Kamae Y. A review of progress towards understanding the transient global mean surface temperature response to radiative perturbation // Progress in Earth and Planetary Science. 2016. V. 3(21). 14 p.
14. Pincus R., Forster P.M., Stevens B. The radiative forcing model intercomparison project (RFMIP): Experimental protocol for CMIP6 // Geosci. Model Dev. 2016. V. 9. P. 3447–3460.
15. Risbey J.S., Grose M.R., Monselesan D.P., O'Kane T.J., Lewandowsky S. Transient response of the global mean warming rate and its spatial variation // Weather and Climate Extremes. 2017. V. 18. P. 55–64.
16. Taylor K.E., Crucifix M., Braconnot P., Hewitt C.D., Doutriaux C., Broccoli A.J., Mitchell J.F.B., Webb M.J. Estimating shortwave radiative forcing and response in climate models // J. Clim. 2007. V. 30. P. 2530–2543.
17. Gritsun A.S., Branstator G., Dymnikov V.P. Construction of the linear response operator of an atmospheric general circulation model to small external forcing // Russ. J. Numer. Anal. Math. Model. 2002. V. 17. P. 399–416.
18. Westervelt D.M., Horowitz L.W., Naik V., Go­­laz J.-C., Mauzerall D.L. Radiative forcing and climate response to projected 21st century aerosol decreases // Atmos. Chem. Phys. 2015. V. 15. P. 12681–12703.
19. Cheridan R., Quaas J., Salzmann M., Tomassini L. Black carbon indirect radiative effects in a climate model // Tellus B. 2017. V. 69, iss. 1. P. 1369342.
20. MacMartin D.G., Ricke K.L., Keith D.W. Solar geoengineering as part of an overall strategy for meeting the 1.5 °C Paris target // Phil. Trans. Roy. Soc. A. 2018. V. 376. 20160454.
21. Irvine P.J., Kravitz B., Lawrence M.G., Muri H. An overview of the Earth system science of solar geoengineering // WIREs Clim. Change. 2016. V. 7. P. 815–833.
22. Izrael Yu.A., Volodin E.M., Kostrykin S.V., Revokatova A.P., Ryaboshapko A.G. The ability of stratospheric climate engineering in stabilizing global mean temperatures and an assessment of possible side effects // Atmos. Sci. Lett. 2014. V. 15. P. 140–148.
23. Kravitz B., Robock A., Tilmes S., Boucher O., English J. M., Irvine P.J., Jones A., Lawrence M.G., MacCracken M., Muri H., Moore J.C., Niemeier U., Phipps S.J., Sillmann J., Storelvmo T., Wang H., Watanabe S. The Geoengineering Model Intercomparison Project Phase 6 (GeoMIP6): Simulation design and preliminary results // Geosci. Model Dev. 2015. V. 8. P. 2279–2292.
24. Soldatenko S.A., Yusupov R.M. Optimal'noe upravlenie protsessom primeneniya iskusstvennyh sul'fatnyh aerozolej dlya smyagcheniya global'nogo potepleniya // Optika atmosf. i okeana. 2018. V. 31, N 10. P. 821–828; Soldatenko S.A., Yusupov R.M. Optimal control of artificial sulfate aerosols usage to mitigate global warming // Atmos. Ocean. Opt. 2019. V. 32, N 1. P. 55–63.
25. Soldatenko S.A., Yusupov R.M. Optimal'noe upravlenie aerozol'nymi emissiyami v stratosferu dlya stabilizatsii klimata Zemli // Izv. RAN. Fiz. atmosf. i okeana. 2018. V. 54, N 5. P. 566–574.
26. Kondrat'ev K.Ya. Aerozol' i klimat: sovremennoe sostoyanie i perspektivy razrabotok. 3. Aerozol'noe radiatsionnoe vozmushchayushchee vozdejstvie // Optika atmosf. i okeana. 2006. V. 19, N 7. P. 565–575.
27. Volodin E.M. Predstavlenie potokov tepla, vlagi i impul'sa v klimaticheskoj modeli. Radiatsionnye potoki // Fundam. i prikl. klimatol. 2017. V. 3. P. 5–15.
28. Zhang Z., Moore J.C. Mathematical and physical fundamentals of climate change. Boston: Elsevier, 2014. 494 p.
29. Stensrud D.J. Parameterization Schemes: Keys to understanding numerical weather prediction models. Cambridge: Cambridge University Press, 2007. 459 p.
30. Budyko M.I. Izmeneniya klimata. L.: Gidrometeoizdat, 1974. 280 p.
31. North G.R., Kim K.-Y. Energy balance climate model. Weinheim: Wiley-VCH, 2017. 369 p.
32. Konovalov G.F. Radioavtomatika. M.: Vyssh. shk., 1990. 335 p.
33. Rypdal K. Global warming projections derived from an observation-based minimal model // Earth System Dynamics. 2016. V. 7. P. 51–70.
34. Gregory J.M. Vertical heat transport in the ocean and their effect on time-dependent climate change // Clim. Dyn. 2000. V. 16. P. 501–515.
35. Held I.M., Winton M., Takahashi K., Delworth T., Zeng F., Vallis G.K. Probing the fast and slow components of global warming by returning abruptly to preindustrial forcing // J. Clim. 2010. V. 23. P. 2418–2427.
36. Trenberth K.E. Climate system modelling. Cambridge: Cambridge University Press, 1992. 788 p.
37. Geoffroy O., Saint-Martin D., Olivié D.J.L., Voldoire A., Bellon G., Tytéca S. Transient climate response in a two-layer energy-balance model. Part I: Analytical solution and parameter calibration using CMIP5 AOGCM experiments // J. Clim. 2012. V. 26. P. 1841–1857.
38. Taylor K.E., Stouffer R.J., Meehl G.A. An overview of CMIP5 and the experiment design // Bull. Am. Meteor. Soc. 2011. V. 93. P. 485–498.
39. Meinshausen M., Smith S.J., Calvin K., Daniel J. S., Kainuma M.L.T., Lamarque J.-F., Matsumoto K., Montzka S.A., Raper S.C.B., Riahi K., Thomson A., Velders G.J.M., van Vuuren D.P.P. The RCP greenhouse gas concentrations and their extensions from 1765 to 2300 // Clim. Change. 2011. V. 109. P. 213–241.
40. Riahi K., Gruebler A., Nakicenovic N. Scenarios of long-term socio-economic and environmental development under climate stabilization // Technol. Forecast. Soc. Change. 2007. V. 74, N 7. P. 887–935.
41. Schneider L., Smerdon J.E., Pretis F., Hartl-Meier C., Esper J. A new archive of large volcanic events over the past millennium derived from reconstructed summer temperatures // Environ. Res. Lett. 2017. V. 12. P. 094005.
42. Arfeuille F., Weinsenstein D., Mack H., Rozanov E., Peter T., Brönnimann S. Volcanic forcing for climate modelling: A new microphysics-based data set covering years 1600-present // Clim. Past. 2014. V. 10. P. 359–375.
43. Kinne S., O’Donnel D., Stier P., Kloster S., Zhang K., Schmidt H., Rast S., Giorgetta M., Eck T.F., Stevens B. MAC-v1: A new global aerosol climatology for climate studies // J. Adv. Model. Earth Syst. 2013. V. 5. P. 704–740.
44. Ivlev L.S., Dovgalyuk Yu.A. Fizika atmosfernyh aerozol'nyh sistem. SPb.: NIIH SPbGU, 1999. 194 p.
45. Myhre G., Highwood E.J., Shine K.P., Stordal F. New estimates of radiative forcing due to well mixed greenhouse gases // Geophys. Res. Lett. 1998. V. 25. P. 2715–2718.
46. Myhre G.D., Shindell F.-M., Bréon W., Collins W., Fuglestvedt L., Huang J., Lamarque J.-F., Lee D., Mendoza B., Nakajima T., Robock A., Stephens G., Takemura T., Zhang H. Anthropogenic and natural radiative forcing // Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge, United Kingdom, New York: Cambridge University Press, 2013. P. 659–740.
47. Hansen J., Sato M., Ruedy R., Nazarenko L., Lacis A., Schmidt G.A., Russell G., Aleinov I., Bauer M., Bauer S., Bell N., Cairns B., Canuto V., Chandler M., Cheng Y., Del Genio A., Faluvegi G., Fleming E., Friend A., Hall T., Jackman C., Kelley M., Kiang N., Koch D., Lean J., Lerner J., Lo K., Menon S., Miller R., Minnis P., Novakov T., Oinas V., Perlwitz Ja., Perlwitz Ju., Rind D., Romanou A., Shindell D., Stone P., Sun S., Tausnev N., Thresher D., Wielicki B., Wong T., Yao M., Zhang S. Efficacy of climate forcing // J. Geophys. Res. 2005. V. 110. D18104. 45 p.
48. Sato M., Hansen J.E., McCormick M.P., Pollack J.B. Stratospheric aerosol optical depth, 1850–1990 // J. Geophys. Res. 1993. V. 98. P. 22987–22994.
49. Summary for Policymakers // Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge, United Kingdom, New York: Cambridge University Press, 2013. 28 p.
50. Ward P. Sulfur dioxide initiates global climate change in four ways // Thin Solid Films. 2009. V. 517. P. 3188–3203.
51. Parker D.E., Wilson H., Jones P.D., Christy J.R., Folland C.K. The impact of Mount Pinatubo on world-wide temperatures // Int. J. Climatol. 1996. V. 16. P. 487–497.
52. Grieser J., Schönwiese C.-D. Parameterization of spatio-temporal patterns of volcanic aerosol induced stratospheric optical depth and its climate radiative forcing // Atmosfera. 1999. V. 12. P. 111–133.