Skip to main content

Advertisement

Log in

On the invalidity of the ordinary least squares estimate of the equilibrium climate sensitivity

  • Original Paper
  • Published:
Theoretical and Applied Climatology Aims and scope Submit manuscript

Abstract

The equilibrium climate sensitivity is often estimated by the ordinary least squares applied to annual data of observed/calculated temperature and forcing series. One of the conditions under which the ordinary least squares estimator is consistent is the uncorrelatedness of the regressor and regression error. However, this condition can fail in a regression using historical data of temperature and forcing. Alternative estimators established in econometrics are shown to mitigate the impact of the correlated regressor and regression error and deliver a more reliable estimate of the equilibrium climate sensitivity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

Availability of data and material

The data used in this study are available from the author upon reasonable request.

Notes

  1. See a review article by Forster (2016) for more of related studies.

  2. Some early contributions statistically analyzing the existence of an increasing trend in GMST include (Bloomfield 1992; Fomby and Vogelsang 2002) among others. Since GMST in a steady state would not exhibit secular variations, the existence of an increasing trend implies that the climate system is in transition to a new steady state.

  3. If \({u_{t}^{y}}\) is not stationary due to its own stochastic trend, yt and xt cannot be linearly related, violating the energy balance equation.

  4. Only one slope change is considered since the sample starts at 1960.

  5. Climate at a Glance: Global Time Series, published April 2019, retrieved on May 13, 2019, from https://www.ncdc.noaa.gov/cag/

  6. Hansen et al. (2010). Dataset accessed 2019-5-13 at https://data.giss.nasa.gov/gistemp/

  7. Morice et al. (2012). Dataset accessed 2019-5-13 at https://www.metoffice.gov.uk/hadobs/hadcrut4

  8. Miller et al. (2014). Dataset accessed 2019-5-13 at https://data.giss.nasa.gov/modelforce/

  9. TRF series smoothed by exponentially decaying weights and TRF without stratospheric aerosols are also analyzed. The results remain qualitatively the same and thus are not reported.

  10. World pentadal time series for 0\(\sim \)2000 m from the NOAA National Centers for Environmental information at https://www.nodc.noaa.gov/OC5/3M_HEAT_CONTENT/

  11. The reported confidence intervals are obtained by applying the delta method to the asymptotic distribution of each estimator.

  12. See Table 1 in Forster (2016).

References

  • Andrews T, Gregory JM, Paynter D, Silvers LG, Zhou C, Mauritsen T, Webb MJ, Armour KC, Forster PM, Titchner H (2018) Accounting for changing temperature patterns increases historical estimates of climate sensitivity. Geophys Res Lett 45(16):8490–8499

    Article  Google Scholar 

  • Armour KC (2017) Energy budget constraints on climate sensitivity in light of inconstant climate feedbacks. Nat Clim Chang 7:331–335

    Article  Google Scholar 

  • Bengtsson L, Schwartz SE (2013) Determination of a lower bound on earth’s climate sensitivity. Tellus B Chem Phys Meteorol 65(1):21533

    Article  Google Scholar 

  • Bloomfield P (1992) Trends in global temperatures. Clim Chang 21:275–287

    Article  Google Scholar 

  • Estrada F, Gay C, Sánchez A (2010) A reply to “does temperature contain a stochastic trend? evaluating conflicting statistical results” by r. k. kaufmann et al. Clim Chang 101(3/4):407–414

    Article  Google Scholar 

  • Estrada F, Perron P (2014) Detection and attribution of climate change through econometric methods. Bol Soc Mat Mex 20(1):107–136

    Article  Google Scholar 

  • Estrada F, Perron P, Martinez-Lopez B (2013) Statistically derived contributions of diverse human influences to twentieth-century temperature changes. Nat Geosci 6:1050–1055

    Article  Google Scholar 

  • Fomby TB, Vogelsang TJ (2002) The application of size-robust trend statistics to global-warming temperature series. J Climate 15(1):117–123

    Article  Google Scholar 

  • Forster PM (2016) Inference of climate sensitivity from analysis of earth’s energy budget. Annu Rev Earth Planet Sci 44:85–106

    Article  Google Scholar 

  • Forster PM, Gregory JM (2006) The climate sensitivity and its components diagnosed from earth radiation budget data. J Climate 19:39–52

    Article  Google Scholar 

  • Gregory JM, Forster PM (2008) Transient climate response estimate from radiative forcing and observed temperature change. J Geophys Res 113:D23105

    Article  Google Scholar 

  • Hansen J, Ruedy R, Sato M, Lo K (2010) Global surface temperature change. Rev Geophys 48:RG4004

    Article  Google Scholar 

  • Kaufmann RK, Kauppi H, Mann ML, Stock JH (2013) Does temperature contain a stochastic trend: linking statistical results to physical mechanisms. Clim Chang 118(3/4):729–743

    Article  Google Scholar 

  • Kaufmann RK, Kauppi H, Stock JH (2010) Does temperature contain a stochastic trend? Evaluating conflicting statistical results. Clim Chang 101(3/4):395–405

    Article  Google Scholar 

  • Kaufmann RK, Stern DI (2002) Cointegration analysis of hemispheric temperature relations. J Geophys Res 107(D2):ACL 8–1–ACL 8–10

    Google Scholar 

  • Knutti R, Rugenstein MAA (2015) Feedbacks, climate sensitivity and the limits of linear models. Philos Trans R Soc A Math Phys Eng Sci 373(2054)

  • Marvel K., Schmidt GA, Miller RL, Nazarenko L. S (2016) Implications for climate sensitivity from the response to individual forcings. Nat Clim Chang 6:386–389

    Article  Google Scholar 

  • Miller RL, Schmidt GA, Nazarenko LS, Tausnev N, Bauer SE, Genio ADD, Kelley M, Lo KK, Ruedy R, Shindell DT, Aleinov I, Bauer M, Bleck R, Canuto V, Chen YH, Cheng Y, Clune TL, Faluvegi G, Hansen JE, Healy RJ, Kiang NY, Koch D, Lacis AA, LeGrande AN, Lerner J, Menon S, Oinas V, García-Pando CP, Perlwitz JP, Puma MJ, Rind D, Romanou A, Russell GL, Sato M, Sun S, Tsigaridis K, Unger N, Voulgarakis A, Yao MS, Zhang J (2014) Cmip5 historical simulations (1850-2012) with giss modele2. J Adv Model Earth Syst 6(2):441–477

    Article  Google Scholar 

  • Morice CP, Kennedy JJ, Rayner NA, Jones PD (2012) Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: the hadcrut4 dataset. J Geophys Res 117:D08101

    Google Scholar 

  • Park JY (1992) Canonical cointegrating regressions. Econometrica 60:119–143

    Article  Google Scholar 

  • Pretis F (2020) Econometric modelling of climate systems: the equivalence of energy balance models and cointegrated vector autoregressions. J Econ 214:256–273

    Article  Google Scholar 

  • Richardson M, Cowtan K, Hawkins E, Stolpe MB (2016) Reconciled climate response estimates from climate models and the energy budget of earth. Nat Clim Chang 6:931–935

    Article  Google Scholar 

  • Saikkonen P (1991) Asymptotically efficient estimation of cointegration regressions. Econ Theory 7:1–21

    Article  Google Scholar 

  • Schwartz SE (2007) Heat capacity, time constant, and sensitivity of earth’s climate system. J Geophys Res 112:D24S05

    Google Scholar 

  • Schwartz SE (2012) Determination of earth’s transient and equilibrium climate sensitivities from observations over the twentieth century: strong dependence on assumed forcing. Surv Geophys 33:745–777

    Article  Google Scholar 

  • Spencer RW, Braswell WD (2008) Potential biases in feedback diagnosis from observational data: a simple model demonstration. J Climat 21:5624–5628

    Article  Google Scholar 

Download references

Acknowledgements

An earlier draft of this paper was presented at the EGU 2019 in Vienna, Austria. Special thanks go to the conference participants who kindly provided the author with valuable comments. Two anonymous referees and the editors gave insightful comments, which helped improve the paper.

Funding

This research is supported by the Korea University Grant (K1911951).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dukpa Kim.

Ethics declarations

Conflict of interest

The author declares no competing interests.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, D. On the invalidity of the ordinary least squares estimate of the equilibrium climate sensitivity. Theor Appl Climatol 146, 21–27 (2021). https://doi.org/10.1007/s00704-021-03719-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00704-021-03719-5

Navigation