Solar-Terrestrial Influences Laboratory, BAS, Department Stara Zagora, Stara Zagora, Bulgaria

1. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method R. Werner 1, D. Valev 1, D. Danov 2, M. Goranova 3 • Solar-Terrestrial Influences Laboratory, BAS, Department Stara • Zagora, StaraZagora, Bulgaria • 2. Solar-Terrestrial Influences Laboratory, BAS, Sofia, Bulgaria3. Technical University Sofia, Faculty of Computer Systems and Control, • Sofia,Bulgaria

2. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 The main goal of the presentation: 1.To explain of the Cochrane-Orcutt method to errror auto-correlation removing 2. To demonstrate how is working this method 3. Application of the method to climate data However it is not the main goal to explain the global warming in detail

3. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 Radiative forcing (RF) is a concept used for quantitative comparisons of the strength of different human and natural agents in causing climate change. For balanced incoming solar radiance FS and outgoing terrestrial radiation energy FT If the climate system perturbed by a change Δof initial fluxes then the difference is the radiative forcing. Assumed the system is re-balanced by a change of the surface temperature TS, then , Where is the climate sensitive factor. Following: Atmospheric Chemistry and Global Change, ed.G.P. Brasseur et al., 1999 3

4. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 We are know, that the climate is changing by different drivers, as greenhouse gases, aerosols and so on. The radiation forcing therefore has several components (not taking in account climate feedbacks) R.E. Benestad and G.A. Schmidt, Solar trends and global warming, JGR., VOL. 114, D14101, 2009 When we using observed values for ΔTSand for the climate drivers, then this equation can be interpreted as a lin. regression equation and for expl.: where and are the аctual and the initial CO2 mixing ratios However, ΔTS and the climate drivers depends of the time! ais determed by the Earth‘s geometric factor ¼ and the surface albedo α≈ 0.3 4

5. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 Estim. slope ß : 0.003684 °C/year Std. err.: 0.00033 t=11.2 ε: error term 5

6. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 The error term can be modeled by an AR(1) process The error term in the classical lin. Regressions for cross-section data have to be non-correlated (and have to be N(0,σ) distributed)! 6

7. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 Cochrane-Orcutt method to overcome the error term auto-correlation: What we have to do? • Determination of regr. coef. α and ß by ord. least sqare • Determination of ρ by help of the autocorrelation function Substit.: • Transform y x and α in to y*, x* and α* • Regression of y* on x*, estimation of α*and βand the standard errors • Test the residuals • for autocorrelation  autocorrelation function, DW-test, • if u autocorrelated  3 7 Cochrane, Orcutt, J. Americ. Statistical Ass., 44, 1949, pp. 32-61

8. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 Durbin-Watson-test: d=2.05, du(134,1)=1,73 d>du no autocorrelation stationary 8

9. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 Estim. slope ß : 0.00368 °C/year Std. err.: 0.00033 t=11.2 Estim. slope ß : 0.00395 °C/year Std. err.: 0.00077 t=5.1 β=0.395±0.15°C/100 years 9

10. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 The following data sets are used for multiple regression analysis: Temperature: Combined land and sea surface global annual temperature anomalies – Hadcrut3 (wrt. the mean of 1961-1990) from the Met Office (UK) http://hadobs.metoffice.com/hadcrut3/diagnostics/global/nh+sh/annualupdate 2009 CO2:http://www.climateaudit.info/data/hansen/giss_ghg.2007.dat Solar irradiance: total solar irradiance reconstruction, Lean 2000 (with background) ftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/solar_variability/lean2000_irradiance.txt Southern Oscillation indices (SOI), differences of the mean sea level pressure anomalies at Tahitiand Darwin http://www.cgd.ucar.edu/cas/SOIcatalog/climind/SOI.signal.ascii Aerosol data http://data.giss.nasa.gov/modelforce/strataer/tau_line.txt Sato, M., et al., 1993.,J.G.R. 98, 22987-22994. 10

11. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 11

12. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 Lin. function! We decomposed: then:

13. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 Regression coeff. for the non-detrended series regre. coeff. t std. err. sign level: 0.05 Tcrit(0.975,130)=1.98 sign. level: 0.10 Tcrit(0.95,130)=1.66 Regression coeff. for the detrended series the coeff are sign. if: ltl >tcrit 12

14. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method ? Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 ? stationary, no auto-correlation 13

15. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 CO2: ΔT= + 0.6 °C SOI: ΔT= ± 0.1 °C Tau: ΔT= - 0.15 °C TSI: ΔT= + 0.1 ± 0.05°C 14

16. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 CO2: ΔT= ± 0.35 °C SOI: ΔT= ± 0.1 °C Tau: ΔT= - 0.15 °C TSI: ΔT= ± 0.07°C 15

17. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 16

18. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 17

19. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 Benestad and Schmidt, JGR, vol. 114, D14101, 2009 18

20. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010 Conclusions: • Тhe application of the Cochrane –Orcutt method allows easily to remove autocorrelations in the error terms of statistical climate models. • The climate impact of the total solar irradiation is at the limit of statistical significance and is at the order of only 0.1K for the period from 1866 up to 2000. • The climate sensitivity of CO2 determinated by the model with not detrended and detrended time series are different. This differences can be generated by significant climate factors not included in the model, by nonlinearities or by feedback mechanisms. • The local minimum at 1910 and the local maximum at 1940 are not well described by statistical climate models.

21. Long and short time variability of the global temperature anomalies – Application of the Cochrane-Orcutt method Acknowledgement I would like to acknowledge the support of this work by the Ministry of Education, Science and Youth under the DVU01/0120 Contract Second Workshop "Solar influences on the ionosphere and magnetosphere", Sozopol, Bulgaria, 7-11 June, 2010