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Statistical separation of natural and anthropogenic signals in observed surface air temperature time series T. Staeger, J. Grieser and C.-D. Schönwiese Meteorological Environmental Research / Climatology Institute for Meteorology and Geophysics J.W. Goethe-University, Frankfurt /M., Germany

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Global mean temperature 1856 – 2003 after P.D. Jones et al. Which parts of the variations in observed temperature are assignable to natural and anthropogenic forcings? Are anthropogenic signals distuingishable from noise?

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Approach: Causes for the structures in the time series under consideration are being postulated. A pool of potential regressor time series is collected out of the forcings / processes considered. A selection routine is applied to obtain a multiple linear regression model. Stepwise Regression The effects are seen to be linear and additive.

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Forcings / processes considered: - Greenhouse gases(GHG) - El Niño - Southern Oscillation(SOI) - Explosive volcanism(VUL) - Solar forcings(SOL) - North atlantic oscillation(NAO) - Tropospheric sulphate aerosol(SUL)

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GHG forcing: logarithmic CO 2 equivalent concentration

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EOF-transformierte Säulendichten Sulfate forcing: The first 3 PCs of 8 zonal means of emission rates:

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Variations of the Solar constant after Lean:

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Explosive volcanism: first three PCs out of 16 zonal means of volcanic radiative forcing after Grieser:

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Southern-Oscillation-Index annual mean 1876 – 2001 (CRU)

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NAO index after P.D. Jones:

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reservoir R pot forward selection: MLR with R i and R pot for each single R pot is the most significant reg. coeff. above threshold? backward elimination: MLR with all R i except R j for each single R j is the less significant reg. coeff. above threshold? end - model: no model: yes R d back to reservoir Stepwise Regression: deselection of R d no

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Signal separation:

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Significance test of the regression coefficients: t-test: :degrees of freedom r i.,part :partial correlation coefficient of R i j: lenght of time series n:number of regressors

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global mean temperature 1878 – 2000, annual mean after P.D. Jones

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GHG global mean temperature 1878 – 2000, annual mean after P.D. Jones

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GHG + SOL global mean temperature 1878 – 2000, annual mean after P.D. Jones

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GHG + SOL + SOI global mean temperature 1878 – 2000, annual mean after P.D. Jones

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GHG + SOL + SOI + VUL explained variance: 78.9% global mean temperature 1878 – 2000, annual mean after P.D. Jones

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explained variance of the complete model and and for single forcings on the global mean temperatur

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Significance of signals: A signal has to be distuingished sufficiently from noise: Given a Gaussian distributed noise term, the significance of a signal to noise ratio can be computed.

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significance of the greenhouse signal: For Gaussian distributed residuals: A signal has to be distuingished sufficiently from noise:

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What is noise? Case 1:noise represents chance: To obtain the component representing chance, the residual is separated into a structured and unstructered component. The question to be answered here: Is the greenhouse signal distuingishable from chance?

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What is noise? Case 2:noise comprises of natural variability and unexplained variance The question to be ansewered here: Is the greenhouse signal distuingishable from variability of non- anthropogenic origin?

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Case 1:noise represents chance

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Case 2:noise = natural variability + unexplained

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Existing area means, temperature annual means Data fields: Spatial distinction leads to area means which are not independent, because they all describe a part of the same field of meteorological data.

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Transformation of the data field into principal components, which contain structures of the whole field: EOF-Transformation EOF:spacial components PC:time dependent components :Eigen value Empirical Orthogonal Functions:

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data field EOF-Transformation PC Stepwise Regression backtransformation signal fields, residual field Treatment of data fields:

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Eigen spectrum:

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First PC and EOF of the global temperature field 1878 – 2000: 1. PC; e.V.: 40.7%Variance spectrum of the 1. PC 1. EOF

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GHG signal field for the year 2000 relative to 1901 in [K]:

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GHG signal field, seasonal means for 2000 relative to 1901 in [K]: NH winterNH spring NH summerNH autum

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Solar signal field for 2000 relative to 1906 (first sunspot maximum analyzed) in [K]:

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NAO signal field winter 1993 relative to mean values in [K]:

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Sulfate signal in the global temperature field : For 1970 relative to 1901 For 2000 relative to 1901

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Explained variance of the full model and of single forcings for the global temperature data field

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Significance of the GHG signal for 2000 relative to 1901 in percentages: Case 1:noise represents chance Case 2:noise = natural variability + unexplained

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Significance of the GHG signal for 2000 relative to 1878 in percentages: Case 1:noise represents chance Case 2:noise = natural variability + unexplained

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1. PC; e.V.: 53,1%Varianzspektrum der 1. PC 1. EOF First PC and EOF of the european temperature field 1878 – 2000:

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GHG signal field Europe for 2000 relative to 1878 in [K]:

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Significance of the european GHG signal for 2000 relative to 1878 in percentages: Case 1:noise represents chance Case 2:noise = natural variability + unexplained

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Explained variance of the full model and of single forcings for the european temperature data field

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NAO in the european temperature field: NAO signal field in winter 1925 relative to mean values in [K] Significance of the NAO signal in Winter 1925 in pecentages Case 2:complete residual and natural variability as noise (without NAO)

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Signficance of the GHG signal in the german mean temperature : Case 1:noise represents chance

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Signficance of the GHG signal in the german mean temperature : Case 1: noise = natural variability + unexplained

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Explained variance of the full model and of single forcings for the german mean temperature

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SLP Europe 1896 – 1995: GHG signal field annual mean 1995 relative to 1896 in [hPa] Significance of the GHG signal annual mean 1995 in percentages Case 1:unstructured residual component as noise

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NAO in the european SLP field: NAO signal field winter 1989 relative to mean values in [hPa] Significance of the GHG signal annual mean 1995 in percentages Case 1:unstructured residual component as noise

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Explained variance of the full model and of single forcings for the european SLP field

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Precipitation Europe 1900 – 1998: GHG signal field annual totals 1998 relative to 1900 in [mm] Significance of the GHG signal annual totals 1998 Case 1:unstructured residual component as noise

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NAO in the european precipitation field: NAO signal field winter 1989 relative to mean values in [mm] Significance of the NAO signal winter 1989 Case 1:unstructured residual component as noise

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Explained variance of the full model and of single forcings for the european precipitation field

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Comparism of explained variances for the full models and for single forcings for different temperature data sets :

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Time moving analysis:

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Conclusions: Explained variance is highest in global and hemispheric mean temperatures (ca. 70% - 80%) and is reduced in data sets with high spacial resolution. On the global scale, GHG forcing is most important and significant. On the european scale NAO is dominant – GHG forcing is not significant. Time moving analysis shows a growing meaning of GHG forcing compared to natural forcings, especially since around 1985 on the global scale.

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