Reconstruction of the mean European temperature over the past 600 - PowerPoint PPT Presentation

Reconstruction of the mean European temperature over the past 600 years using the proxy data Dmitriev E.V. Institute of Numerical Mathematics RAS

Reconstruction methods Up-scaling problem u – reconstructed large-scale parameter averaging operator =  u Az →  y – proxy data = + ν  y Sz z – small-scale field separating operator Solution of the direct problem Solution of the inverse problem = Gu + ε = Ry + η y u Observation operator G is unknown Simple multiple linear regression estimate − = ˆ 1 u C C y Step 2: Step 1: SMLR uy yy estimating u estimating G SMLR with EOF filtering of the predictor − Mann's method for the case of 1d predictand = 1 a ˆ u C C , C EOF ua aa = ~ ˆ uu = ϕ u C y i ( , ) a y ~ where and Mann u y C C i ~ ~ u y y u ϕ i ~ C y y are eigen vectors of where is the vectors normalized on its STD yy

Instrumental and proxy data Spatial interpolation of the surface Proxy data locations. temperature from stations to grid points. The employed proxy dataset ( CRU , www.cru.uea.ac.uk) is the gridded time series of tree-ring maximum-latewood- The mean temperature in June 1961. density from the "Schweingruber" network. Locations of Cressmann interpolation (R=2.5) with the 26 European grid boxes that contained at least one chronology are presented here. The time period for those exponential weighting function. data is 1400-1975. An extra low frequency (> 25 year) n ∑ variations that were originally lost when the tree-ring data i w Tst −  2 ij d were standardized is added in employing the age-band-   = = = ij j i 1 Tgr , w exp   decomposition method of processing the tree-ring data ij n 2 ∑  2 R  w ( Briffa et al. 2001 ). ij = i 1

Comparison of mean European temperature estimates Mean summer temperature Mean annual temperature Correlation coefficients: Correlation coefficients: • CRUTEM2v vs GHCN GGP: 0.93<0.95<0.97 • CRUTEM2v vs GHCN GGP: 0.80<0.85<0.90 • CRUTEM2v vs Cressmann: 0.91<0.94<0.96 • CRUTEM2v vs Cressmann: 0.76<0.83<0.88 Mean-square value of maximum difference: 0.20 Mean-square value of maximum difference: 0.29 Standard deviations: Standard deviations: • CRUTEM2v: 0.39 • CRUTEM2v: 0.44 • GHCN GGP: 0.43 • GHCN GGP: 0.44 • Cressmann: 0.39 • Cressmann: 0.39

Reconstruction of April-September European temperature Cross validation of the EOF-regression Cross validation of the Mann's method. method. Cross validation a priori estimate Cross validation a priori estimate Correlation 0.57< 0.69 < 0.78 0.68 < 0.78 < 0.85 0.60 < 0.72 < 0.79 0.63 < 0.74 < 0.81 Correlation RMSE 0.25 < 0.29 < 0.33 0.22 < 0.25 < 0.28 0.32 < 0.37 < 0.41 0.32 < 0.37 < 0.41 RMSE STD (exact) 0.34 < 0.40 < 0.45 0.34 < 0.40 < 0.45 0.35 < 0.40 < 0.45 0.34 < 0.40 < 0.45 STD (exact) 0.26 < 0.47 < 0.60 0.46 < 0.60 < 0.71 RE RE -0.25 < 0.13 < 0.42 -0.28 < 0.16 < 0.42

Reconstruction of mean annual European temperature Cross validation of the EOF-regression Cross validation of the Mann's method. method. Cross validation a priori estimate Cross validation a priori estimate 0.47 < 0.59 < 0.69 0.62 < 0.71 < 0.79 0.45 < 0.58 < 0.69 0.49 < 0.61 < 0.71 Correlation Correlation 0.29 < 0.33 < 0.37 0.25 < 0.28 < 0.31 0.45 < 0.53 < 0.60 0.45 < 0.52 < 0.59 RMSE RMSE 0.35 < 0.40 < 0.45 0.36 < 0.40 < 0.45 0.35 < 0.40 < 0.44 0.36 < 0.40 < 0.45 STD (exact) STD (exact) 0.16 < 0.33 < 0.47 0.38 < 0.50 < 0.61 -1.40 < -0.73 < -0.26 -1.42< - 0.68 < -0.19 RE RE

Fidelity tests using ECHO-G GCM based pseudo-proxy data Test with adding a spurious signal Test with removing a true signal White noise with the spurious low- frequency signal of small amplitude may be the reason of a "hockey stick" shaped reconstruction

Fidelity tests using observation-based pseudo-proxy data Cross validation of the EOF-regr. method. Cross validation of the Mann's method. Noise-level 0% Noise-level 0% Corr. 0.97 < 0.98 < 0.99 Corr. 0.98 < 0.99 < 1.00 RE 0.94 < 0.96 < 0.97 RE 0.98 < 0.99 < 1.00 Noise-level 75% Noise-level 75% Corr. 0.62 < 0.73 < 0.81 Corr. 0.48 < 0.60 < 0.69 Corr. 0.98 < 0.99 < 1.00 RE 0.06 < 0.36 < 0.56 RE 0.11 < 0.33 < 0.48 RE 0.98 < 0.99 < 1.00

Temporal changes of reconstruction accuracy (results of cross validation) A priori estimate of change of The same a priori estimate for data with reconstruction quality characteristics removed low-frequency variability Correlation Correlation Calibration period 0.44 0.47 Data filtering Reduction Reduction of error of error Calibration period 0.19 0.22

Reconstruction of mean annual European temperature from long-period meteorological observations Reconstruction European temperature back to 1776 year. Location of stations which keep observations for more Dalton Calibration period than 200 years minimum EOF-regression was used for 0.96 < 0.97 < 0.98 Correlation reconstruction. Cressmann interpolation was applied for 0.09 < 0.10 < 0.11 RMSE gaps filling in 30 stations. 10 Locations where observations available down to 1776 0.35 < 0.40 < 0.45 STD (exact) first modes used for the year are marked in blue. Starting from 1776 year there reconstration contain not less RE 0.92 < 0.94 < 0.95 are not less than 15 stations available. than 95% of variations.

Reconstruction of mean annual European temperature using GCM simulation of the past climate. Reconstruction from dendrochronologies corr. 0.71 RE 0.50 Spoerer Maunder minimum minimum Gridded time series of tree-ring maximum- latewood-density from the "Schweingruber" network (www.cru.uea.ac.uk). Age-band- decomposition method was used for processing the tree-ring data [Briffa et al. 2001]. Reconstruction from dendrochronologies & GCM simulation corr. 0.73 RE 0.53 ERIK - annual temperature simulation over 1000 years by the ECHO-G global coupled model [Zorita, Gonzalez-Rouco & Legutke, J.Clim., 2003] Forcing: • effective solar constant • atmospheric concentrations of CO2, CH4 & N2O

Conclusions The problem of reconstruction of the mean European temperature over the past 600 years is considered here. For this period we have a quantity of various proxy data and the dataset of instrumental measurements of the surface temperature at the dense network of meteorological stations for the last 150 years. Following problems must be underlined: a) difference between values of the mean European temperature obtained by diverse methods from instrumental data for the last 150 years exceeds the error of “idealized” reconstruction from instrumental data at the locations of proxy data; b) tests produced for the calibration period show that reconstruction accuracy slightly increase after removing low-frequency signal from proxy and instrumental data. Therefore low-frequency variability (>20yrs) of dendrochronologies is appreciably distorted. This can be the reason of some strong spurious extremums of reconstruction. So it is probably better to unify low-resolution proxy data using GCM and combine them with filtered high-resolution proxies.