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

Reconstruction of the mean European temperature

• ver the past 600 years

using the proxy data

Dmitriev E.V. Institute of Numerical Mathematics RAS

Simple multiple linear regression estimate

Up-scaling problem

Reconstruction methods

z y u Sz y Az u →    + = = ν

averaging operator

– reconstructed large-scale parameter – proxy data – small-scale field

ε + = Gu y

separating operator

Solution of the direct problem Solution of the inverse problem

Observation operator G is unknown

η + = Ry u y C C u

yy uy SMLR 1

ˆ

−

= , ˆ

1a

C C u

aa ua EOF −

= ) , ( y a

i i

ϕ =

i

ϕ

yy

C

SMLR with EOF filtering of the predictor where and are eigen vectors of

y C C C C u

y u u y y u uu Mann

~ ˆ

~ ~ ~

=

Mann's method for the case of 1d predictand

y ~ y

where is the vectors normalized on its STD Step 1: estimating G Step 2: estimating u

Spatial interpolation of the surface temperature from stations to grid points.

The mean temperature in June 1961. Cressmann interpolation (R=2.5) with the exponential weighting function.

       − = =

∑ ∑

= = 2 2 1 1

2 exp , R d w w Tst w Tgr

ij ij n i ij n i i ij j

Instrumental and proxy data

Proxy data locations.

The employed proxy dataset (CRU, www.cru.uea.ac.uk) is the gridded time series of tree-ring maximum-latewood- density from the "Schweingruber" network. Locations of 26 European grid boxes that contained at least one chronology are presented here. The time period for those data is 1400-1975. An extra low frequency (> 25 year) variations that were originally lost when the tree-ring data were standardized is added in employing the age-band- decomposition method of processing the tree-ring data (Briffa et al. 2001).

Mean annual temperature

Correlation coefficients:

• CRUTEM2v vs GHCN GGP: 0.80<0.85<0.90
• CRUTEM2v vs Cressmann: 0.76<0.83<0.88

Mean-square value of maximum difference: 0.29 Standard deviations:

• CRUTEM2v: 0.44
• GHCN GGP: 0.44
• Cressmann: 0.39

Mean summer temperature

Correlation coefficients:

• CRUTEM2v vs GHCN GGP: 0.93<0.95<0.97
• CRUTEM2v vs Cressmann: 0.91<0.94<0.96

Mean-square value of maximum difference: 0.20 Standard deviations:

• CRUTEM2v: 0.39
• GHCN GGP: 0.43
• Cressmann: 0.39

Comparison of mean European temperature estimates

Cross validation of the EOF-regression method.

0.46 < 0.60 < 0.71 0.26 < 0.47 < 0.60

RE

0.34 < 0.40 < 0.45 0.34 < 0.40 < 0.45

STD (exact)

0.22 < 0.25 < 0.28 0.25 < 0.29 < 0.33

RMSE

0.68 < 0.78 < 0.85 0.57< 0.69 < 0.78

Correlation a priori estimate Cross validation

Cross validation of the Mann's method.

• 0.28 < 0.16 < 0.42
• 0.25 < 0.13 < 0.42

RE

0.34 < 0.40 < 0.45 0.35 < 0.40 < 0.45

STD (exact)

0.32 < 0.37 < 0.41 0.32 < 0.37 < 0.41

RMSE

0.63 < 0.74 < 0.81 0.60 < 0.72 < 0.79

Correlation a priori estimate Cross validation

Reconstruction of April-September European temperature

Cross validation of the EOF-regression method.

0.38 < 0.50 < 0.61 0.16 < 0.33 < 0.47

RE

0.36 < 0.40 < 0.45 0.35 < 0.40 < 0.45

STD (exact)

0.25 < 0.28 < 0.31 0.29 < 0.33 < 0.37

RMSE

0.62 < 0.71 < 0.79 0.47 < 0.59 < 0.69

Correlation a priori estimate Cross validation

Cross validation of the Mann's method.

• 1.42< -0.68 < -0.19
• 1.40 < -0.73 < -0.26

RE

0.36 < 0.40 < 0.45 0.35 < 0.40 < 0.44

STD (exact)

0.45 < 0.52 < 0.59 0.45 < 0.53 < 0.60

RMSE

0.49 < 0.61 < 0.71 0.45 < 0.58 < 0.69

Correlation a priori estimate Cross validation

Reconstruction of mean annual European temperature

Fidelity tests using ECHO-G GCM based pseudo-proxy data

White noise with the spurious low- frequency signal of small amplitude may be the reason of a "hockey stick" shaped reconstruction

Test with adding a spurious signal Test with removing a true signal

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 75% Noise-level 75%

0.06 < 0.36 < 0.56 RE 0.62 < 0.73 < 0.81 Corr. 0.94 < 0.96 < 0.97 RE 0.97 < 0.98 < 0.99 Corr. 0.98 < 0.99 < 1.00 RE 0.98 < 0.99 < 1.00 Corr. 0.98 < 0.99 < 1.00 RE 0.98 < 0.99 < 1.00 Corr. 0.11 < 0.33 < 0.48 RE 0.48 < 0.60 < 0.69 Corr.

Noise-level 0%

Temporal changes of reconstruction accuracy

(results of cross validation) A priori estimate of change of reconstruction quality characteristics

Correlation Reduction

• f error

The same a priori estimate for data with removed low-frequency variability

Correlation Reduction

• f error

Calibration period Calibration period

0.44 0.19 0.47 0.22

Data filtering

Reconstruction of mean annual European temperature from long-period meteorological observations

0.92 < 0.94 < 0.95

RE

0.35 < 0.40 < 0.45

STD (exact)

0.09 < 0.10 < 0.11

RMSE

0.96 < 0.97 < 0.98

Correlation

Location of stations which keep observations for more than 200 years

Locations where observations available down to 1776 year are marked in blue. Starting from 1776 year there are not less than 15 stations available.

EOF-regression was used for reconstruction. Cressmann interpolation was applied for gaps filling in 30 stations. 10 first modes used for the reconstration contain not less than 95% of variations.

Calibration period

Reconstruction European temperature back to 1776 year.

Dalton minimum

Reconstruction of mean annual European temperature using GCM simulation of the past climate.

Reconstruction from dendrochronologies

Maunder minimum Spoerer minimum

Reconstruction from dendrochronologies & GCM simulation

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

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].

• corr. 0.73

RE 0.53

• corr. 0.71

RE 0.50

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.