Calibration should be done locally, but not sure how to combine the resulting non-normally distributed outputs to a global average. Median tree -approach (once you’ve seen one tree…) might actually work well. ]]>

Which means the reconstruction can’t be used to rule out the null hypothesis that there’s been no temperature rise in the past 2k years.

Correct. Statements such as in Mann08,

Our results extend previous conclusions that recent Northern Hemisphere surface temperature increases are likely anomalous in a long-term context.

are based on unrealistic CIs. M&M reply made it clear.

]]>Looks to me like if you draw a line through 0 (and lots of other values) well over 95% of the values are within the 95% envelope. Which means the reconstruction can’t be used to rule out the null hypothesis that there’s been no temperature rise in the past 2k years.

]]>Nice picture.

I think it’s ok, given the quality of scientifically published reconstructions.

**Pros:**

Proxy screening was done locally, by using published method, without restrictive AR(1)-noise assumption.

Calibration result and CIs are obtained using Brown82 equations.

**Cons:**

Local proxy vs. global temperature calibration

No dynamic model for temperature applied

Some proxies used might have some problems ( search CA )

]]>I’ll check how many of Mann08 proxies survive this test..

It seems that only

1070 tornetrask

1061 tiljander_2003_darksum

survive this test in the early steps. At AD1400 step there following proxies get through:

271 ca630

272 ca631

287 cana106

314 cana175

362 co556

397 fisher_1996_cgreenland

424 gisp2o18

628 mo037

654 mt110

778 nm560

796 norw010

820 nv516

908 schweingruber_mxdabd_grid1

909 schweingruber_mxdabd_grid10

910 schweingruber_mxdabd_grid100

920 schweingruber_mxdabd_grid11

927 schweingruber_mxdabd_grid12

933 schweingruber_mxdabd_grid18

934 schweingruber_mxdabd_grid19

935 schweingruber_mxdabd_grid2

936 schweingruber_mxdabd_grid20

937 schweingruber_mxdabd_grid21

938 schweingruber_mxdabd_grid22

959 schweingruber_mxdabd_grid42

960 schweingruber_mxdabd_grid44

961 schweingruber_mxdabd_grid45

977 schweingruber_mxdabd_grid6

988 schweingruber_mxdabd_grid70

1002 schweingruber_mxdabd_grid89

1070 tornetrask

1061 tiljander_2003_darksum

1104 ut509

1122 vinther_2004_scgreenland

427 haase_2003_srca

330 chuine_2004_burgundyharvest

Leave Tiljander out, calibrate with iHAD_NH_reform: http://signals.auditblogs.com/files/2009/04/cce.png ..

]]>But before going to sea level business, here’s the interesting thing:

This method is published in high-quality journal, and used by sea level experts. Why wouldn’t Mann use it for testing significant correlations in proxy vs. temperature series? Because it gives critical r values that are in the range of 0.2 – 0.3 ? I’ll check how many of Mann08 proxies survive this test..

]]>http://sealevel.colorado.edu/MG_Leuliette2004.pdf

wherein it is said that

This from of bootstrapping is robust when the residuals are serially correlated, as is the case for mean sea level (Ebisuzaki 1997)

The paper cited is:

Wesley Ebisuzaki: A Method to Estimate the Statistical Significance of a Correlation When the Data Are Serially Correlated, Journal of Climate, Volume 10, Issue 9 (September 1997)

and I even found the Matlab code :

http://www.ldeo.columbia.edu/~kja/access/code/ebisuzaki.m

Then I tried the code with data in #94

and got the result

Creating synthetic time series…

Performing Monte Carlo significance test

—

Observed correlation coefficent: 0.20057

Fraction of |coefficients| larger than Observed: 0.117 [Threshold Value:0.05]Critical R Value: 0.24506

Critical R is quite close to the value I computed in #119 , where I knew how the process was made. Not bad!

Possibly related posts:

http://www.climateaudit.org/?p=5341

http://wattsupwiththat.com/2009/04/06/sea-level-graphs-from-uc-and-some-perspectives/

http://www.climateaudit.org/?p=3720

Did you invent the sqrtm(MI) method, or has this been around? If it’s new you should definitely publish it somewhere other than on CA!

I did invent it. Then I mentioned the method to one math professor, who said it’s trivial. That happens all the timeðŸ˜‰ Yet, I have something to publish from CA work, and that won’t go to climate science journal.

My home computer has an old version 4 of Matlab, on which sqrtm(MI) is very slow, not to mention inaccurate, for n = 512. Version 5+ works much faster and accurately, so the computational practicality of your sqrtm(MI) method is a relatively recent thing.

I wrote more efficient, recursive way, to compute that matrix. Will clean it up and email.

]]>