From	Michael E. Mann	Date	Thu, 31 Jul 2003 11:18:24 -0400
To	Tim Osborn
Subject	Re: reconstruction errors
Tim, Attached are the calibration residual series for experiments based on available networks back to: AD 1000 AD 1400 AD 1600 I can't find the one for the network back to 1820! But basically, you'll see that the residuals are pretty red for the first 2 cases, and then not significantly red for the 3rd case--its even a bit better for the AD 1700 and 1820 cases, but I can't seem to dig them up. In any case, the incremental changes are modest after 1600--its pretty clear that key predictors drop out before AD 1600, hence the redness of the residuals, and the notably larger uncertainties farther back... You only want to look at the first column (year) and second column (residual) of the files. I can't even remember what the other columns are! Let me know if that helps. Thanks, mike p.s. I know I probably don't need to mention this, but just to insure absolutely clarify on this, I'm providing these for your own personal use, since you're a trusted colleague. So please don't pass this along to others without checking w/ me first. This is the sort of "dirty laundry" one doesn't want to fall into the hands of those who might potentially try to distort things... At 02:58 PM 7/31/2003 +0100, you wrote: Thanks for the explanation, Mike. Now I see it, it looks familiar - so perhaps you've explained it to me previously (if you have, then sorry for asking twice!). I now understand how you compute them in theory. I have two further questions though (sorry): (1) how do you compute them in practise? Do you actually integrate the spectrum of the residuals? (2) how would I estimate an uncertainty for a particular band of time scales (e.g. decadal to secular, f=0.0 to 0.1)? If integrating the spectrum of the residuals, I wonder whether integrating from f=0 to f=0.02 and then f=0.02 to (e.g.) f=0.1 (note this last limit has changed) would give me the right error for time scales of 10 years and longer (i.e. for a 10-yr low pass filter)? The way I had planned to do this was to assume the residuals could be modelled as a first order autoregressive process, with lag-1 autocorrelation r1=0.0 after 1600 (essentially white) and r1=??? before 1600. Do you know what the lag-1 autocorrelation of the residuals is for the network that goes back to 1000 AD? The stuff back 2000 years will be interesting, though the GCM runs we're starting to look at go back only 500 (Hadley Centre) or 1000 (German groups), so MBH99 seems fine for now. Cheers Tim At 14:28 31/07/2003, you wrote: Tim, The one-sigma *total* uncertainty is determined from adding the low f and high f components of uncertainty in quadrature. The low f and high f uncertainties aren't uncertainties for a particular (e.g. 30 year or 40-year) running mean,they are band integrated estimates of uncertainties (high-frequency band from f=0 to f=0.02, low-frequency band from f=0.02 to f=0.5 cycle/year) taking into account the spectrum of the residual variance (the broadband or "white noise" mean of which is the nominal variance of the calibration residuals) Alternatively, one could calculate uncertainties for a particular timescale average using the standard deviation of the calibration residuals, and applying a square-root-N' argument (where N' is the effective degrees of freedom in the calibration residuals). I believed I did this at one point, and got similar results. Let me know if this needs further clarification. Thanks, mike p.s. you might want to try to using Mann and Jones N. Hem if you're going back further than AD 1000? Crowley has some EBM results now back to 0 AD, and is in the process of comparing w/ that. SHould be interesting... At 02:04 PM 7/31/2003 +0100, you wrote: Hi Mike, we've recently been making plans with Simon Tett at the Hadley Centre for comparing model simulations with various climate reconstructions, including the MBH98 and MBH99 Northern Hemisphere temperatures. I was stressing the importance of including uncertainty estimates in the comparison and that the error estimates should depend on the timescale (e.g. smoothing filter or running mean) that had been applied. I then looked at the file that I have been using for the uncertainties associated with MBH99 (see attachment), which I must have got from you some time ago. Column 1 is year, 2 is the "raw" standard error, 3 is 2*SE. But what are columns 4 and 5? I've been plotting column 4, labelled "1 sig (lowf)" when plotted your smoothed reconstruction, assuming that this is the error appropriate to low-pass filtered data. I'd also assumed that the last column "1 sig (highf)" was appropriate to high-pass filtered data. I also noticed that the sum of the squared high and low errors equalled the square of the raw error, which is nice. But I've realised that I don't understand how you estimate these errors, nor what time scale the lowf and highf cutoff uses (maybe 40-year smoothed as in the IPCC plots?). From MBH99 it sounds like post-1600 you assume uncorrelated gaussian calibration residuals. In which case you would expect the errors for a 40-year mean to be reduced by sqrt(40). This doesn't seem to match the values in the attached file. Pre-1600 you take into account that the residuals are autocorrelated (red noise rather than white), so presumably the reduction is less than sqrt(40), but some factor (how do you compute this?). The reason for my questions is that I would like to (1) check whether I've been doing the right thing in using column 4 of the attached file with your smoothed reconstruction, and (2) I'd like to estimate the errors for a range of time scales, so I can compare decadal means, 30-year means, 50-year means etc. Thanks in advance for any help you can give me here. Tim Dr Timothy J Osborn Climatic Research Unit School of Environmental Sciences, University of East Anglia Norwich NR4 7TJ, UK e-mail: t.osborn@uea.ac.uk phone: +44 1603 592089 fax: +44 1603 507784 web: [1]http://www.cru.uea.ac.uk/~timo/ sunclock: [2]http://www.cru.uea.ac.uk/~timo/sunclock.htm ______________________________________________________________ Professor Michael E. Mann Department of Environmental Sciences, Clark Hall University of Virginia Charlottesville, VA 22903 _______________________________________________________________________ e-mail: mann@virginia.edu Phone: (434) 924-7770 FAX: (434) 982-2137 [3]http://www.evsc.virginia.edu/faculty/people/mann.shtml Dr Timothy J Osborn Climatic Research Unit School of Environmental Sciences, University of East Anglia Norwich NR4 7TJ, UK e-mail: t.osborn@uea.ac.uk phone: +44 1603 592089 fax: +44 1603 507784 web: [4]http://www.cru.uea.ac.uk/~timo/ sunclock: [5]http://www.cru.uea.ac.uk/~timo/sunclock.htm ______________________________________________________________ Professor Michael E. Mann Department of Environmental Sciences, Clark Hall University of Virginia Charlottesville, VA 22903 _______________________________________________________________________ e-mail: mann@virginia.edu Phone: (434) 924-7770 FAX: (434) 982-2137 [6]http://www.evsc.virginia.edu/faculty/people/mann.shtml Attachment Converted: "c:\documents and settings\tim osborn\my documents\eudora\attach\nh-ad1000-resid.dat" Attachment Converted: "c:\documents and settings\tim osborn\my documents\eudora\attach\nh-ad1400-resid.dat" Attachment Converted: "c:\documents and settings\tim osborn\my documents\eudora\attach\nh-ad1600-resid.dat" References 1. http://www.cru.uea.ac.uk/~timo/ 2. http://www.cru.uea.ac.uk/~timo/sunclock.htm 3. http://www.evsc.virginia.edu/faculty/people/mann.shtml 4. http://www.cru.uea.ac.uk/~timo/ 5. http://www.cru.uea.ac.uk/~timo/sunclock.htm 6. http://www.evsc.virginia.edu/faculty/people/mann.shtml