From	Michael E. Mann	Date	Fri, 05 Sep 2003 13:51:08 -0400
To	Phil Jones
CC	Keith Briffa
Subject	Re: Something for the weekend !
sorry, meant "is just the minimum slope" constraint, in first sentence... apologies for the multiple emails, mike At 01:47 PM 9/5/2003 -0400, Michael E. Mann wrote: Actually, I think Dave's suggestion "reflecting the data across the endpoints" is really just the "minimum norm" constraint, which insures zero slope near the boundary. In other words, he's probably only talking about reflecting about the time axis. I assert that a preferable alternative, when there is a trend in the series extending through the boundary is to reflect both about the time axis and the amplitude axis (where the reflection is with respect to the y value of the final data point). This insures a point of inflection to the smooth at the boundary, and is essentially what the method I'm employing does (I simply reflect the trend but not the variability about the trend--they are almost the same)... mike At 01:34 PM 9/5/2003 -0400, Michael E. Mann wrote: sorry phil, one more relevant item. I've cc'd in Keith on this, since you had mentioned that you had discussed the issue w/ him. This is from Dave Meko's (quite nice!) statistics lecture notes: [1]http://www.ltrr.arizona.edu/~dmeko/notes_8.pdf See page 2, section 8.1. He provides two (in reality, as I mentioned before, there are really 3!) basic boundary constraints on a smooth (ie, in "filtering"). The first method he refers to is what I called the "minimum norm" constraint (assuming the long-term mean beyond the boundary). The second, which he calls "reflecting the data across the endpoints", is the constraint I have been employing which, again, is mathematically equivalent to insuring a point of inflection at the boundary. This is the preferable constraint for non-stationary mean processes, and we are, I assert, on very solid ground (preferable ground in fact) in employing this boundary constraint for series with trends... mike At 05:20 PM 9/5/2003 +0100, Phil Jones wrote: Mike, Attached some more plots. 1. Figure 7 - Forcing. Guess this is it. Could cut the y scale to -6 and say in caption that 1258 or 1259 is the only event to go beyond this, then give value in caption. Scale will then widen out. OK to do ? Caspar's solar now there. 2. Fig 2a - first go at coverage. This is % coverage over 1856-2002 from HadCRUT2v. 3. Fig 4 again. Moved legends and reduced scale. Talked to Keith and we both think that the linear trend padding will get criticised. Did you use this in GRL and or Fig 5 for RoG with Scott. If so we need to explain it. On this plot all the series are in different units, so normalised over 1751-1950 (or equiv for decades) then smoothed. Again here I can reduce scale further and Law Dome can go out of the plot. Thoughts ? Think all should be same scale. Have got GKSS model runs for Fig 8. Were you happy Hans' conditions. If so I'll send onto Scott. Next week I only have Fig 2b to do. This will be annual plot of NH, Europe and CET, smoothed in some way. For the SOI I and Tim reckon that it won't work showing this at interannual timescale with 3 plots. It will then not be like the NAO plot. Thoughts on colours as well. Have a good weekend. Logging off once this has gone. Cheers Phil Prof. Phil Jones Climatic Research Unit Telephone +44 (0) 1603 592090 School of Environmental Sciences Fax +44 (0) 1603 507784 University of East Anglia Norwich Email p.jones@uea.ac.uk NR4 7TJ UK ---------------------------------------------------------------------------- ______________________________________________________________ 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 [2]http://www.evsc.virginia.edu/faculty/people/mann.shtml ______________________________________________________________ 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 ______________________________________________________________ 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 [4]http://www.evsc.virginia.edu/faculty/people/mann.shtml References 1. http://www.ltrr.arizona.edu/~dmeko/notes_8.pdf 2. http://www.evsc.virginia.edu/faculty/people/mann.shtml 3. http://www.evsc.virginia.edu/faculty/people/mann.shtml 4. http://www.evsc.virginia.edu/faculty/people/mann.shtml