I wanted to see how quickly the differences grew when an identical model was run on different processors. UK_Nick has uploaded some of his sulphur cycle runs files to compare against mine. I think all the sulphur cycle runs are the same (certainly some are the same as Nick's Athlon XP has calculated the same as my Athlon 64).

I saved the a csv dump of temperatures for each of the first 8 quarters in the different runs (My Athlon 64 3500+ S939 and Nick's Dual Xeon machine)

Calculating the sum of the variance in temperature squared produces:
<img src="http://cpdn.tuxie.org/crandles/rundiffvar^2.PNG">

It occured to me that this gave too much weighting to the polar areas where cells have a smaller area so I also calculated an area weighted Root Mean Square Error.

<img src="http://cpdn.tuxie.org/crandles/rundiffrmse.PNG">

I am not too suprised to see these graphs which do not appear to show much if any trend. If we want to see the departure from each other rising before reaching some steady level of differences then we are going to have to look at how the differences evolve over a period of no more than 3 months. The quarterly averages saved by the model are not frequent enough.

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To put in context what an area adjusted RMSE of 1 degree looks like. This is the 8th Quarter (autumn 1812) temperature difference map.

<img src="http://cpdn.tuxie.org/crandles/naewka.pe11c10_5_07.JPG">

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I am not at all sure about whether I got the area averaging correct. Is there any information on the correct way to do it? I think I remember Matin Sykes saying he had got details of this from one of the CP team.

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Martin Sykes seems to use the formula

float adj = (sin(theta*PI/180)-sin((theta-2.5)*PI/180))/m_pSeriesDefn-&gt;GetX()/2;

where theta = latitude
m_pSeriesDefn-&gt;GetX() = number of cells in the X direction ?

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____________________________<br>
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Thanks Mike

I think that makes reasonable sense. I presume that m_pSeriesDefn-&gt;GetX() =96 except for the the two poles when there is only 1 'cell in the x direction' being the pole itself.

I would have probably eventually got to a formula something like
(sin(theta+1.25*PI/180)-sin((theta-1.25)*PI/180))/96/2 but used something completely different for the poles. I do of course want to use the official version rather than something home brewed.

I have updated the graph below.

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&gt; Thanks Mike
&gt;
&gt; I think that makes reasonable sense. I presume that m_pSeriesDefn-&gt;GetX()
&gt; =96 except for the the two poles when there is only 1 'cell in the x
&gt; direction' being the pole itself.
&gt;
&gt; I would have probably eventually got to a formula something like
&gt; (sin(theta+1.25*PI/180)-sin((theta-1.25)*PI/180))/96/2 but used something
&gt; completely different for the poles. I do of course want to use the official
&gt; version rather than something home brewed.
&gt;
&gt; I have updated the graph below.

Cool plots. It might be interesting to see if the difference is greater or the same (or less) in phases 2 &amp; 3: in phase 1 surface things get relaxed back to climatological means, so there is less scope for discrepancies to freely evolve. In phase 2, there might be more scope for the models to prowl around on their own (of course, you could get a quasi-random(?) cold equator happening, which would mess up the calculation a bit...) Not sure exactly where Sylvia, Neil, etc are on the duplicates paper.

Dave

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Hi Dave,

Thanks for your comments. I was also thinking about phases 2 and 3 being more able to 'prowl around' as you put it. Am I right to presume this means running phase 1 on one computer then copying to another computer so that both have got the same phase 1 details?

I am also a bit hazy on what differences we are interested in. If one develops a higher temperature than the other, this is going to increase the RMSE. Are we interested in this or is an adjustment for the global temperature appropriate so that we are looking at regional difference? I suppose it is not a lot of extra work to look at both.

Now what would be nice would be a tool that could save the temperatures in each cell every 144 timesteps (or better the average for each cell over 144 timesteps) for the first couple of months of phase 2 (and 3). However those are going to vary far more than the seasonal averages, so we would also have to do that for phase 1 as well.

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William Connolley has done a much better version of this see how quickly the differences grow excercise:

<a href=\"http://mustelid.blogspot.com/2005/10/butterflies-notes-for-post.html#comments\">here</a>

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