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	<title>Comments on: Lack of Convergence, Under-Resolution, and Numerical Errors</title>
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	<link>http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/</link>
	<description>by Dan Hughes</description>
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		<title>By: John A</title>
		<link>http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/comment-page-1/#comment-140</link>
		<dc:creator>John A</dc:creator>
		<pubDate>Sat, 17 Feb 2007 20:20:05 +0000</pubDate>
		<guid isPermaLink="false">http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/#comment-140</guid>
		<description>I updated the formatting of this post to aid readability. For some reason my eyes glaze over if there are not enough paragraphs or differentiation between paragraph titles and paragraphs.

I hope you don&#039;t mind.</description>
		<content:encoded><![CDATA[<p>I updated the formatting of this post to aid readability. For some reason my eyes glaze over if there are not enough paragraphs or differentiation between paragraph titles and paragraphs.</p>
<p>I hope you don&#8217;t mind.</p>
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		<title>By: Dan Hughes</title>
		<link>http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/comment-page-1/#comment-141</link>
		<dc:creator>Dan Hughes</dc:creator>
		<pubDate>Sat, 17 Feb 2007 19:28:59 +0000</pubDate>
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		<description>fFreddy, the reports by Cloutman contain relatively simple examples that illustrate some of the problems.  Here is a short &lt;a href=&quot;http://sprott.physics.wisc.edu/chaos/eulermap.htm&quot; rel=&quot;nofollow&quot;&gt;online note&lt;/a&gt; that shows numerical chaos based on numerical integration problems. The 3-equation Lorenz system is not very complex either.

Let me know if these are what you&#039;re looking for</description>
		<content:encoded><![CDATA[<p>fFreddy, the reports by Cloutman contain relatively simple examples that illustrate some of the problems.  Here is a short <a href="http://sprott.physics.wisc.edu/chaos/eulermap.htm">online note</a> that shows numerical chaos based on numerical integration problems. The 3-equation Lorenz system is not very complex either.</p>
<p>Let me know if these are what you&#8217;re looking for</p>
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		<title>By: Margo</title>
		<link>http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/comment-page-1/#comment-139</link>
		<dc:creator>Margo</dc:creator>
		<pubDate>Fri, 16 Feb 2007 16:39:49 +0000</pubDate>
		<guid isPermaLink="false">http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/#comment-139</guid>
		<description>&lt;blockquote&gt;Several professional engineering societies

I&#039;d fudge this by inserting that the societies will no longer accept papers for publications for which Verification and convergence&lt;/blockquote&gt;

I think it&#039;s more accurate to say: societies &lt;i&gt;have published policies stating they will no longer accept will no longer accept papers for publications&lt;/i&gt;.

The sad fact is, scholarly journals use a peer review process that involves sending papers to mostly univerisity professors, who, let me assure you, do not check to find out whether tests for grid independence etc. were done.  They all agree that it should be done. Most perform these checks when doing their own computations (though I&#039;m sure many don&#039;t).  However, the peer review system is appallingly bad at *actually checking* *this particular* sort of thing and you&#039;ll almost never see any proof these checks were done appearing in a scholarly article.

I think in the bit on Numerical Solutions of PDEs, you might be able to say something rather stronger in regards to GCM&#039;s.  I suspect that  GCMs are &lt;i&gt;known&lt;/i&gt; to give different results using different grid sizes.  Since &lt;i&gt;all&lt;/i&gt; computations involve coarse grids, this could lead to systematic errors or biases if we decide to try to determine what might be &quot;real&quot; by averaging the results of a variety of codes all of which are known to use coarse grids. (Basically, if they all share the same type of flaw, the average will retain this flaw. It won&#039;t average out.)

On the semi-implicit time step: Do GCM codes use semi-implicit time steps? (My impression from reading the text of the GISS papers is they run into the courant condition, and overcome it by inserting false numerical diffusion at the poles. Maybe they use explicit time stepping? You could look at the actual code for that-- or check the wording in the papers. I don&#039;t happen to know.)


You might have to dig to find the references that tell use we &lt;i&gt;know&lt;/i&gt; the solutions are not grid independent, but I&#039;m pretty sure I&#039;ve read that somewhere.


&lt;blockquote&gt;This situation does not exempt developers and users of such models and codes from providing detailed information about the limitations of the presented results. &lt;/blockquote&gt;
Absolutely true.

&lt;blockquote&gt;The presented results are numbers, not solutions of the underlying continuous equations.&lt;/blockquote&gt;

I guess I&#039;d be a bit less severe here. I think they &lt;i&gt;may&lt;/i&gt; not be solutions.  (But then, I haven&#039;t looked at these things all that long. )</description>
		<content:encoded><![CDATA[<blockquote><p>Several professional engineering societies</p>
<p>I&#8217;d fudge this by inserting that the societies will no longer accept papers for publications for which Verification and convergence</p></blockquote>
<p>I think it&#8217;s more accurate to say: societies <i>have published policies stating they will no longer accept will no longer accept papers for publications</i>.</p>
<p>The sad fact is, scholarly journals use a peer review process that involves sending papers to mostly univerisity professors, who, let me assure you, do not check to find out whether tests for grid independence etc. were done.  They all agree that it should be done. Most perform these checks when doing their own computations (though I&#8217;m sure many don&#8217;t).  However, the peer review system is appallingly bad at *actually checking* *this particular* sort of thing and you&#8217;ll almost never see any proof these checks were done appearing in a scholarly article.</p>
<p>I think in the bit on Numerical Solutions of PDEs, you might be able to say something rather stronger in regards to GCM&#8217;s.  I suspect that  GCMs are <i>known</i> to give different results using different grid sizes.  Since <i>all</i> computations involve coarse grids, this could lead to systematic errors or biases if we decide to try to determine what might be &#8220;real&#8221; by averaging the results of a variety of codes all of which are known to use coarse grids. (Basically, if they all share the same type of flaw, the average will retain this flaw. It won&#8217;t average out.)</p>
<p>On the semi-implicit time step: Do GCM codes use semi-implicit time steps? (My impression from reading the text of the GISS papers is they run into the courant condition, and overcome it by inserting false numerical diffusion at the poles. Maybe they use explicit time stepping? You could look at the actual code for that&#8211; or check the wording in the papers. I don&#8217;t happen to know.)</p>
<p>You might have to dig to find the references that tell use we <i>know</i> the solutions are not grid independent, but I&#8217;m pretty sure I&#8217;ve read that somewhere.</p>
<blockquote><p>This situation does not exempt developers and users of such models and codes from providing detailed information about the limitations of the presented results. </p></blockquote>
<p>Absolutely true.</p>
<blockquote><p>The presented results are numbers, not solutions of the underlying continuous equations.</p></blockquote>
<p>I guess I&#8217;d be a bit less severe here. I think they <i>may</i> not be solutions.  (But then, I haven&#8217;t looked at these things all that long. )</p>
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		<title>By: fFreddy</title>
		<link>http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/comment-page-1/#comment-144</link>
		<dc:creator>fFreddy</dc:creator>
		<pubDate>Wed, 14 Feb 2007 13:42:51 +0000</pubDate>
		<guid isPermaLink="false">http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/#comment-144</guid>
		<description>Dan, this all sounds very familiar from the sort of modelling I am used to. Can you point me at a simple worked example of one of these problems, so I can try to recast it in the way I am used to dealing with things ?</description>
		<content:encoded><![CDATA[<p>Dan, this all sounds very familiar from the sort of modelling I am used to. Can you point me at a simple worked example of one of these problems, so I can try to recast it in the way I am used to dealing with things ?</p>
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		<title>By: Reid</title>
		<link>http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/comment-page-1/#comment-143</link>
		<dc:creator>Reid</dc:creator>
		<pubDate>Tue, 13 Feb 2007 19:17:25 +0000</pubDate>
		<guid isPermaLink="false">http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/#comment-143</guid>
		<description>Excellent post Dan.  What you say has been known for decades yet AOLGCM models are accepted by many respected scientists.  The willful ignorance is stunning.

Dan,
Is it possible that if you code an AOLGCM on different software development platforms or run it on different hardware processor platforms you will get divergent runs of the same model?  Same data, same algorithms, different software development and/or operating system, different hardware processors.  I would bet that the same exact AOLGCM algorithms and data would produce divergent model runs on different platforms.</description>
		<content:encoded><![CDATA[<p>Excellent post Dan.  What you say has been known for decades yet AOLGCM models are accepted by many respected scientists.  The willful ignorance is stunning.</p>
<p>Dan,<br />
Is it possible that if you code an AOLGCM on different software development platforms or run it on different hardware processor platforms you will get divergent runs of the same model?  Same data, same algorithms, different software development and/or operating system, different hardware processors.  I would bet that the same exact AOLGCM algorithms and data would produce divergent model runs on different platforms.</p>
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		<title>By: Dan Hughes</title>
		<link>http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/comment-page-1/#comment-142</link>
		<dc:creator>Dan Hughes</dc:creator>
		<pubDate>Tue, 13 Feb 2007 18:38:17 +0000</pubDate>
		<guid isPermaLink="false">http://danhughes.auditblogs.com/2007/02/13/lack-of-convergence-under-resolution-and-numerical-errors/#comment-142</guid>
		<description>I have attempted to upload a pdf file that has the reference citations given in the post along with the abstracts.  I hope it is here &lt;a href=&#039;http://danhughes.auditblogs.com/files/2007/02/underresolvepderefs.pdf&#039; title=&#039;UnderResolveRefs&#039; rel=&quot;nofollow&quot;&gt;UnderResolveRefs&lt;/a&gt;</description>
		<content:encoded><![CDATA[<p>I have attempted to upload a pdf file that has the reference citations given in the post along with the abstracts.  I hope it is here <a href='http://danhughes.auditblogs.com/files/2007/02/underresolvepderefs.pdf' title='UnderResolveRefs'>UnderResolveRefs</a></p>
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