{"id":9108,"date":"2010-02-01T16:57:25","date_gmt":"2010-02-01T22:57:25","guid":{"rendered":"http:\/\/rankexploits.com\/musings\/?p=9108"},"modified":"2010-02-02T08:57:15","modified_gmt":"2010-02-02T14:57:15","slug":"hadcrut-compared-to-ipcc-simulations-ending-dec-2009","status":"publish","type":"post","link":"https:\/\/rankexploits.com\/musings\/2010\/hadcrut-compared-to-ipcc-simulations-ending-dec-2009\/","title":{"rendered":"HadCrut Compared to IPCC Simulations Ending Dec. 2009."},"content":{"rendered":"

In a previous post,<\/a> I reported trend analysis of the difference between GISSTemp observations and the model mean projection for surface temperatures from simulation from IPCC models extended into the 21st century using the A1B scenario tell us we should reject the hypothesis that the model mean simulation agrees with the observations reported by GISS. Specifically, trend analysis beginning with start dates prior to 1980 all indicate we should reject the multi-model mean trend as reproducing the observed trend. <\/p>\n

In that post, I also said I would apply the same analysis to Hadley when the December 2009 data arrived. Below, I have a figure showing mean trends for the difference between observations and the multi-model mean and uncertainty intervals based on HadCrut NH&SH<\/a> through Dec. 2009. <\/p>\n

\"\"<\/a>
\nBecause the trend is fit to the difference<\/i> between observations and the multi-model mean simulation, we expect a trend of 0C\/century if the multi-model mean simulation faithfully reproduced the mean trend. (The IPCC projections in the AR4 were based on this assumption.)<\/p>\n

Examining the figure above, we see the notion the multi-model mean of simulations for the earth’s surface trend faithfully reproduce the HadCRUT observations should be rejected<\/em> at a confidence of 95% if we elect to do the analysis with start years beginning in 1950, 1960, 1970, 1980, and 2000 or 2001. The uncertainty intervals are based on the assumption the residuals from a straight line can be described by an ARMA(1,1) noise model, and the influence of El Nino has been accounted for using the MEI index. <\/p>\n

Some readers may be curious as to whether this result differs from the similar analysis using data through Nov. 2009. Of course, they don’t differ much, but interestingly enough, the trend computed from1980 just kicked over into “rejection” territory; it was in “fail to reject” before the December anomaly was reported. (For earlier results see previous post.<\/a> Of course, this is a mostly rhetorical issue, since in both cases, the upper range of the uncertainty intervals just grazes the key “0 C\/decade” value. <\/p>\n

What if the IPCC had used different models?<\/h3>\n

The analysis above is just fine if we consider the IPCC projection to be based on the specific ensemble of models they actually used. However, when I presented a similar analysis for GISS, Nick Stokes objected that I did not consider how the results might have varied if the IPCC had used a different collection of models. <\/p>\n

Fortunately, it is very easy to extend the method to account for this. To account for this, I modified the standard error in the trend by taking the square-root of the sum of the square in the standard error in trends across all 22 models and the standard error in the difference in the mean. The latter is used to form the uncertainty intervals in the figure shown above. <\/p>\n

The standard error in trends across all 22 models was computed by finding the variance in the trends across all 22 models, subtracting an estimate of contribution of “weather” from this, and then dividing by 21, which is the number of degrees of freedom for the models and then taking the square root of the resulting value. (The contribution of “weather” was subtracted to avoid double counting as it is already contained in the difference between observations and models. I estimated by assuming the “weather noise” for models and observations are identical, obtained this value from the uncertainty in the trend based on the linear fit to the difference between the model mean and the observation.)<\/p>\n

Of course, these algebraic manipulations did widen the uncertainty intervals somewhat, particularly for start dates beginning at earlier times. The new results are shown below:<\/p>\n

\"\"<\/a><\/p>\n

As you can see, accounting for the possibility that IPCC might have used other some other set of models selected randomly from the universe of all possible models, the notion that the model mean of simulations from “IPCC-like” models faithfully reproduces HadCRUT should be rejected at a confidence of 95% if we being trend analysis in 1950, 1960, 1970, 2000 and 2001. However, we fail to reject if we begin trend analysis in 1980 or 1990.<\/p>\n

That is to say: If we are counting rejections based on analyses beginning in January of each decade, we dial back one ‘reject’ to a ‘fail to reject’. This is the rejection from 1980. However, for the most part, accounting for the variability due to the choice of individual models or runs makes only a small difference in the general assessment of whether the multi-model mean surface temperature from of some hypothetical set of models selected from a universe of all possible models would faithfully reproduce the earth’s surface temperature. <\/p>\n

Why are we getting so many rejections?<\/h3>\n

Readers always ask me what these rejections mean. The answer is: based on the choice of statistical model for the ‘weather noise’ (i.e. ARMA), the simulations probably do not faithfully predict observations of the earth’s surface temperature. This statistical analysis cannot tell us anymore than that. <\/p>\n

Reasons why the difference exists could range from a) the weather noise might not be ARMA, b) the forcings under the SRES were higher than on earth, c) some physics in the models are inadequate, d) the observations do not reflected the change in surface temperature of the earth’s surface, e) other I haven’t even thought of, f) the MEI index is nothing more than a fiddle factor that overfit the data and so causes spurious shrinkage of the uncertainty intervals. The current analysis can’t distinguish this.<\/p>\n

That said, the current analysis tells us: If the assumptions are correct, the trend in the difference between the multi-model mean and the earth’s surface temperature is statistically significant. That is, the multi-model mean is overpredicting warming and that difference appears statistically significant. <\/p>\n

Posts discussing some analytical choices<\/h3>\n
    \n
  1. Why taking the difference deals with volcanoes and other non-linearities<\/a> better than other methods.<\/li>\n
  2. How I estimate the uncertainty intervals for ARMA(1,1) noise. <\/a> <\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    In a previous post, I reported trend analysis of the difference between GISSTemp observations and the model mean projection for surface temperatures from simulation from IPCC models extended into the 21st century using the A1B scenario tell us we should reject the hypothesis that the model mean simulation agrees with the observations reported by GISS. … Continue reading HadCrut Compared to IPCC Simulations Ending Dec. 2009.<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17],"tags":[21,93],"class_list":["post-9108","post","type-post","status-publish","format-standard","hentry","category-gcms","tag-gmst","tag-hadley"],"_links":{"self":[{"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/posts\/9108","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/comments?post=9108"}],"version-history":[{"count":0,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/posts\/9108\/revisions"}],"wp:attachment":[{"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/media?parent=9108"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/categories?post=9108"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/tags?post=9108"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}