{"id":21441,"date":"2012-12-30T14:33:54","date_gmt":"2012-12-30T20:33:54","guid":{"rendered":"http:\/\/rankexploits.com\/musings\/?p=21441"},"modified":"2013-01-03T09:07:32","modified_gmt":"2013-01-03T15:07:32","slug":"comment-on-surface-air-temperature-trends-in-the-eurasian-arctic-region","status":"publish","type":"post","link":"https:\/\/rankexploits.com\/musings\/2012\/comment-on-surface-air-temperature-trends-in-the-eurasian-arctic-region\/","title":{"rendered":"Comment on “… surface air temperature trends in the Eurasian Arctic region”"},"content":{"rendered":"

Rasmus<\/a> posted a brief comment on On the statistical significance of surface air temperature trends in the Eurasian Arctic region<\/a>, by C. Franzke, suggesting the analysis in the paper suffers from confusing ‘signal’ with ‘noise’. If I understand Rasmus correctly, he is suggesting that Franze’s autocorrelations for “noise” in the time series are computed based on the time series either without detrending or with improper detrending. Either mistake can result estimates for the autocorrelation of noise that show long term persistence when none exists. I discussed this in un-naturally trendy<\/a>. <\/p>\n

After reading Rasmus’s post — and posting two comments– I read Franzke’s paper. Having read Rasmus’s post, I expected to discover that <\/p>\n

[Franzke] examined the autocorrelation functions (ACF) of fitted noise models with the autocorrelation of the temperature records, and found that the ACF for phase scrambling was the same as for the original data. This similarity is expected, however, due to the fact that the phase scrambling preserves the spectral power. <\/p><\/blockquote>\n

Update Jan 3: Rasmus’s description appears to be entirely accurate. Franzke did not detrend in anyway.<\/b> <\/p>\n

However, it seems to me that this is not precisely<\/em> what Franzke did. The paper itself states<\/p>\n

\n14] Thus, for the significance tests, I will focus on the cubic regression trends<\/em>. The magnitude of a trend is defined as the range between the minimum and maximum value of the trend line which in most cases corresponds to the start and end of the time series. This is a robust definition because it is a very smooth function and variability on interannual and decadal time scales has thus been removed. The cubic regression is very similar to the EEMD trend and EEMD has been shown to be able to extract climate variability on interannual and decadal time scales [Wu et al., 2007; Franzke, 2009; Franzke and Woollings, 2011] and meaningful trends. Furthermore, defining the magnitude of the trend as the range between the start and end point gives similar results.<\/p>\n

[15] After identifying the trends I have to assess their statistical significance. This has been done by examining how often they are outside the trend ranges of the ensembles of surrogate time series generated by the three null models representing the background climate variability of the respective stations. To create ensembles of surrogate time series I use a first order autoregressive model (AR(1) [Franzke, 2010, 2012]) as a SRD model, and an autoregressive fractionally integrated moving average model (ARFIMA(0,d,0)) [Robinson, 2003; Franzke, 2010, 2012] as a LRD model, were d denotes the LRD parameter.<\/em> As a non-parametric way of computing surrogate data with exactly the same autocorrelation function I use the phase scrambling method by Theiler et al. [1992]. This method computes the power spectrum of a time series and then randomises the phase spectrum. Because the power spectrum is the Fourier transform of the autocorrelation function (Wiener-Khinchin theorem) randomising the phase spectrum does not affect the autocorrelation function (see Figure 1).<\/p><\/blockquote>\n

I think this means that separated the signal and noise and found the autocorrelation functions (acf) for his estimate of the noise. That noise would have been the detrended<\/I> time series. Moreover, his estimate of the signal was a cubic. This means that he will have attributed some (and I would guess most) of the non-linearity in the true deterministic signal to “signal”– thereby keeping it out of his estimate of the noise.<\/p>\n

While it is true that any<\/I> deviation of his estimate of the signal from the “true” signal could affect his estimate of the acf, it seems to me Franzke took quite a bit of care to remove this signal from the noise.<\/p>\n

If so, Rasmus’s criticism which hypothetically<\/I> could be valid– appears to be off the mark. Rasmus’s criticism would be valid if Franzke’s acf is computed from time series data that (a)are not detrended at all or (b) are detrended using a straight line (when we anticipate warming is non-linear) and it might<\/i> be valie if (c) detrending with a cubic is insufficient. But it seems Franzke’s him(her?)self has not confused signal for noise and. Moreover, detrending with a cubic — as I think s\/he did appears sufficient to prevent– or at least reduce– the degree to which non-linearities in the deterministic signal would likely inflate estimate of power in the low frequency components of the noise. <\/p>\n

I admit I’m not entirely certain of whether Franzke detrended. If s\/he did not then Rasmus’s criticism is valid. I’ve emailed Franzke asking for clarification and if possible the processing code to see whether I have misinterpreted what s\/he might have done. But the text<\/I> suggests efforts to separate the signal from noise. <\/p>\n","protected":false},"excerpt":{"rendered":"

Rasmus posted a brief comment on On the statistical significance of surface air temperature trends in the Eurasian Arctic region, by C. Franzke, suggesting the analysis in the paper suffers from confusing ‘signal’ with ‘noise’. If I understand Rasmus correctly, he is suggesting that Franze’s autocorrelations for “noise” in the time series are computed based … Continue reading Comment on “… surface air temperature trends in the Eurasian Arctic region”<\/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":[15],"tags":[],"class_list":["post-21441","post","type-post","status-publish","format-standard","hentry","category-data-comparisons"],"_links":{"self":[{"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/posts\/21441","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=21441"}],"version-history":[{"count":0,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/posts\/21441\/revisions"}],"wp:attachment":[{"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/media?parent=21441"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/categories?post=21441"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rankexploits.com\/musings\/wp-json\/wp\/v2\/tags?post=21441"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}