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<p class="MsoNormal">Hi Lyndz and Dennis,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">The text book “Statistical Methods in the Atmospheric Sciences” by Daniel Wilks talks about the upper and lower bounds that Dennis described (I checked 2<sup>nd</sup> edition, chapter 10 Time Series).<o:p></o:p></p>
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<p class="MsoNormal"><a href="https://www.elsevier.com/books/statistical-methods-in-the-atmospheric-sciences/wilks/978-0-12-815823-4?countrycode=US&format=print&utm_source=google_ads&utm_medium=paid_search&utm_campaign=usashoppinglr&gclid=CjwKCAjw4qCKBhAVEiwAkTYsPEtJFMKRw9uQOjJlQKPg7DtFOcKElxtvpbph_-pqlHHDGw3XjcMzNRoCwlAQAvD_BwE&gclsrc=aw.ds">https://www.elsevier.com/books/statistical-methods-in-the-atmospheric-sciences/wilks/978-0-12-815823-4?countrycode=US&format=print&utm_source=google_ads&utm_medium=paid_search&utm_campaign=usashoppinglr&gclid=CjwKCAjw4qCKBhAVEiwAkTYsPEtJFMKRw9uQOjJlQKPg7DtFOcKElxtvpbph_-pqlHHDGw3XjcMzNRoCwlAQAvD_BwE&gclsrc=aw.ds</a><o:p></o:p></p>
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<p class="MsoNormal">Koichi<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><b><span style="font-size:12.0pt;color:black">From: </span></b><span style="font-size:12.0pt;color:black">ncl-talk <ncl-talk-bounces@mailman.ucar.edu> on behalf of Dennis Shea via ncl-talk <ncl-talk@mailman.ucar.edu><br>
<b>Reply-To: </b>Dennis Shea <shea@ucar.edu><br>
<b>Date: </b>Monday, September 20, 2021 at 2:59 PM<br>
<b>To: </b>Lyndz <olagueralyndonmark429@gmail.com><br>
<b>Cc: </b>Ncl-talk <ncl-talk@ucar.edu><br>
<b>Subject: </b>Re: [ncl-talk] Question on specx_ci confidence limits<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<span style="font-family:"Arial",sans-serif;color:black">Check twice before you click! This email originated from outside PNNL.</span><span style="font-family:"Arial",sans-serif"><o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">There is no official reference. It was something from an applied math class .
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">It requires the degrees of freedom and uses the inverse chi-distribution to get the upper and lower bounds.
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<p class="MsoNormal">I am not sure where in the statistical literature this is described.
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">Sorry<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">On Mon, Sep 20, 2021 at 11:59 AM Lyndz via ncl-talk <<a href="mailto:ncl-talk@mailman.ucar.edu">ncl-talk@mailman.ucar.edu</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal">Dear NCL-experts,<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">I would like to know the reference used for estimating the lower and upper bounds of the red noise spectrum. These are computed using the specx_ci function:<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><a href="https://gcc02.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.ncl.ucar.edu%2FDocument%2FFunctions%2FShea_util%2Fspecx_ci.shtml&data=04%7C01%7CKoichi.Sakaguchi%40pnnl.gov%7C4255eea64ab54a42c8c808d97c81ea0e%7Cd6faa5f90ae240338c0130048a38deeb%7C0%7C0%7C637677719705586712%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=VUpLdjoXk26dadFQ8ZAqXnExJ9fdnZX0%2BNGq93sEIuQ%3D&reserved=0" target="_blank">https://www.ncl.ucar.edu/Document/Functions/Shea_util/specx_ci.shtml</a><o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">According to the description, the lag-1 autocorrelation was used to estimate these lines.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">I'll appreciate any help on this.<o:p></o:p></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">-Lyndz<o:p></o:p></p>
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