{"id":33,"date":"2014-06-14T02:13:50","date_gmt":"2014-06-14T02:13:50","guid":{"rendered":"http:\/\/www.jamesrising.net\/blog\/?p=33"},"modified":"2014-06-14T02:15:23","modified_gmt":"2014-06-14T02:15:23","slug":"ssa-and-nino","status":"publish","type":"post","link":"http:\/\/www.jamesrising.net\/blog\/?p=33","title":{"rendered":"SSA and NINO"},"content":{"rendered":"<p><a href=\"https:\/\/www.ncdc.noaa.gov\/teleconnections\/enso\/indicators\/sst.php\">NINO 3<\/a> is a measure of El Ni\u00f1o\/La Ni\u00f1a (ENSO) intensity.  It&#8217;s often said that ENSO has a period of 3-7 years.  Why is it so hard to identify a single period?  This is a job for <a href=\"http:\/\/en.wikipedia.org\/wiki\/Singular_spectrum_analysis\">SSA<\/a>!<\/p>\n<p><a href=\"http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninoscree.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninoscree-300x300.png\" alt=\"ninoscree\" width=\"300\" height=\"300\" class=\"alignnone size-medium wp-image-34\" srcset=\"http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninoscree-300x300.png 300w, http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninoscree-150x150.png 150w, http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninoscree-1024x1024.png 1024w, http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninoscree.png 1050w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>The scree plot shows that there are a ton of significant eigenvectors&#8211; this is a very complicated signal&#8211; but I want to focus on the first four, which are a shade more significant than the rest.  They come in two pairs, which for SSA means that they represent two sinusoids.  Here are the eigenvectors.<\/p>\n<p><a href=\"http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninovects.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninovects-300x300.png\" alt=\"ninovects\" width=\"300\" height=\"300\" class=\"alignnone size-medium wp-image-35\" srcset=\"http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninovects-300x300.png 300w, http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninovects-150x150.png 150w, http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninovects-1024x1024.png 1024w, http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninovects.png 1050w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>How well do these two capture the ENSO signal?<\/p>\n<p><a href=\"http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninossar.png\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninossar-300x300.png\" alt=\"ninossar\" width=\"300\" height=\"300\" class=\"alignnone size-medium wp-image-36\" srcset=\"http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninossar-300x300.png 300w, http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninossar-150x150.png 150w, http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninossar-1024x1024.png 1024w, http:\/\/www.jamesrising.net\/blog\/wp-content\/uploads\/2014\/06\/ninossar.png 1050w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>Not great, but it gets most of the ups and downs.  Just not the peaks.<\/p>\n<p>So what are the periods of these two?  The first two are at 5.8 years, and the second two at 3.5 years.  To note: those are relatively prime, so the two frequencies are always going to be going in and out of sync.  So it&#8217;s not so much that ENSO has a clear frequency (it doesn&#8217;t), nor that that frequency is 3-7 years (because what would that mean anyway).  It has two main frequencies, like a dial tone.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NINO 3 is a measure of El Ni\u00f1o\/La Ni\u00f1a (ENSO) intensity. It&#8217;s often said that ENSO has a period of 3-7 years. Why is it so hard to identify a single period? This is a job for SSA! The scree plot shows that there are a ton of significant eigenvectors&#8211; this is a very complicated &hellip; <a href=\"http:\/\/www.jamesrising.net\/blog\/?p=33\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">SSA and NINO<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[4],"class_list":["post-33","post","type-post","status-publish","format-standard","hentry","category-research","tag-n"],"_links":{"self":[{"href":"http:\/\/www.jamesrising.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/33","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.jamesrising.net\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.jamesrising.net\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.jamesrising.net\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.jamesrising.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=33"}],"version-history":[{"count":1,"href":"http:\/\/www.jamesrising.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/33\/revisions"}],"predecessor-version":[{"id":37,"href":"http:\/\/www.jamesrising.net\/blog\/index.php?rest_route=\/wp\/v2\/posts\/33\/revisions\/37"}],"wp:attachment":[{"href":"http:\/\/www.jamesrising.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=33"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.jamesrising.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=33"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.jamesrising.net\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=33"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}