{"id":6693,"date":"2018-08-15T15:50:05","date_gmt":"2018-08-15T19:50:05","guid":{"rendered":"http:\/\/www.decisionsciencenews.com\/?p=6693"},"modified":"2018-08-24T09:32:59","modified_gmt":"2018-08-24T13:32:59","slug":"its-not-the-heat-its-the-heat-index","status":"publish","type":"post","link":"https:\/\/www.decisionsciencenews.com\/?p=6693","title":{"rendered":"It&#8217;s not the heat, it&#8217;s the heat index"},"content":{"rendered":"<p>PERCEIVED TEMPERATURE<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/hi16.png\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" width=\"1800\" height=\"1200\" class=\"aligncenter size-full wp-image-6701\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/shi16.png\" alt=\"\" \/><br \/>\n<\/a><br \/>\nClick to enlarge<\/p>\n<p>(We got a request for a Celsius version of this post and since we are a full service website we created one and <a href=\"http:\/\/www.decisionsciencenews.com\/2018\/07\/11\/its-not-the-heat-its-the-heat-index-celsius-edition\/\">put it here<\/a>).<\/p>\n<p>So, we were wondering, what&#8217;s this heat index we hear about? We went to the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Heat_index\">Wikipedia article on it<\/a>. It is an index that combines air temperature and relative humidity to convert a (hot) temperature into something like perceived temperature, how hot it feels. It formalizes the adage &#8220;it&#8217;s not the heat, it&#8217;s the humidity.&#8221;<\/p>\n<p>The equation to get heat index from temperature and relative humidity is big:<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/eq1.png\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" width=\"968\" height=\"338\" class=\"aligncenter size-full wp-image-6695\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/seq1.png\" alt=\"\" \/><br \/>\n<\/a><br \/>\nClick to enlarge<\/p>\n<p>This heat index chart is also complicated, but it allows one to look up the heat index rather easily.<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/heat_index_chart.png\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" width=\"1386\" height=\"1111\" class=\"aligncenter size-full wp-image-6697\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/sheat_index_chart.png\" alt=\"\" \/><br \/>\n<\/a><br \/>\nClick to enlarge<\/p>\n<p>We wanted a better way to see what the heat index is doing. So we made this plot:<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/hi16.png\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" width=\"1800\" height=\"1200\" class=\"aligncenter size-full wp-image-6701\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/shi16.png\" alt=\"\" \/><br \/>\n<\/a><br \/>\nClick to enlarge<\/p>\n<p>When it&#8217;s 90 degrees outside with 90% relative humidity, it feels 30 degrees hotter. That&#8217;s a lot of degrees.<\/p>\n<p>It turns out there is another heat index formula. This one&#8217;s even more complicated.<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/eq2.png\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" width=\"1288\" height=\"279\" class=\"aligncenter size-full wp-image-6696\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/seq2.png\" alt=\"\" \/><br \/>\n<\/a><br \/>\nClick to enlarge<\/p>\n<p>We wanted to see how it compared to the first, so we plotted both together:<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/hi8hi16.png\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" width=\"1800\" height=\"1200\" class=\"aligncenter size-full wp-image-6700\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/shi8hi16.png\" alt=\"\" \/><br \/>\n<\/a><br \/>\nClick to enlarge<\/p>\n<p>We like averaging, so we plotted the average of the two outputs:<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/blendhi8hi16.png\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6708\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/sblendhi8hi16.png\" alt=\"\" width=\"485\" height=\"323\" \/><br \/>\n<\/a><br \/>\nClick to enlarge<\/p>\n<p>We thought it looks not so far from linear so we fit a regression model to the average and plotted that:<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/linblendhi8hi16.png\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" width=\"1800\" height=\"1200\" class=\"aligncenter size-full wp-image-6702\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/slinblendhi8hi16.png\" alt=\"\" \/><br \/>\n<\/a><br \/>\nClick to enlarge<\/p>\n<p>Then we couldn&#8217;t resist coming up with a simple heuristic (shown in dots):<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/heurlinblendhi8hi16.png\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" width=\"1800\" height=\"1200\" class=\"aligncenter size-full wp-image-6699\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/sheurlinblendhi8hi16.png\" alt=\"\" \/><br \/>\n<\/a><br \/>\nClick to enlarge<\/p>\n<p>The heuristic comes pretty close to the regression model. <\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/heurlin.png\"><br \/>\n<img loading=\"lazy\" decoding=\"async\" width=\"1800\" height=\"1200\" class=\"aligncenter size-full wp-image-6698\" src=\"http:\/\/www.decisionsciencenews.com\/wp-content\/uploads\/2018\/08\/sheurlin.png\" alt=\"\" \/><br \/>\n<\/a><br \/>\nClick to enlarge<\/p>\n<p>The error (mean absolute deviation) of the heuristic to the average model is about 3 degrees. The error of the regression model to the average model is about 2 degrees, so it&#8217;s not bad, considering that the two different heat index formulae can differ by over 5 degrees.<\/p>\n<p>So what&#8217;s the heuristic?<\/p>\n<ul>\n<li>Relative Humidity of 50%: Add 10 degrees for every 10 degrees above 80<\/li>\n<li>Relative Humidity of 70%: Add 20 degrees for every 10 degrees above 80<\/li>\n<li>Relative Humidity of 90%: Add 30 degrees for every 10 degrees above 80 + 5<\/li>\n<\/ul>\n<p>It&#8217;s quite a bit simpler than the 9 and 16 term equations above and should be good enough for everyday use.<\/p>\n<p>R CODE<br \/>\nFor those who want it<br \/>\n<script src=\"https:\/\/gist.github.com\/dggoldst\/58c0ad3d962b871cd5dad19e87bca222.js\"><\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>PERCEIVED TEMPERATURE Click to enlarge (We got a request for a Celsius version of this post and since we are a full service website we created one and put it here). So, we were wondering, what&#8217;s this heat index we hear about? We went to the Wikipedia article on it. It is an index that [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[4,16,74],"tags":[1208],"class_list":["post-6693","post","type-post","status-publish","format-standard","hentry","category-encyclopedia","category-ideas","category-r","tag-r"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4LKj-1JX","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/6693","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6693"}],"version-history":[{"count":20,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/6693\/revisions"}],"predecessor-version":[{"id":6751,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/6693\/revisions\/6751"}],"wp:attachment":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6693"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6693"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6693"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}