{"id":109500,"date":"2009-12-17T12:18:23","date_gmt":"2009-12-17T17:18:23","guid":{"rendered":"http:\/\/blog.metasd.com\/?p=686"},"modified":"2009-12-17T12:18:23","modified_gmt":"2009-12-17T17:18:23","slug":"cumulative-emissions-right-and-wrong","status":"publish","type":"post","link":"https:\/\/mereja.media\/index\/109500","title":{"rendered":"Cumulative emissions, right and wrong"},"content":{"rendered":"<p>During C-ROADS development, we explored several ways of accounting for cumulative per capita emissions. One practice that seems to be widespread is to accumulate (integrate) emissions divided by population, i.e.<\/p>\n<table border=\"0\">\n<tbody>\n<tr>\n<td>cumulative emissions per cap<\/td>\n<td>= INTEGRAL( emissions per capita(t) )<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>= INTEGRAL( emissions(t)\/population(t) )<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>This is physically meaningless. Emissions per capita is an <a href=\"http:\/\/en.wikipedia.org\/wiki\/Intensive_and_extensive_properties\">intensive variable<\/a>, and you can&#8217;t average or accumulate intensive variables in this way. It&#8217;s like averaging the temperature of a duck and a supertanker without accounting for the tankers 100,000x greater mass.<\/p>\n<p>A proper thing to do is integrate emissions, then divide by population:<\/p>\n<table border=\"0\">\n<tbody>\n<tr>\n<td>cumulative emissions per cap<\/td>\n<td>= INTEGRAL( emissions per capita(t) ) \/ population<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>That yields a physically meaningful number, interpreted as cumulative emissions of a nation per current inhabitant. That&#8217;s a bit like per capita national debt.<\/p>\n<p><span id=\"more-686\"><\/span>A big question is what population to use as a basis. If you use current population, that&#8217;s fine, but it&#8217;s important to recognize that a comparison of per caps in 2100 between countries with slow and rapid population growth in effect gives credit for creating more people &#8211; possibly not a desirable incentive. Here are cumulative per capita emissions for developed and developing countries on a current basis, along a hypothetical 2C path with stricter commitments for developed countries:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-696\" title=\"CumPerCapCurrent\" src=\"http:\/\/blog.metasd.com\/wp-content\/uploads\/2009\/12\/CumPerCapCurrent.png\" alt=\"CumPerCapCurrent\" width=\"414\" height=\"367\" \/><\/p>\n<p>If you don&#8217;t want your metric to credit future population growth, you can freeze population in the denominator at current levels, which looks like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-698\" title=\"Cum Per Cap Emissions 2010 population basis\" src=\"http:\/\/blog.metasd.com\/wp-content\/uploads\/2009\/12\/CumPerCap2010.png\" alt=\"Cum Per Cap Emissions 2010 population basis\" width=\"417\" height=\"337\" \/><\/p>\n<p>If you wanted to ponder history, you could use a 1900 population basis:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-699\" title=\"Cum Per Cap Emissions, 1900 population basis\" src=\"http:\/\/blog.metasd.com\/wp-content\/uploads\/2009\/12\/CumPerCap1900.png\" alt=\"Cum Per Cap Emissions, 1900 population basis\" width=\"428\" height=\"338\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>During C-ROADS development, we explored several ways of accounting for cumulative per capita emissions. One practice that seems to be widespread is to accumulate (integrate) emissions divided by population, i.e. cumulative emissions per cap = INTEGRAL( emissions per capita(t) ) = INTEGRAL( emissions(t)\/population(t) ) This is physically meaningless. Emissions per capita is an intensive variable, [&hellip;]<\/p>\n","protected":false},"author":818,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-109500","post","type-post","status-publish","format-standard","hentry","category-news"],"_links":{"self":[{"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/posts\/109500","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/users\/818"}],"replies":[{"embeddable":true,"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/comments?post=109500"}],"version-history":[{"count":0,"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/posts\/109500\/revisions"}],"wp:attachment":[{"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/media?parent=109500"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/categories?post=109500"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mereja.media\/index\/wp-json\/wp\/v2\/tags?post=109500"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}