{"id":313,"date":"2019-09-26T12:09:15","date_gmt":"2019-09-26T10:09:15","guid":{"rendered":"https:\/\/meteo-wagenborgen.nl\/wp\/?p=313"},"modified":"2021-03-27T08:14:59","modified_gmt":"2021-03-27T07:14:59","slug":"corrections-to-the-august-roche-magnus-equation-in-pwsfwi","status":"publish","type":"post","link":"https:\/\/meteo-wagenborgen.nl\/wp\/2019\/09\/26\/corrections-to-the-august-roche-magnus-equation-in-pwsfwi\/","title":{"rendered":"Corrections to the August-Roche-Magnus equation in pwsFWI"},"content":{"rendered":"

Now that version 0.9.0 of my Fire Weather Index for personal weather stations (pwsFWI) has been released<\/a> in the context of CumulusUtils (I may separate it later into an independent program), it is time to look at formula corrections.<\/p>\n

<\/p>\n

For the calculation of the pwsFWI, I make use of the VPD, the Vapour Pressure Deficit. In my blog describing the theory<\/a>, I indicate a correction for altitude must be made and I give a pressure drop per 100m (which must then still be converted to the partial water pressure). However, after thinking this over, at the moment I believe no correction has te be made: the VPD is available through direct measurement and no corrections are necessary. No doubt I will think this over again and I may come back on this.<\/p>\n

The saturation pressure for water is a calculation dependent on temperature and I make use of the August-Roche-Magnus<\/a> equation (the Clausius\u2013Clapeyron equation for water vapour under typical atmospheric conditions (near standard temperature and pressure<\/a>)) :<\/p>\n

 <\/p>\n

\"\\dpi{120}<\/p>\n

Where A = 6.1094, B= 17.625 and C= 243.04 are the coefficients of the August-Roche-Magnus<\/em> equation as found here<\/a>. Psat<\/sub> in hPa and T in \u00b0C<\/p>\n

 <\/p>\n

The constants were found on the Wikipedia but recently I turned to the Guide to Meteorological Instruments and Methods of Observation<\/em> (WMO-No. 8, CIMO Guide<\/a>). In Chapter 4. Measurement Of Humidity, Annex 4.B. Formulae For The Computation Of Measures Of Humidity<\/em> you will find the formulas needed.
\n<\/em><\/p>\n

I will add the following corrections:<\/p>\n

    \n
  1. I will add the Saturation Pressure for water over ice, so for sub-zero temperatures;<\/li>\n
  2. I will use the constants as shown in the CIMO-guide (slightly different from the ones I use now;<\/li>\n
  3. I will abandon the idea of altitude correction unless I am convinced otherwise.<\/li>\n<\/ol>\n

    So for above zero temperatures the constants for the Agust-Roche-Magnus equation become: A = 6.112, B=17.62 and C=243.12; for sub zero temperatures these constants become: A = 6.112, B=22.46 and C=272.62.<\/p>\n

    No other corrections in the pwsFWI equation will be implemented at this moment.<\/p>\n

    These will be available from 0.91 onwards.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Now that version 0.9.0 of my Fire Weather Index for personal weather stations (pwsFWI) has been released in the context of CumulusUtils (I may separate it later into an independent program), it is time to look at formula corrections.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[6],"tags":[26,12,52,60,55],"class_list":["post-313","post","type-post","status-publish","format-standard","hentry","category-meteorology","tag-cumulus","tag-fwi","tag-programming","tag-pwsfwi","tag-saturation-pressure"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack-related-posts":[{"id":226,"url":"https:\/\/meteo-wagenborgen.nl\/wp\/2019\/08\/19\/an-effort-for-a-simpler-fire-weather-index\/","url_meta":{"origin":313,"position":0},"title":"An effort for a simpler fire weather index","author":"HansR","date":"19th August 2019","format":false,"excerpt":"In this blog I will propose a fire weather index for PWSs. The goal is to get fuel parameters out of the equation. This means that species, litter type or geography, will not play a role as they do in the Canadian FWI. As such, it connects with a recent\u2026","rel":"","context":"In "Forestry"","block_context":{"text":"Forestry","link":"https:\/\/meteo-wagenborgen.nl\/wp\/category\/forestry\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":669,"url":"https:\/\/meteo-wagenborgen.nl\/wp\/2020\/08\/27\/about-pwsfwi\/","url_meta":{"origin":313,"position":1},"title":"About pwsFWI","author":"HansR","date":"27th August 2020","format":false,"excerpt":"pwsFWI is now a bit more than a year old and has proven its value : it relates very well to the existing indices and the EFFIS Current Situation viewer. This means that the note : Behavioural testing still under way! will be removed from the pwsFWI page at the\u2026","rel":"","context":"In "Forestry"","block_context":{"text":"Forestry","link":"https:\/\/meteo-wagenborgen.nl\/wp\/category\/forestry\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":447,"url":"https:\/\/meteo-wagenborgen.nl\/wp\/2019\/12\/07\/impact-of-anthropogenic-climate-change-on-wildfire\/","url_meta":{"origin":313,"position":2},"title":"Impact of anthropogenic climate change on wildfire","author":"HansR","date":"7th December 2019","format":false,"excerpt":"I designed and developed my Fire Weather Index (FWI) for Personal Weather stations (PWSs) starting with basic logic reasoning (wet wood does not burn), with scientific background and made it usable in the context of PWSs. I found a very interesting and confirming article from October 2016: Impact of anthropogenic\u2026","rel":"","context":"In "Climatology"","block_context":{"text":"Climatology","link":"https:\/\/meteo-wagenborgen.nl\/wp\/category\/climatology\/"},"img":{"alt_text":"Fire events 7 dec 2019 in NSW","src":"https:\/\/i0.wp.com\/meteo-wagenborgen.nl\/wp\/wp-content\/uploads\/2019\/12\/Phils-backyard-9.jpg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":253,"url":"https:\/\/meteo-wagenborgen.nl\/wp\/2019\/08\/30\/evaluating-fwi-for-personal-weather-station\/","url_meta":{"origin":313,"position":3},"title":"Evaluating FWI for Personal Weather Station","author":"HansR","date":"30th August 2019","format":false,"excerpt":"In An effort for a Simpler Fire Weather Index I described my new FWI and the theory behind it. In short, this pwsFWI (as I have baptised it) is meant to be a generic FWI, valid everywhere and independent of geology and vegetation. The pwsFWI is a (not too) complex\u2026","rel":"","context":"In "Forestry"","block_context":{"text":"Forestry","link":"https:\/\/meteo-wagenborgen.nl\/wp\/category\/forestry\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":362,"url":"https:\/\/meteo-wagenborgen.nl\/wp\/2019\/10\/06\/behaviour-of-pwsfwi-with-first-rain\/","url_meta":{"origin":313,"position":4},"title":"Behaviour of pwsFWI with first rain","author":"HansR","date":"6th October 2019","format":false,"excerpt":"One of the goals of the current implementation of pwsFWI is to see its behaviour under all conditions. It is therefore very interesting to see that behaviour in the two stations in semi-arid zones (in Australia and in Spain) where long dry periods may suddenly alternate with rain after which\u2026","rel":"","context":"In "Forestry"","block_context":{"text":"Forestry","link":"https:\/\/meteo-wagenborgen.nl\/wp\/category\/forestry\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":409,"url":"https:\/\/meteo-wagenborgen.nl\/wp\/2019\/11\/08\/analysis-of-pwsfwi-prediction\/","url_meta":{"origin":313,"position":5},"title":"Analysis of pwsFWI prediction","author":"HansR","date":"8th November 2019","format":false,"excerpt":"Introduction In my previous blog I described why and how the predictions on pwsFWI were implemented. Also I promised a short analysis: We\u2019re now in version 1.8.3 and it seems all to be working OK. The testing is back on the meteorological level, trying to find out how much a\u2026","rel":"","context":"In "Forestry"","block_context":{"text":"Forestry","link":"https:\/\/meteo-wagenborgen.nl\/wp\/category\/forestry\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/meteo-wagenborgen.nl\/wp\/wp-json\/wp\/v2\/posts\/313","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/meteo-wagenborgen.nl\/wp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/meteo-wagenborgen.nl\/wp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/meteo-wagenborgen.nl\/wp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/meteo-wagenborgen.nl\/wp\/wp-json\/wp\/v2\/comments?post=313"}],"version-history":[{"count":0,"href":"https:\/\/meteo-wagenborgen.nl\/wp\/wp-json\/wp\/v2\/posts\/313\/revisions"}],"wp:attachment":[{"href":"https:\/\/meteo-wagenborgen.nl\/wp\/wp-json\/wp\/v2\/media?parent=313"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/meteo-wagenborgen.nl\/wp\/wp-json\/wp\/v2\/categories?post=313"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/meteo-wagenborgen.nl\/wp\/wp-json\/wp\/v2\/tags?post=313"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}