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Theoretical background on pwsFWI: Difference between revisions
Theoretical background on pwsFWI (view source)
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<math>P_{Sat}\ {{=}}\ {A} \times {e}^{\frac{{B}\times{T}} {({C}\ +\ {T})} }</math> | <math>P_{Sat}\ {{=}}\ {A} \times {e}^{\frac{{B}\times{T}} {({C}\ +\ {T})} }</math> | ||
Where A = 6.112, B= 17.62 and C= 243.12 are the coefficients of the August-Roche-Magnus equation as found in the Guide to Meteorological Instruments and Methods <ref>[https://www.wmo.int/pages/prog/www/IMOP/CIMO-Guide.html Guide to Meteorological Instruments and Methods of Observation (WMO-No. 8, CIMO Guide)], In Chapter 4. Measurement Of Humidity, Annex 4.B. Formulae For The Computation Of Measures Of Humidity.</ref> | Where A = 6.112, B= 17.62 and C= 243.12 are the coefficients of the August-Roche-Magnus equation as found in the Guide to Meteorological Instruments and Methods <ref>[https://www.wmo.int/pages/prog/www/IMOP/CIMO-Guide.html Guide to Meteorological Instruments and Methods of Observation (WMO-No. 8, CIMO Guide)], In Chapter 4. Measurement Of Humidity, Annex 4.B. Formulae For The Computation Of Measures Of Humidity.</ref>. P<sub>sat</sub> in hPa and T in °C. The coefficients are slightly different from the ones found in the [https://en.wikipedia.org/wiki/Vapour_pressure_of_water#Approximation_formulas Wikipedia]. | ||
With this estimator for P<sub>Sat</sub> we can work straight on to an FWI for personal weather stations (which from here on I will call pwsFWI or rough pwsFWI). | With this estimator for P<sub>Sat</sub> we can work straight on to an FWI for personal weather stations (which from here on I will call pwsFWI or rough pwsFWI). | ||
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<math>{pwsFWI}\ {{=}}\ {VPD} \times {Windspeed}</math> | <math>{pwsFWI}\ {{=}}\ {VPD} \times {Windspeed}</math> | ||
The VPD must be seen as the largest driving factor in evaporation and as such in the drying of the fuel(s). For the Meteorological variables in the calculation per day, the daily high or total (T, Wind, Rain) or daily low (RH) values are taken. | The VPD must be seen as the largest driving factor in evaporation and as such in the drying of the fuel(s). For the Meteorological variables in the calculation per day, the daily high or total (T, Wind, Rain) or daily low (RH) values are taken. | ||
== Some reasoning == | == Some reasoning == | ||
The whole process of evaporation and drying is implicit. I will not try to quantify the waterbalance exactly which would result in a quantification of the [[Charts_-_Misc_charts#Daily_EVT_.28Evapotranspiration.29|Evapotranspiration]]. Evaporation is an extremely complex process | The whole process of evaporation and drying is implicit. I will not try to quantify the waterbalance exactly which would result in a quantification of the [[Charts_-_Misc_charts#Daily_EVT_.28Evapotranspiration.29|Evapotranspiration]]. Evaporation is an extremely complex process, too much for this wiki page, see some pages on the wikipedia <ref>[https://en.wikipedia.org/wiki/Evaporation Evaporation], [https://en.wikipedia.org/wiki/Hydrology_(agriculture) Hydrology (agriculture)] and the [http://www.fao.org/3/X0490E/x0490e00.htm FAO Irrigation and drainage paper 56].</ref>, which is far beyond the scope of a fire weather index. But even for professionals it is a complex phenomenon, as it is influenced by vegetation, crop, soil etc… In short, the whole environment. That would be a bit too much although I think in principle it can be done. | ||
High VPD implies also high evaporation. | High VPD implies also high evaporation. | ||
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Wind, although not a direct factor in igniting fire, contributes very much to the drying process and after ignition, it contributes to the propagation. Strong winds will quickly create dangerous fire weather. The longer the period of dry (and strong) wind and high temperatures, the drier the fuel will be and the easier it will ignite. | Wind, although not a direct factor in igniting fire, contributes very much to the drying process and after ignition, it contributes to the propagation. Strong winds will quickly create dangerous fire weather. The longer the period of dry (and strong) wind and high temperatures, the drier the fuel will be and the easier it will ignite. | ||
So, relative humidity (fraction), wind (in km/h) and temperature (in °C) are the measurements used for the daily calculation as shown above. Furthermore the effect of the duration of dry and (possibly windy) weather needs to be taken into account and that is done through a process of testing and adjusting (a kind of calibration) until the output delivers consistent warning levels comparable with experience and existing fire weather indices. | So, relative humidity (fraction), wind (in km/h) and temperature (in °C) are the measurements used for the daily calculation as shown above. Furthermore the effect of the duration of dry and (possibly windy) weather needs to be taken into account and that is done through a process of testing and adjusting (a kind of calibration) until the output delivers consistent warning levels comparable with experience and existing fire weather indices. | ||
== Quenching and smoothing the fire weather index == | == Quenching and smoothing the fire weather index == | ||
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#If on one day an amount of rain between 1 and 5 mm has fallen, '''that day''' is skipped so that its value of pwsFWI does not contribute to the average of the five days | #If on one day an amount of rain between 1 and 5 mm has fallen, '''that day''' is skipped so that its value of pwsFWI does not contribute to the average of the five days | ||
#if on one day an amount of more than 5 mm has fallen, '''that day and the next day''' are skipped so that their values of pwsFWI do not contribute to the average of the the five days | #if on one day an amount of more than 5 mm has fallen, '''that day and the next day''' are skipped so that their values of pwsFWI do not contribute to the average of the the five days | ||
And finally a minor contribution, a fine tuning, is made to the pwsFWI by the length of the dry period in days because long dry periods take all moisture from deep within thick wood. Thick wood however does not easily ignite by a spark, not even when it is dry. | And finally a minor contribution, a fine tuning, is made to the pwsFWI by adding the length of the dry period in days to pwsFWI because long dry periods take all moisture from deep within thick wood. Thick wood however does not easily ignite by a spark, not even when it is dry. | ||
== Word of thanks == | == Word of thanks == | ||
H/T for the original testers and contributors of information who worked with me to achieve the final result. | H/T for the original testers and contributors of information who worked with me to achieve the final result. | ||
You can find the listing in the blog : [https://meteo-wagenborgen.nl/wp/2019/09/21/sites-which-carry-the-fire-weather-index-pwsfwi/ Sites which carry the Fire Weather Index pwsFWI]. Most of them still carry the Fire Weather Index page but because updating the software is not so very important for them, they fell of the map which replaced the list and became part of CumulusUtils. Once they upgrade they will automatically be shown on the map again. | You can find the listing in the blog : [https://meteo-wagenborgen.nl/wp/2019/09/21/sites-which-carry-the-fire-weather-index-pwsfwi/ Sites which carry the Fire Weather Index pwsFWI]. Most of them still carry the Fire Weather Index page but because updating the software is not so very important for them, they fell of the [[Map - Users of CumulusUtils|map]] which replaced the list and became part of CumulusUtils. Once they upgrade they will automatically be shown on the [[Map - Users of CumulusUtils|map]] again. | ||
== References == | == References == | ||