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Theoretical background on pwsFWI: Difference between revisions
Theoretical background on pwsFWI (view source)
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[[File:PwsFWI legend.jpg|center|none|PwsFWI legend.jpg]] | [[File:PwsFWI legend.jpg|center|none|PwsFWI legend.jpg]] | ||
== Introduction == | == Introduction == | ||
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'''NOTE: This Fire Weather Index is an original development and bears no relation to any other existing fire weather index and the resulting (absolute) value can not be compared to any of those. It is the resulting warning level which can be compared and which should be used.''' | |||
'''NOTE: This wiki article differs in some important aspects from the original blog ''[https://meteo-wagenborgen.nl/wp/2019/08/19/an-effort-for-a-simpler-fire-weather-index/ An effort for a simpler fire weather index]'' on which it is based.''' | |||
<br> | |||
<br> | |||
The Fire Weather Index for a personal weather station, in short '''pwsFWI''', is probably one of the most complex modules of ''CumulusUtils''. Not so much for the calculations, which once you know what to do are not that complex, but more for the interpretation and understanding of what is shown. This Wiki article will show the science background to pwsFWI. | The Fire Weather Index for a personal weather station, in short '''pwsFWI''', is probably one of the most complex modules of ''CumulusUtils''. Not so much for the calculations, which once you know what to do are not that complex, but more for the interpretation and understanding of what is shown. This Wiki article will show the science background to pwsFWI. | ||
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On my ([https://cumulus.hosiene.co.uk/memberlist.php?mode=viewprofile&u=9016 HansR]) blog you may read [https://meteo-wagenborgen.nl/wp/tag/pwsfwi/ several posts] on the pwsFWI but also on the other fire weather indices in the world notably [https://meteo-wagenborgen.nl/wp/2019/08/11/fire-weather-the-canadian-fwi/ the Canadian FWI]. This complex FWI is used in many places but it is so complex that it is not summarized in equations, but referenced by the articles. The complexity of this FWI was one of the main reasons to create pwsFWI. Other fire indexes such as the Ångström index and the Chandler Burning Index, though often seen on amateur weather sites, have been looked at but these are not discriminating enough. | On my ([https://cumulus.hosiene.co.uk/memberlist.php?mode=viewprofile&u=9016 HansR]) blog you may read [https://meteo-wagenborgen.nl/wp/tag/pwsfwi/ several posts] on the pwsFWI but also on the other fire weather indices in the world notably [https://meteo-wagenborgen.nl/wp/2019/08/11/fire-weather-the-canadian-fwi/ the Canadian FWI]. This complex FWI is used in many places but it is so complex that it is not summarized in equations, but referenced by the articles. The complexity of this FWI was one of the main reasons to create pwsFWI. Other fire indexes such as the Ångström index and the Chandler Burning Index, though often seen on amateur weather sites, have been looked at but these are not discriminating enough. | ||
After describing different indices for fire weather, in reverse order | After describing different indices for fire weather, in reverse order: [https://meteo-wagenborgen.nl/wp/2019/08/11/fire-weather-the-canadian-fwi/ the Canadian FWI] (Contains a longer literature list), [https://meteo-wagenborgen.nl/wp/2019/07/27/fire-weather-at-the-end-of-the-heatwave/ At the end of the heatwave], [https://meteo-wagenborgen.nl/wp/2019/07/10/fire-weather-the-angstrom-index-and-the-fmi-index/ The Ångström index and the FMI index] and [https://meteo-wagenborgen.nl/wp/2019/07/08/the-chandler-burning-index/ The Chandler Burning Index], the following was concluded: | ||
#Wet wood does not burn easily (if at all); | #Wet wood does not burn easily (if at all); | ||
#Moisture content of the fuel (wood) is of great importance; | #Moisture content of the fuel (wood) is of great importance; | ||
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== Some remarks on Humidity == | == Some remarks on Humidity == | ||
One addition must be made: there are woods which burn more easily than other woods (eucalyptus, pinus etc…), but they also burn only when they are dry. | One addition must be made: there are woods which burn more easily than other woods (eucalyptus, pinus etc…), but they also burn only when they are dry. [https://meteo-wagenborgen.nl/wp/wp-content/uploads/2019/08/ja_2018_goodrick_001.pdf Goodrick et.al.]<ref name="HDW">Alan F. Srock, Joseph J. Charney, Brian E. Potter and Scott L. Goodrick, The Hot-Dry-Windy Index: A New FireWeather Index. Atmosphere 2018, 9, 279</ref> state very clearly that: | ||
''[…] we want to isolate the effects of weather on a wildland fire, so we define a fire weather index (FWI) as an index that includes only weather inputs and thus does not include explicit or implicit information about the state of wildland fuels or topography.'' | ''[…] we want to isolate the effects of weather on a wildland fire, so we define a fire weather index (FWI) as an index that includes only weather inputs and thus does not include explicit or implicit information about the state of wildland fuels or topography.'' | ||
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I assume the same attitude here. | I assume the same attitude here. | ||
[https://meteo-wagenborgen.nl/wp/wp-content/uploads/2019/08/Using-Correlative-Data-Analysis-to-Develop-Weather-Index-That-Estimates-the-Risk-of-Forest-Fires-In-Lebanon-Assessment-versus-Prevalent-Meteorological-Indices.pdf Hamadeh et.al.]<ref>Nizar Hamadeh, Ali Karouni, Bassam Daya, Pierre Chauvet. Using Correlative Data Analysis to Develop Weather Index That Estimates the Risk of Forest Fires In Lebanon: Assessment versus Prevalent Meteorological Indices. International Journal of Physical Science Research. Vol.1, No.2, pp.14- 38, August 2017.</ref> made an analysis of the correlation between meteorological measurements and fire occurrences. In their paper, the team produced graphs, indicating the probability of fire occurring for a meteorological parameter. They more or less contradict the observations above concerning humidity and wind. | |||
But it is not these parameters alone, but in interaction they play their role. Relative humidity and wind together dry out the fuels and it does occur over days or weeks, therefore there is no direct relation between those parameters and fire occurrence. | But it is not these parameters alone, but in interaction they play their role. Relative humidity and wind together dry out the fuels and it does occur over days or weeks, therefore there is no direct relation between those parameters and fire occurrence. | ||
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<math>{VPD}\ {{=}}\ {P_{Sat}} \times (1\ -\ {RH}) </math> | <math>{VPD}\ {{=}}\ {P_{Sat}} \times (1\ -\ {RH}) </math> | ||
The vapor pressure(s) can be calculated (approximately) by | The vapor pressure(s) can be calculated (approximately) by formulas well known in meteorology<ref>See [https://en.wikipedia.org/wiki/Vapor_pressure Vapor Pressure] , [https://en.wikipedia.org/wiki/Relative_humidity Relative Humidity], [https://en.wikipedia.org/wiki/Saturation_vapor_density Saturation Vapor Density], [https://en.wikipedia.org/wiki/Vapour_pressure_of_water Vapor Pressure of Water] and [https://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation Clausius-Clapeyron Relation].</ref>. | ||
The Antoine equation: | The Antoine equation: | ||
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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>. In Chapter 4. Measurement Of Humidity, Annex 4.B. Formulae For The Computation Of Measures Of Humidity. 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]. | 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>. In Chapter 4. Measurement Of Humidity, Annex 4.B. Formulae For The Computation Of Measures Of Humidity. 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). | 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). | ||
<math>{pwsFWI}\ {{=}}\ {VPD} \times {Windspeed}</math> | <math>{pwsFWI}\ {{=}}\ {VPD} \times {Windspeed}</math> | ||
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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 == | |||
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 See some pages on the wiki<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. Even professionally, 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 temperatures are a measure of the energy input into the system and has no influence directly on ignition of fire. The VPD reflects this, as temperature is input to the equation: increasing temperature increases the saturation pressure of water and thus reflects increased drying. The energy required for this drying process comes from the sun and thermodynamic calculations could be made. Again, this is beyond the scope of a fire weather index for a personal weather station (though a nice hobby in itself). | |||
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. | |||
== Quenching and smoothing the fire weather index == | |||
The process of calibration resulted in two factors to be taken into account to dampen the heavy fluctuations which occur in practice with the pwsFWI as calculated as above through the rough equations. | |||
#Duration | |||
#Rain amount | |||
When the index suddenly becomes high after a period with low index, it means that the fuel will be wet and needs some time to dry. That needs to be taken into account such that with a constant temperature and wind, the index will reach a stable level (in practice of course it will always vary). | |||
It must be understood, that processes in nature take time. Drying is not instantaneous and neither is the absorption of water by wood. When rain occurs, the drying process will be stopped and possibly reversed. This also will not be immediate and a single shower will have little effect. Semi-arid locations may have evaporation of 9 mm/day or higher. This means that a shower there needs to be more than 9 mm, to actually quench the drying process (for a day) and a lot more for reversal. So a heuristic quenching process has been implemented as follows<ref>This quantification has been heavily played with/modified during calibration but is stable now</ref>: | |||
#Rain less than 1 mm is completely ignored | |||
#Rain between 1 and 5 mm results in a 50% reduction of pwsFWI as calculated (the rough pwsFWI) | |||
#Rain more than 5 mm results in a 67% reduction of the pwsFWI as calculated (the rough pwsFWI) | |||
Then for a period of five days (the so called smoothing days) for each day: | |||
#The average of the last five days of the calculated (the rough) pwsFWI is calculated and if no rain has fallen (or less than 1 mm) that average is the new pwsFWI (or smoothed pwsFWI) as presented to the user | |||
#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 | |||
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. | |||
== Word of thanks == | |||
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. | |||
== References == | == References == | ||