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Theoretical background on pwsFWI: Difference between revisions
Theoretical background on pwsFWI (view source)
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Relative Humidity is defined as the ratio of the vapor pressure and the saturation vapor pressure: | Relative Humidity is defined as the ratio of the vapor pressure and the saturation vapor pressure: | ||
<math>{RH} {{=}} \frac{P}{P_{Sat}} </math> | <math>{RH}\ {{=}}\ \frac{P}{P_{Sat}} </math> (1) | ||
Relative humidity is measured directly by the weather station and as such is easy to use. However, the point is that the relative humidity does not cover the whole story. The same RH will require another pressure to become saturated at different temperatures. In other words: at lower temperatures, the same RH requires less evaporation to saturate than at higher temperatures. Or, if looked at a single temperature, the drive to evaporate (to dry the fuel), is given by the difference between the current vapor pressure and the saturated vapor pressure. We call this the vapor pressure deficit (VPD)<ref name="HDW" />. In formula: | Relative humidity is measured directly by the weather station and as such is easy to use. However, the point is that the relative humidity does not cover the whole story. The same RH will require another pressure to become saturated at different temperatures. In other words: at lower temperatures, the same RH requires less evaporation to saturate than at higher temperatures. Or, if looked at a single temperature, the drive to evaporate (to dry the fuel), is given by the difference between the current vapor pressure and the saturated vapor pressure. We call this the vapor pressure deficit (VPD)<ref name="HDW" />. In formula: | ||
<math>{VPD}\ {{=}}\ {P_{Sat}}\ -\ {P} </math> (2) | |||
Reworking 1 and 2 gives: | |||
<math>{VPD}\ {{=}}\ {P_{Sat}}\ -\ {P_{Sat}} \times {RH} </math> | |||
which can be written as: | |||
<math>{VPD}\ {{=}}\ {P_{Sat}} \times (1\ -\ {RH}) </math> | |||
The vapor pressure(s) can be calculated (approximately) by <ref>formulas well known in meteorology : 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: | |||
<math>{P_{Sat}}\ {{=}}\ 10^{A\ +\ \frac{B}{({C}\ +\ {T})}}</math> | |||
Where A = 8.07131, B = 1730.63 en C = 233.426 are the coefficients of the Antoine equation as [https://en.wikipedia.org/wiki/Vapour_pressure_of_water#Approximation_formulas found here]. | |||
P<sub>sat</sub> is in mmHg and T in °C, so we need a correction to convert to hPa [https://www.convertunits.com/from/mmHG/to/hPa which is 1,3332239]. | |||
Or by the August-Roche-Magnus equation (which is used in the pwsFWI): | |||
<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>. 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). | |||
<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. | |||
== References == | == References == | ||
<references /> | <references /> | ||