Theoretical background on pwsFWI

Still under construction

Introduction

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.

For external reference on the theory behind the pwsFWI you can go the The Hot-Dry-Windy Index: A New FireWeather Index site of Michigan State University who adopted it as a tool for climatological analysis. The 2018 article on which I based the software is The Hot-Dry-Windy Index: A New Fire Weather Index. This is an open access article under the Creative Commons Attribution License.

On my (HansR) blog you may read several posts on the pwsFWI but also on the other fire weather indices in the world notably 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 , , and , I concluded the following:

1. Wet wood does not burn easily (if at all);
2. Moisture content of the fuel (wood) is of great importance;
3. Wind does not spark fire but assists drying and is dangerous for propagation;
4. Rain contradicts drying but not immediately;
5. Drying timber in a forest is not a single day event.

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. 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.

   […] However, when a fire index is formulated using an explicit or implicit fuel relationship, the effects of the fuel-based parameters add variability due to the embedded non-linear computations. So, if a “true” FWI fails to identify a dangerous fire event, the index failed either because the weather was not adequately represented in the index or the weather did not have a significant impact on the fire. If a non-weather-only fire index fails to identify a fire event, it could be because of the aforementioned reasons but also could be due to the fuels and/or topography information in the calculation, which makes determining attribution, efficacy, and failure modes for the index more difficult.

This means, they take only meteorology into account. I assume the same attitude here.

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.

Generally, people will go out – for a picnic or whatever – with nice weather light winds, no rain etc… And on a picnic, a thrown cigarette can light a fire if the fuel is dry enough. Therefore, nice picnic weather characteristics will have higher probability with fire occurrence. Yes, I assume implicitly most wildfires have human origin (maybe as a result of stupidity, definitely not always malicious).

Humidity – the science

Relative Humidity is defined as the ratio of the vapor pressure and the saturation vapor pressure:

 ${RH}\ {=}\ {\frac {P}{P_{Sat}}}$ (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). In formula:

 ${VPD}\ {=}\ {P_{Sat}}\ -\ {P}$ (2)

Reworking 1 and 2 gives:

 ${VPD}\ {=}\ {P_{Sat}}\ -\ {P_{Sat}}\times {RH}$

which can be written as:

 ${VPD}\ {=}\ {P_{Sat}}\times (1\ -\ {RH})$

The vapor pressure(s) can be calculated (approximately) by . The Antoine equation:

 ${P_{Sat}}\ {=}\ 10^{A\ +\ {\frac {B}{({C}\ +\ {T})}}}$

 Where A = 8.07131, B = 1730.63 en C = 233.426 are the coefficients of the Antoine equation as found here.  
 Psat is in mmHg and T in °C, so we need a correction to convert to hPa which is 1,3332239.

Or by the August-Roche-Magnus equation (which is used in the pwsFWI):

 $P_{Sat}\ {=}\ {A}\times {e}^{\frac {{B}\times {T}}{({C}\ +\ {T})}}$

 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 . In Chapter 4. Measurement Of Humidity, Annex 4.B. Formulae For The Computation Of Measures Of Humidity. Psat in hPa and T in °C. The coefficients are slightly different from the ones found in the Wikipedia.

With this estimator for P_Sat we can work straight on to an FWI for personal weather stations (which from here on I will call pwsFWI).

 ${pwsFWI}\ {=}\ {VPD}\times {Windspeed}$

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.