An effort for a simpler fire weather index

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 new development described by Goodrick 2 .


After describing different indices for fire weather [1], I conclude 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.

I need to elaborate 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. Goodrick [2] 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.

Hamadeh [3] 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}}


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, see also footnote 2). In formula:


VPD = P_{sat} - P


which can be written as:


VDP = P_{sat} - P_{sat}\times RH


VDP = P_{sat}\times (1 - RH)


The vapor pressure(s) can be calculated (approximately) by formulas well  known in meteorology, the Antoine equation [4] :


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 :


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

Where A = 6.1094, B= 17.625 and C= 243.04 are the coefficients of the August-Roche-Magnus equation as found here. Psat in hPa and T in °C


From here we can work straight on to an FWI for personal weather stations (from here on I will name it the pwsFWI).

For a start, I propose the pwsFWI-index as follows:


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).

Some reasoning

The whole process of evaporation and drying is implicit. I will not try to quantify the waterbalance exactly. Evaporation [5] is an extremely complex process, 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 PWS (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, barometric pressure (in hPa), 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.

Quenching the fire weather index

Here I take into account two mayor influences on fire weather have not been discussed yet:

    1. Duration
    2. Rain

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).

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. I know from semi-arid locations where evaporation has been measured to be 9 mm / day. 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.

As I will not attempt to catch the evaporation into a single formula (at least for now), I will experiment with a quenching component containing duration and amount of rainfall starting from a certain limit.

After two days of enough (above the limit) consecutive rain, the process restarts without history to build up again.

Fire season and heights


I claim this fire weather index to be general and valid everywhere. That means it must be valid in seasonal areas (such as Northern Europe) and it must be valid in areas without season (such as tropics). As the energy input in seasonal areas is only high enough to create dangerous fire weather during the fire season. I take the fire season to be dependant of latitude (positive is North, negative is South) according to the following table:

Absolute                   Start month/end month
Latitude                    (included)
0 – 25                       January / December
25 – 35                     February / November
35 – 45                     March / October
45 – 55                     April/September
55 – 90                     May / August


For heights a correction needs to be made for the Psat. There are two things required to understand:

    1. The Barometric formula and
    2. The Lapse Rate

I will correct Psat for altitude, not according to the formula’s but, for the time being, with a very simple approximation as indicated in the wiki:

The pressure drops approximately by 11.3 Pa per meter in first 1000 meters above sea level

As such the altitude of the PWS will give the correction on Psat and pwsFWI will not calculate above 1000  meters.

(edit 10/10/2019)
NOTE: this is not a correct reasoning. If the barometric pressure is the sum of the partial pressure of dry air and  the partial pressure of water vapour (Dalton’s law) and the saturation pressure of water is only dependent on temperature (see above), then the measurements of relative humidity and temperature at any height are enough for calculating the VPD on any altitude.

Closing remarks

In this blog I presented the starting arguments for a fire weather index which can be easily used in personal weather stations (PWS). The measurements made by the station are enough for the required calculations and most software utilities have easy access to the data. I will implement this for Cumulus in the coming time to have it ready for the next season. The software will be made available to the Cumulus community in my additions to Cumulus program (add2cumulus) through the support forum, the software will be in Github. Given the feedback I may finetune the pwsFWI.

Evaluation will be done over the course of the years.


[1] In  reverse order: The Canadian FWI (with longer literature list), At the end of the heatwave, The Ångström index and the FMI index and The Chandler Burning Index.

[2] 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

[3] 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.

[4] See also: Vapor Pressure , Relative Humidity, Saturation Vapor Density, Vapor Pressure of Water and Clausius-Clapeyron Relation.

[5] See some pages on the wiki: Evaporation, Hydrology (agriculture) and the FAO Irrigation and drainage paper 56.

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