I will describe the Canadian FWI as it appears in (scientific) literature. The basic reason for describing this complex fire-weather index is, that it is heavily used in some big countries, notably Canada, France, Australia and New Zealand and that the description of the method of calculation is not readily available.
Some extensive studies have been made, to measure its performance and its relevance. FWI also contains most parameters relevant to estimating the danger level of the weather in relation to nature fires. In short: the FWI is an important tool for estimating and studying fire weather and fire spreading, with a huge knowledge base spanning almost 100 years.
This is also the index, which forms the basis for the computer program FWIcalc, created by Graeme Kates for use in the world of the PWS’s , as I described in my blog on the Chandler Burning Index. It is also used on my own site. Nevertheless, searching for the equations which are behind the FWI – and thus form the basis of understanding the index – are not easy to find. You have to claw your way through a disguise of surface scratching website descriptions. Even the site of National Resources of Canada does not have an in depth article on the equations and theory behind the index, so I had to search the scientific literature. Footnote 4 en 5 give the main describing articles, footnote 3 gives the best analytical article I found.
All in all, this FWI is a really important index, both from a practical as from a theoretical point of view. I will try to give an overview (part I), and an effort to make it practical for PWSs (part II).
An important article, used as a basis for this series, is a comparison between different meteorological indices by Hamadeh et.al.  They write:
Natural crises such as earthquakes, tornados, floods and forest fires may cause damage to the shape of the land besides their threat to living things. Forest Fires are considered among the most dangerous. Their frequencies are increasing day after day especially in the prevailing local and global climate changes which make these kind of natural disasters a complex phenomenon to tackle. This is despite the fact that wildfire is an important part of nature. It plays a key role in shaping ecosystems by serving as an agent of renewal and change.
This is why research on prediction of forest fire danger receives a lot of study today. Study which started in 1928 (see footnote 4) and 1940’s (e.g. Angstrom). The National Resources Canada (and/or its predecessors) developed the FWI around 1970 from prior work and modified it around 1976 and 1987. In 1974 C.E. van Wagner  published the theory and background on the index and his article contains a nice historical overview. In 1985 van Wagner  published the modifications as a short technical report on the FORTRAN program which does the actual work. These three articles form the basis of this blog.
It is important to understand, that the theory behind the forest fire warning system came from practical idea’s about the parameters which play a role. Forming simple unrelated equations and then developing into a coherent and dependent system of parameters and equations, evolving into and supported by a fully formed scientific system for forest fire simulation. It was an evolution.
As such, in my opinion, the warning system and the theory, kind of grew apart: the theory (the model) became more or less too big for a practical warning system. Definitely too big for amateur (PWS) websites. I will come back on this issue as it is the cause for writing my blog on the fire weather indices.
So what is the index made of? The summary of van Wagner’s 1974 article says:
The Canadian Forest Fire Weather Index (FWI) was issued in 1970 after several years work by a number of fire researchers in the Canadian Forestry Service. The best features of the former fire danger index were incorporated in the FWI, and a link was preserved between old and new. The FWI is based on the moisture content of three classes of forest fuel plus the effect of wind on fire behaviour. It consists of six components : three primary subindexes representing fuel moisture, two intermediate subindexes representing rate of spread and fuel consumption, and a final index representing fire intensity as energy output rate per unit length of fire front.
Apart from indicating this index is work of a large team over a long period of time, the text shows it was work, well thought over and not some quick and dirty trick like the CBI and Angstrom indices. That is important.
In figure this becomes (see NRC, which is similar to the one in footnote 4):
The three primary components are subindexes that follow from day to day the moisture contents of three classes of forest fuel of different drying rates. Each block has an equation connected to it which satisfies the science behind it.
- The FFMC says something on the moisture content of litter on the forest floor containing small branches and leaves: “[…] which represents the moisture content of litter and other cured fine fuels in a forest stand, in a layer of dry weight about 0.05 lb/ft2” (which equals 0.244 kg/m2).
- Duff Moisture Code (DMC) , which represents the moisture content of loosely compacted, decomposing organic matter 2 to 4 inches deep and weighing about 1 lb/ft2 when dry (which equals 4,88 kg/m2).
- Drought Code (DC) , which represents a deep layer of compact organic matter weighing perhaps 10 lb/ft2 when dry (which equals 48,824 kg/m2).
I personally interpret the above subindices as the dominant factors for the ignition of a fire. The following two subindices are important for (initial) propagation:
- Initial Spread Index (ISI) , a combination of wind and the FFMC that represents rate of spread alone without the influence of variable quantities of fuel;
- Adjusted Duff Moisture Code (ADMC) , a combination of the DMC and the DC that represents the total fuel available to the spreading fire;
Finally, 4 and 5 are combined into the FWI :
- Fire Weather Index (FWI) , a combination of the lSI and the ADMC that represents the intensity of the spreading fire as energy output rate per unit length of fire front.
The equations are basically derived from theory and laboratory experiments for drying. Van Wagner states:
Each fuel is considered to dry exponentially, so that the instantaneous drying rate is proportional to the current free moisture content. The proper measure of drying speed is then either the time constant (i . e . time to lose 1-1/e [about 2/3 ] of the free moisture above equilibrium) , or the slope of the exponential curve, called here the log drying rate.
Table 1 : gives for each moisture code the time constant in terms of normal days with noon temperature and relative humidity at 70°F (= 21,1 °C) and 45%, as well as water capacity and daily weather parameters required for operation.
|Code||Time constant days||Water capacity inches||Required weather|
|FFMC||2/3||0.01 – 0.02||T,H,W,r|
IT – temperature, H – humidity, W – wind, r – rain .
All subindices are described by equations. Some pragmatic adaptations to theory are incorporated e.g. Long-term drought effect was worked in by giving the DC a small but variable weight as an adjustment to the DMC.
Also it is explicitly stated that the fuel type is taken out of the equation and some standardized average is being used. Behaviour of fire as a function of fuel type is considered a separate problem. An approach which is debatable: an Eucalyptus stand ignites much easier than a beech forest, which means different equations would be required for different types of fuel (types of forest).
So which equations are proposed by van Wagner and his team? The actual calculations are done daily, through a series of equations which are published by van Wagner in 1974 and in 1987 (see footnotes 4 and 5). It is of little use and probably repulsive, to actually publish those equations here. If you think of studying or using them: read the articles. You can download local copies through the links in the footnotes.
After the description above, I do have some remarks.
- Although the FWI seems an exact and deterministic system, it is not. At best, the whole set of equations is a model of forest fire behavior under certain meteorological conditions and fuel assumptions (Eucalyptus forest is quite different from a swamp forest). The model contains assumptions, approximations and adaptations to reality which are logical and practical, but as such create a hybrid model which stands between exact science and forest management practice.
- There does not exist any deterministic description of the interaction between forest and the weather, it should be probabilistic. As such, the extrapolation of the equations which came from laboratory tests to the field is over-stretching the possibilities : practical circumstances in a forest (or scrub or grassland) are nature and not conditioned to laboratory equations.
- Calculating the current FWI is an elaborate process, which originated as an administrative act by several layers in the Canadian forest service and locally completed by the forest keepers (if I understand the whole procedure well). With the help of computers the process has been automated but still runs over different layers of interaction.
- The export of the FWI to Australia and Europe, with its accompanying warning colours and dial, has definitely contributed to the public knowledge of a danger of forest fires in dry, hot weather.
- However, the distribution of the FWI throughout the world of amateur meteorologists without knowledge of the parametrization and of the theoretical background, has set back the value of the FWI.
So, here we are. CBI and Angstrom definitely are far too simple and FWI is – I think – too complex. The national warning levels are far too global and thus not very accurate in estimating a chance for forest fire from deterministic equations.
The local PWS warning levels are often badly parametrized, or simply use defaulted values. The PWS owners rarely have the knowledge required for setting up a tool like FWIcalc. If it’s warm, the meter rises anyway. As such, the current use of FWI is not very useful.
True, the EFFIS-effort is great, and maybe even the best around. But still, understanding what is happening there is very difficult (the FWI has been adjusted and adapted) and reproducing it for PWSs probably is very hard. A good thing is, that EFFIS is using a spatial resolution of 8×8 km. That is a fine resolution which satisfies the differences in vegetation, fuel and weather which occur in practice.
So, what can we do to create a tool for PWSs, which actually creates a warning system which works. My next blog will investigate that subject. In the mean time you have something to read using the list of articles on the subject of fire danger rating systems supplied in this blog and supplemented with some more:      .
To be continued…
 PWS : Personal Weather Station.
 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.
 C.E. van Wagner. Structure of the Canadian Forest Fire Weather Index. Department of the Environment, Canadian Forestry Service, Publication No. 1333, Ottawa, 1974.
 C.E. van Wagner and T.L. Pickett. Equations and FORTRAN program for the Canadian Forest Fire Weather Index System. Canadian Forestry Service, Forestry Technical Report 33, Ottawa, 1985.
 Stuart Matthews, A comparison of fire danger rating systems for use in forests. Australian Meteorological and Oceanographic Journal 58 (2009) 41-48
 Alexander Arpaci & Chris S. Eastaugh & Harald Vacik, Selecting the best performing fire weather indices for Austrian ecoregions. Theor Appl Climatol (2013) 114:393–406
 Andrew J. Dowdy, Graham A. Mills, Klara Finkele and William de Groot, Index sensitivity analysis applied to the Canadian Forest Fire Weather Index and the McArthur Forest Fire Danger Index. Meteorol. Appl. 17: 298–312 (2010)
 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
 J.J. Sharples, R.H.D. McRae, R.O. Weber, A.M. Gill, A simple index for assessing fire danger rating. Environmental Modelling & Software 24 (2009) 764–774
 J.J. Sharples, R.H.D. McRae, R.O. Weber, A.M. Gill, A simple index for assessing fuel moisture content. Environmental Modelling & Software 24 (2009) 637–646