# The Ångström index and the FMI index

#### NOTE:

Please note, that this blog is one in a series culmination in an argument for a new Fire Weather Index for Personal Weather Stations developed by me. The articles in this blog often are not standalone but related. To appreciate this please check out the tags FWI or pwsFWI (more specific).

#### The indices

The Ångström index and the FMI index are highly similar indices in understanding, functioning and behaviour using only two meteorological parameters: temperature and humidity.

These indices are interesting because they are historically important, they are still in use and because, in discussing these indices, they shed some light on the understanding of the what and how of trying to understand estimating fire weather danger.

They are defined as follows:

Ångström index [1] [2] [3]  $\dpi{120}&space;\fn_cm&space;=&space;\frac{H}{20}&space;-&space;\frac{\left&space;(&space;29&space;-&space;T&space;\right&space;)}{10}$

FMI index [4] $\dpi{120}&space;\fn_cm&space;=&space;10&space;-&space;0.25\times&space;\left&space;(&space;T&space;-&space;H&space;\right&space;)$

Where in both cases: H = current air humidiy in percent and T = current air temperature in degree Celsius.

Both indices are referenced by many foresters and researchers and are very much alike. The similarity becomes clearer if we look at the plotted graphs for values of the index against humidity for different temperatures. Much like the graph in my blog about the Chandler Burning Index, we see lines drawn for different temperatures from 0 to 48 degrees Celsius in steps of 4 degrees, representing the index on the y-axis against the humidity on the x-axis. First the graph of the Ångström index, then the one for the FMI index. Note the different scales of the Y-axis.

Ångström index versus Humidity

FMI index versus humidity

The striking similarity shows both indices are actually the same. As we can see from the references the Ångström index is older (from 1942) and developed in Sweden to be used all over Scandinavia. In literature it is found that the FMI index is from the 1990’s, e.g. referenced with some history in Eastaugh et.al. (See footnote 1).

#### Discussion

As we can see from the graphs, both indexes are principally the same, only the Ångström index has a range from -2 to 8 (so a scale of 10) over all temperatures and the full humidity range. Meaning for the index has been generally defined as :

• Index > 4.0 Fire occurrence unlikely
• 4.0 > index > 2.5 Fire conditions unfavourable
• 2.5 > index > 2.0 Fire conditions favourable
• Index < 2.0 Fire occurrence very likely

I did not work it out, but with the same parameters one could define the danger values for the FMI. As a result, meaningful values – e.g. with occurrence in Scandinavian reality – lie in the range of T  = 10 – 30 degrees and a humidity between 10 and 100, meaning the meaningful Ångström index value lies between 0.6 and 6.5 and the FMI value lies between 4.5 and 32. The transitions between danger levels will be more or less arbitrary. The ranges in the FMI index will be a bit larger because the lines are steeper.

Apparently, the indices work very well in the field (the Ångström is said to be designed, to be calculated from the head) and are popular. With scientific progress and machine computation I am having my doubts about these indices. I will sum these up:

1. Basically the indices try to say something about the dryness of the fuel in the wood, the fuel moisture content. How easy does it ignite, how easy does it help to propagate a fire. That alone is important but not enough for a weather warning.
2. Input is only air temperature and air humidity without other meteorological parameters like wind or rain development over days. This means, that the danger estimation will always be from instantaneous values: too high (when the fuel is still too wet e.g. coming out of winter) or too low (when fuel is already dry with just a cool rainy day in summer).
3. The indices – or the model if you wish – is linear. It will be highly unlikely, that a model telling you something about fire weather, about the danger level, will be linear.
4. In relation to the previous remarks: I expect at least the following parameters to be part of a fire weather index:
1. Time
2. Temperature (development)
3. Humidity (development)
4. Wind (development)
5. Fuel type (tree species, undergrowth, litter etc…)

While the models are getting better and more complex, it seems the trade-off between complexity and (publicly) understandable warning systems leads to indices like the ones discussed here. As Eastaugh (Footnote 1) writes:

Numerous fire risk indices have been developed over the past
seventy years, beginning with the purely empirical meteorological indices of Ångström and Nesterov in the 1940s. Käse (1969) modified the Nesterov index to account for higher probability of fire in spring, dependent on the budburst date of birch and robinia trees. Keetch and Byram(1968) developed an index of soil moisture deficit (KBDI) for use by fire agencies, on the principle that soil dryness is likely to be accompanied by fuel dryness. The more sophisticated Canadian Forest Fire Weather Index of Van Wagner (1987) expressly considers how weather conditions affect the moisture content of different fire fuel layers. The more easily ignited fine fuels lose moisture quickly under dry atmospheric conditions, while larger fuels dry only after extended periods.

Tanskanen and Venäläinen (2008) have pointed out however that the accuracy of the indices can vary seasonally depending on the proportion of dead to live fine fuels on the forest floor. […] We chose here the Angström, Nesterov and KBDI indices to represent a continuum of fire index types from a simple instantaneous index, to one that includes consideration of precipitation, to a more complex accumulative index with a physical interpretation.

Although I think, these indices will have some value – knowing undergrowth may ignite easily can be handy for the public – we also know they are limited, so I will look to a more complex fire weather warning system next. More specifically, next I will try to say something about the FWI, the Fire Weather Index. Developed and in use in Canada and adopted by New Zealand and France (among others I think). This treatment will no doubt be split up in several parts because of its complexity.

Apart from the above, I think that real-time computation of fire hazard and the corresponding warnings is not required. It actually implies creating an image of an accurate calculation method for the fire risk. Meteorology alone will never be able to determine the fire hazard, and neither will it be the fuel alone nor just the forest itself. (Note: FWIcalc calculates once a day and takes slope, vegetation type etc… into account though I don’t know exactly how) .

To be continued (sometime).

[1] C.S. Eastaugh, H. Hasenauer. Deriving forest fire ignition risk with biogeochemical process Modeling. Environmental Modelling & Software 55 (2014) 132-142.

[2] 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

[3] Sometimes in literature the temperature term is (29-T) i.s.o. (27-T), see my references 1 and 2. I have no idea where this change comes from. I am not in possession of the original article by Ångström. I use the 29-term but, as shown below, it is quite arbitrary.

[4] 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