# The Chandler Burning Index

#### Introduction

One of the practical applications of meteorology is the objectivation of nature fire risks on the basis of different meteorological parameters (actual or from the past). Rainfall, humidity, temperature and windspeed are typically parameters to calculate a number indicating the risk on nature fire.

The weather-site of  PWS Meteo-Wagenborgen uses the computer program FWIcalc, which has been developed (from 2002 to 2014) by Graeme Kates in New Zealand on the basis of the FWI (Fire Weather Index), developed in Canada and also used in New-Zealand and France. Some other indices like the Angstrom and the CBI (Chandler Burning Index) are calculated by FWIcalc as well. The software is no longer supported but can still be downloaded and used (freeware).

(NB: the firewarning shown on the right is from a widget which is part of a WordPress Weather station plugin. It actually displays the Chandler Burning Index but is otherwise not related to this blog.)

The background theory unfortunately is not always clear and there is no supporting documentation or calculation method given for FWIcalc. With my background as a forester with knowledge of physics and math, something gets triggered:

1. Fire danger in nature is dependent on many factors and you therefore cannot give an absolute figure to represent that danger. You have to understand and know what is being parametrised before giving a meaning to a number. A meaning which must be explainable. That is not always the case as I will show (maybe scientists are aware of this, but apparently not everybody in the outside world).
2. The number(s) produced by FWIcalc must be reproducible by hand. No program is without error and I must be able to check before having – and giving – confidence. Therefore I need to know what and how is being calculated.
3. There is a difference between a Fire Warning Index and a Fire Propagation Index. One is to estimate the risk before the fire starts, the second is afterwards or the difficulty assessment of to  control the fire. Two different things. In first instance I only look at the risk assessment of the fire starting.
4. FWIcalc only runs on PC. The whole weather-station hard and software however is independent of my PC. It would be nice to  implement FWIcalc in such a way that it could run either on my raspberry (the spider in de web) or server side with the web-server. It would have to be migrated or rewritten. In both case the theoretical background would be required.

Either way, I will write some articles in which I will discuss some indices, their theoretical backgrounds, literature and whatever I can find. In the end I will discuss the use – or uselessness – of the indices and will try to address the problem of rewriting and or migration. The basic reason for doing so is to increase my own understanding and knowledge, I publish because somebody else may have some use of it.

#### The Chandler Burning Index

Why the CBI to start with? Because that index is one of the simplest, with the equation directly available and because it is heavily used by the world of PWS’s (like the Sasquatch Station – nice overview of Fire Weather Indices btw – or the Stillwater weathersite), sometimes even with realtime updates as if it is a measurement like temperature itself. This shows how such an index can get a life of its own and thus a truth of its own. Something like: if the warninglevel is low, I can go BBQing in the forest.

So, what now is the Chandler Burning Index (usually indicated as modified CBI)?  The CBI is calculated as (multiple sources, the easiest here ):

$\dpi{120}&space;\fn_cm&space;CBI&space;=&space;\frac{\left&space;(&space;\left&space;(&space;110&space;-&space;1.373*RH&space;\right&space;)&space;-&space;0.54&space;*&space;\left&space;(&space;10.20&space;-&space;T\right&space;)\right&space;)&space;*&space;124&space;*&space;10^{-0.0142*RH}}{60}$

In which: RH = The current relative humidity in percent and T= the current temperature in degrees Celsius (please note that some use averages and future estimations of the values in this formula).

This equation, of which the origin goes back to an article by Chandler et.al. 1983 [1] which unfortunately is not available to me, resonates in the world of PWS’s and is being used as a warning indicator on many websites. Also in the computer program FWIcalc the CBI is being calculated, but it does not form the core of the warning. Look here, here en here.

Although the equation may be the result of the solution of a differential equation or something like that, it’s construction remains a mystery to me, especially because of the complexity. I miss the feeling of reality between the mathematical construct and the forest(fire). It should be possible to construct a similar mathematical response to the input, with a simpler approach. [If anybody can supply me with a copy of the original Chandler publication (see ref 1) I’d be much obliged.]

The CBI is not exclusively used in the world of PWS’s but is also intensively used in the scientific world, e.g. Le Page et.al. [2], Gao et.al. [3]and Matthews [4] (selected out of a wide range of books and articles which are unfortunately not all at my disposition).  Matthews states:

Even though, Chandler Burning Index is not a component of the CFFWI System, it has been utilised widely for fire weather study in the United States (McCutchan & Main 1989) and elsewhere (Roads et al. 2008). The Chandler Burning Index measures susceptibility based on temperature and relative humidity (Chandler et al. 1983).

This scientific use surprises me and it emphasises again the need for explanation of the why of the equation: what is the real world behind the mathematics. Anyway, I thought it useful to analyse the equation on its behaviour and what it expresses.

#### Analysis of the equation

As there are only two parameters a numerical analysis is easy, so I ran the formula for 5% humidity-steps to generate the curves at temperatures of 0 to 48 degrees in 4 degrees steps. This leads to the following figure and table:

CBI versus humidity

Note that I left out some curves because it would make interpretation more difficult and used only multiples of 12. All values are in the table below:

 Temp-> 0 4 8 12 16 20 24 28 32 36 40 44 48 Hum 0 216 220 225 229 234 238 243 247 252 256 261 265 270 5 171 175 179 183 186 190 194 198 202 205 209 213 217 10 135 138 142 145 148 151 155 158 161 164 167 171 174 15 106 109 112 114 117 120 123 125 128 131 134 136 139 20 83 85 87 90 92 94 97 99 101 104 106 108 111 25 64 66 68 70 72 74 76 78 80 82 84 86 88 30 49 51 52 54 56 57 59 61 62 64 66 67 69 35 37 39 40 41 43 44 46 47 49 50 51 53 54 40 28 29 30 31 33 34 35 36 37 39 40 41 42 45 20 21 22 23 24 25 26 27 28 29 31 32 33 50 14 15 16 17 18 19 20 21 21 22 23 24 25 55 10 11 11 12 13 14 14 15 16 17 17 18 19 60 6 7 8 8 9 10 10 11 11 12 13 13 14 65 4 4 5 5 6 6 7 7 8 9 9 10 10 70 2 2 3 3 4 4 4 5 5 6 6 7 7 75 0 1 1 1 2 2 3 3 3 4 4 4 5 80 -1 0 0 0 0 1 1 1 2 2 2 3 3 85 -2 -1 -1 -1 0 0 0 0 1 1 1 1 2 90 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 1 1 95 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 100 -3 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1

In general, the following interpretation of values for the CBI is given:

 cbi > 97.5 Extreme cbi >= 90 Very High cbi >=75 High cbi >= 50 Moderate cbi < 50 Low

which colours I used in the value table to facilitate interpretation.

#### Intepretation

So, what to make of this? I conclude, that the CBI moves from safe to danger between humidity of 35 to 15 % at all temperatures. At 0 degrees it moves from 30 to 15 % humidity to the danger zone, at 48 degrees it starts moving to the danger zone from roughly 40 to 22 % humidity. That is not a great difference.

In other words, the CBI is highly volatile in its expression of firedanger for all temperatures from 0 to 50 degrees Celsius for the range of 40% – 15% humidity.

Apart from reality clauses, which should be included – at 0 degree it will be wet, snowy or icy so there will be little chance on ignition – my basic conclusion is, that the Chandler Burning Index does not have enough touch with reality to be a useful – i.e. public – warning index. I even doubt its scientific value (see my remarks above on the relation between the real world and the mathematics).

Where I live – and lived – a humidity of 40% is already pretty low so the chance of mathematically the index ever reaching the danger levels will be very small in real life. That is contrary to reality where forest fires – nature fires or wildfires – do take place a higher humidity values. I don’t know how this will be in the rest of the world, but I feel it will be the same in many places, apart from maybe the Sahara (where there is little nature to burn).

Yes, temperature and humidity are important parameters in estimating fire danger, but the equation is far to complex  and does not explain enough to justify its use. It actually obfuscates what it wants to bring: clarity in understanding the danger level of the weather in relation to forest fires.

An index requires more parameters, time included, and, I think, less complex equations.

To be continued (sometime).

Footnotes

[1] Chandler, C., Cheney, N.P., Thomas, P., Trabaud, L. and Williams, D. 1983. Fire in Forestry 1. Forest Fire Behavior and Effects. John Wiley and
Sons, New York, 450pp.

[2] Yannick Le Page, Duarte Oom, João M. N. Silva, Per Jönsson and
José M. C. Pereira. 2010. Seasonality of vegetation fires as modified by human action: observing the deviation from eco-climatic fire regimes. Global Ecology and Biogeography, (2010) 19, 575–588.

[3] DM Gao, XF Yin and YF Liu. 2015. Prediction Of Forest Fire Using Wireless Sensor Network. Journal of Tropical Forest Science, Vol. 27, No. 3 (July 2015), pp. 342-350.

[4] Stuart Matthews. A comparison of fire danger rating systems
for use in forests. Australian Meteorological and Oceanographic Journal 58 (2009) 41-48.