The Byram-Keetch Drought Index, Drought Factor and Forest Fire Danger Index

The Byram-Keetch Drought Index (or BKDI, used for fire danger measurements across much of SE Australia) - the higher the BKDI, the more rain is required to return the soil to saturation.

The following are the published equations used for the complete calculation cycle for McArthur Mk 5 Forest Fire Danger Index. All equations are sourced to original references. All inputs are metric. All references to the functions Log and Exp are in base e. All inputs are real numbers. Do not round off to integers, except for display purposes.


1 TEMPY Yesterday's maximum screen temp [degrees Celsius]
2 ANNRF Site's average annual rainfall [mm]
3 LR Last rain [mm], measured over entire period of rainfall (if more than one day).
4 DSLR Days since last rain. Note: care must be taken in deciding what is a non-rainy - i.e. drying - day, especially if: heavily overcast; only light drizzle is recorded; or if all rain fell late yesterday morning, but was still logged as today's rainfall to 9am. Note also DSLR may be calculated off the day of heaviest rainfall, if subsequent rainy days had only light rainfall. Another feature of the onset of a new rain spell is that the canopy is dry and can intercept its full assumed 5mm of rain. Note too that the BKDI model makes no use of wind, even though strong winds may dry out the canopy.
5 1 BKDI Current Byram-Keetch Drought Index. [mm]. (This is identical to the KBDI.) Consider the topmost layers of soil such that their field capacity is 200 mm of available water. The index estimates how much effective rainfall is needed to saturate this depth of soil at any time. Moisture is lost from the soil only by evaporation due to temperature effects. The first 5 mm of rainfall is lost to the canopy. There is a problem if any of the rainfall is lost as surface run-off.
6 1 DBKDI Delta BKDI [mm] - i.e. the daily increment in the running tally of BKDI resulting from yesterday's weather.

If (DSLR = 0) Then

If (LR >= 5) Then

DBKDI = 5 - LR



End If


DBKDI = ((800 - BKDI) * (.968 * Exp(.0486 * (TEMPY * 9 / 5 + 32)) - 8.3) * .001 / (1 + 10.88 * Exp(-.0441 * ANNRF / 25.4)) * .254)

End If


7 2 DF Drought factor [scaled from 0 to 10], which estimates the proportion of fine fuels available for the forward spread of a fire. DF and BKDI assume flat terrain, and thus uniform drying. DF will often vary widely with terrain in hilly country. (There are no equations to compensate for this, but rules-of-thumb can be applied.)

DF = ((.191 * (BKDI + 104) * (DSLR + 1) ^ 1.5) / (3.52 * (DSLR + 1) ^ 1.5 + LR - 1))

If (DF > 10) Then DF = 10

8 RH Relative humidity [%], for fire danger use the forecast minimum for the day, for fire behaviour use the value for the appropriate time. Measure in a Stephenson screen or equivalent.
9 TEMP Temperature [degrees C], for fire danger use the forecast maximum for the day, for fire behaviour use the value for the appropriate time. Measure in a Stephenson screen or equivalent.
10 WINDSPEED Wind speed [km/hr], for fire danger use the forecast average for the worst time-of-day (usually early afternoon), for fire behaviour use the value for the appropriate time. Measure in a large clear site at 10 m height. If measured at 2 m, multiply by 1.25
11 2 FFDI Forest Fire Danger Index [open-ended scale, generally less than 100]. It measures both: the flammability of fuels, and thus the fire danger; and the potential behaviour of a fire.

FFDI = 2 * Exp(-.45 + .987 * Log(DF + .001) - .0345 * RH + .0338 * TEMP + .0234 * WINDSPEED)


  1. Keetch, J.J. & Byram, G.M. (1968). A Drought Index for Forest Fire Control. US Dept of Agriculture Forest Service Research Paper SE-38.
  2. Noble, I.R., Bary, G.A.V. & Gill, A.M. (1980), McArthur's fire-danger equations expressed as equations. Australian Journal of Ecology 5:201-203.

This information courtesy of Rick McRae