a comparison of fire danger rating systems for use in forests · fire danger rating is ‘a fire...

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41

Australian Meteorological and Oceanographic Journal 58 (2009) 41-48

Introduction

Fire danger is the resultant of ‘factors affecting the incep-tion, spread and difficulty of control of fires and the dam-age they cause’ (Chandler et al. 1983). If any of these factors are absent, then there is no fire danger (Cheney and Gould 1995). Fire danger rating is ‘a fire management system that integrates the facets of selected fire danger factors into one or more qualitative or numerical indices of current protec-tion needs’ (Chandler et al. 1983). A variety of fire danger ratings are used around the world, including the McArthur Forest Fire Danger Index (FFDI, McArthur 1967), used in the eastern parts of Australia, the Forest Fire Behaviour Tables (FFBT, Sneeuwjagt and Peet 1998), developed for use in Western Australia1, the Fire Weather Index (FWI, van Wag-

ner 1987) used in Canada, and the National Fire Danger Rat-ing System (Deeming et al. 1977), used in the USA. Fire danger rating systems are used by fire and land man-agement agencies to determine levels of preparedness, to issue public warnings, and to provide an appropriate scale for management, research, and law for fire related matters (Cheney and Gould 1995). All these systems integrate weath-er variables to assess fire danger, calculated as a numerical index. Although fire danger is not the same as fire behaviour, the indices were developed on the assumption that fire dan-ger is related to fire behaviour, quantified as rate of spread or intensity. Index values are classified into rating classes to aid interpretation. All systems use five rating classes: Low, Moderate, High, Very High, and Extreme. Similar indices are available for grasslands but are not examined here. In recent years the FWI, originally developed for use in Canada, has been adapted for application in other countries, has been proposed as the basis for a global fire weather in-dex (de Groot et al. 2006), and has been trialled in Tasma-nia (Mark Chladil, pers. comm.). Also, the FWI system has proved useful when examining fires in pine plantations in Australia (Cruz and Plucinski 2007). In an Australian con-text it is timely in light of these developments to gain a better

A comparison of fire danger rating systems for use in forests

Stuart Matthews1, 2

1Climate Adaptation Flagship – CSIRO Sustainable Ecosystems2Faculty of Agriculture, Food, and Natural Resources, University of Sydney

(Manuscript recieved June 2008;

Revised October 2008)

Fire danger indices are an important tool for fire and land managers. This study examines two fire danger indices developed for use in Australian forests, the For-est Fire Danger Index and the Forest Fire Behaviour Tables, and a third, the Fire Weather Index, which was developed for use in Canadian pine forests but is find-ing use in other countries. The indices are described and their structures exam-ined by comparing the response of each index to wind, fuel moisture, and fuel availability. The application of the indices is examined by comparing their predic-tions across a range of wind, fuel moisture, and fuel availability conditions, and in a case study using weather station data. The three systems are found to have similar structures but to provide widely varying assessments of fire danger for a given set of inputs. In the case study, differences between how weather variables are incorporated by the indices cancelled out some of the differences in structure and the results were in closer agreement, particularly for the two systems devel-oped for eucalypt forest.

Keywords: Fire weather, fire behaviour, eucalyptus, pine plantation.

Stuart Matthews, Faculty of Agriculture, Food, and Natural Resources, Wooley Building A20, University of Sydney, NSW 2006, Australia.Email: [email protected]

1The FFBT is not used for public warnings in Western Australia (McCaw et al. 2007) but is used to set preparedness levels and regulate the activi-ties of the timber industry.

42 Australian Meteorological and Oceanographic Journal 58:1 March 2009

understanding of the FWI and its relationship to the FFDI and FFBT and their suitability for Australian conditions. This paper examines the structure of the FWI, FFDI, and FFBT fire danger indices with the aim of understanding the relationships between their assessments of fire danger. First, the structure of the three systems is described and the FFDI is reformulated to allow direct comparison with the FWI and FFBT. The dependence of each index upon fuel and weath-er variables is then examined. The values of the indices for common input conditions are considered first across the full range of input conditions, and then again in a case study us-ing automatic weather station observations.

The indices

All three systems include methods for calculating fire dan-ger indices and fire behaviour characteristics. For brevity, all references herein are to the fire danger index component of each system. Both the FFDI and FWI are based upon the principle that fire danger is determined by wind speed, fuel moisture content, and fuel availability. The FFBT is based on similar reasoning but includes only fuel moisture and wind speed as determinants for fire danger. An overview of the experimental development of the FFDI and FFBT is given by Burrows and Sneeuwjagt (1991). The development of the FWI is described by van Wagner (1987). Wind speed is the average wind measured at a standard meteorological observing station and higher winds are asso-ciated with higher fire danger. For fire danger calculations, wind speed is measured at 10 m in the open and expressed as km h-1. Fuel moisture content is the amount of water in the fine litter fuels that are consumed in the fire front and higher fuel moisture is associated with lower fire danger. Fuel mois-ture is expressed as a percentage of dry weight and mea-sured values are typically in the range 3 – 250 per cent. For calculation of fire danger rating, fuel availability is defined as the fraction of the forest litter layer that is dry enough to burn, ranging from none to all of the fuel being available. In this application the litter layer is all dead fuels less than 6 mm in diameter from the surface to the mineral soil, including duff if it is present. Greater fuel availability results in higher fire danger. Fuel availability is expressed as a bounded in-dex with the maximum value corresponding to all fuel being available. For the FFDI fuel availability ranges from 0 to 10, for the FWI from 0 to 40. For this study the fire danger equa-tions are modified so that fuel availability ranges from 0 to 1 for both systems, to avoid confusion. These definitions are common to all three systems. Be-cause fuel moisture and fuel availability may not always be readily measured each system includes sub-models to estimate these quantities from weather observations. As the variables used by the fire danger index systems are the same, differences in ratings are determined by differences in the responses of the indices to moisture, wind, or fuel avail-

ability, or by differences in the moisture and fuel availability sub-models. This section summarises the equations used to calculate the FWI, FFDI and FFBT. The standard form of the FWI is the equations given in van Wagner (1987). The standard form of the FFBT is the set of tables given in Sneeuwjagt and Peet (1998). For this study equations fitted to the tables by Beck (1995) were used. The standard method of calculating FFDI is a circular slide-rule presented in McArthur (1967). For numerical analy-sis, equations derived by Noble et al. (1980) and modified by Griffiths (1999) were used to replicate the slide-rule. McArthur’s meter and Noble’s equations calculate FFDI from tempera-ture, relative humidity, wind speed, and fuel availability (called drought factor on the meter). The FFDI differs from the other systems in that there is no explicit calculation of fuel moisture on the slide-rule or in the Noble et al. equations. Instead fuel moisture is calculated implicitly by inclusion of air temperature and relative humidity in the slide-rule and equations. To allow direct comparison with the other indices it is necessary to re-formulate the FFDI to include an explicit fuel moisture calcula-tion. This is done in the section below describing the FFDI. The final part of this section briefly examines the mois-ture and fuel availability sub-models of each system. As the aim of this study is to examine the fire danger indices only, a detailed assessment of the moisture and fuel availability models is not presented. Experimental examinations of the FFDI (Viney and Hatton 1989), FFBT (Viney and Hatton 1989, Gould et al. 2007) and FWI (Simard and Main 1982, Simard et al. 1984, Wotton et al. 2005) moisture models have been presented elsewhere.

The Fire Weather Index

The FWI is calculated progressively, beginning with values for wind speed, W (km h-1), fuel moisture, M (%), and fuel availability, A. Valid ranges are , , and . First, response functions to wind, f(W) and mois-ture, f(M) are calculated (van Wagner 1987) …1 …2

These are combined to calculate the initial spread index, R …3

The initial spread index is multiplied by fuel availability to give an intermediate quantity, the ‘B-scale’ FWI …4

The B-scale is then rescaled to give the final FWI value, S

∈ ≤≥∞W (0,∞)

∈ ≤≥∞M (0,250)

∈A (0,1)

f (W )

f (W ) = e0.05039W

f (M)

f (W)f (M)R = 0.208

f (M) = 91.9e–0.1386M 1 + M 5.31 / 4.93 x 107

B = 4RA

S = { exp(2.72(0.434 lnB)0.647)B

B > 1

B < 1

∈ ≤≥∞W (0,∞)

∈ ≤≥∞M (0,250)

∈A (0,1)

f (W )

f (W ) = e0.05039W

f (M)

f (W)f (M)R = 0.208

f (M) = 91.9e–0.1386M 1 + M 5.31 / 4.93 x 107

B = 4RA

S = { exp(2.72(0.434 lnB)0.647)B

B > 1

B < 1

∈ ≤≥∞W (0,∞)

∈ ≤≥∞M (0,250)

∈A (0,1)

f (W )

f (W ) = e0.05039W

f (M)

f (W)f (M)R = 0.208

f (M) = 91.9e–0.1386M 1 + M 5.31 / 4.93 x 107

B = 4RA

S = { exp(2.72(0.434 lnB)0.647)B

B > 1

B < 1

∈ ≤≥∞W (0,∞)

∈ ≤≥∞M (0,250)

∈A (0,1)

f (W )

f (W ) = e0.05039W

f (M)

f (W)f (M)R = 0.208

f (M) = 91.9e–0.1386M 1 + M 5.31 / 4.93 x 107

B = 4RA

S = { exp(2.72(0.434 lnB)0.647)B

B > 1

B < 1

∈ ≤≥∞W (0,∞)

∈ ≤≥∞M (0,250)

∈A (0,1)

f (W )

f (W ) = e0.05039W

f (M)

f (W)f (M)R = 0.208

f (M) = 91.9e–0.1386M 1 + M 5.31 / 4.93 x 107

B = 4RA

S = { exp(2.72(0.434 lnB)0.647)B

B > 1

B < 1

∈ ≤≥∞W (0,∞)

∈ ≤≥∞M (0,250)

∈A (0,1)

f (W )

f (W ) = e0.05039W

f (M)

f (W)f (M)R = 0.208

f (M) = 91.9e–0.1386M 1 + M 5.31 / 4.93 x 107

B = 4RA

S = { exp(2.72(0.434 lnB)0.647)B

B > 1

B < 1

∈ ≤≥∞W (0,∞)

∈ ≤≥∞M (0,250)

∈A (0,1)

f (W )

f (W ) = e0.05039W

f (M)

f (W)f (M)R = 0.208

f (M) = 91.9e–0.1386M 1 + M 5.31 / 4.93 x 107

B = 4RA

S = { exp(2.72(0.434 lnB)0.647)B

B > 1

B < 1

Matthews: Fire danger rating systems for use in forests 43

…5

Examination of Eqns 3 – 5 shows that the fire weather index is a rescaling of the product of fuel availability and the fuel moisture and wind functions. The FWI does not use fixed values of S to determine fire danger rating class. Instead, values must be assigned for the region in which the index is to be applied (van Wagner 1987). Three methods have been suggested to do this: set the number of Extreme days de-sired then assign ranges based on climatology using geo-metric spacing (van Wagner 1987), use climatology to set range boundaries at 30th, 70th, 90th, and 97th percentile values (Kiil et al. 1977), or set range boundaries so that fire danger is proportional to fire intensity (de Groot et al. 2006). A set of rating class ranges for Canada from van Wagner (1987) is shown in Table 1. The Forest Fire Danger Index

McArthur (1967) presented the FFDI as a circular slide-rule but did not publish the underlying equations. Noble et al. (1980) used statistical methods to derive an equation for FFDI from the meter

…6

where F is the FFDI, T is air temperature (°C), H is relative humidity (%), W is wind speed (km h-1) and A is fuel avail-ability index (numerical value ranges from 0 to 1). Valid ranges for the statistical derivation of the numerical equa-tion from the slide-rule are , , ,and . This equation allows easy computation of FFDI but does not allow direct comparison with the FWI or FFBT. A compatible equation is derived by first rearranging Eqn 6: …7

Next, assume that F is the product of functions of fuel mois-ture, M, wind speed, W, and fuel availability, A …8 …9 …10 …11

T and H can be linked to M using Viney’s (1992) equation for fuel moisture derived from McArthur’s (1967) table

…12

where , , and .

A numerical approximation for f(M) can be constructed by calculating M over the range of T and H values for which Eqn 12 is valid when constrained by Eqn 10. The resulting equation is …13

Functions for curves in Figure 1 of McArthur (1967), show-ing rate of spread as a function of fuel moisture at four wind speeds, were fitted to a scanned image. The fitted curves had exponents ranging from -2.2 to -1.8, similar to Eqn 13. It is possible that the original meter was constructed using an M –2 function. Equations 8, 9, 10, and 13 can be used to calculate FFDI as a function of fuel moisture, wind, and fuel availability. The structure of the FFDI is similar to the FWI in that it is the prod-uct of fuel availability, fuel moisture, and wind functions. The fixed ranges for the FFDI rating classes are shown in Table 1.

The Forest Fire Behaviour Tables

The FFBT index for jarrah forest is calculated as a function of wind speed and fuel moisture F = Y + Ze

W2N …14

where Y = 21.37 – 3.42M + 0.085M2

Z = 48.09Me–0.6M + 11.9

W2 = rW N = –0.096M1.05 + 0.44

∈ ≤≥∞W (0,∞)

∈ ≤≥∞M (0,250)

∈A (0,1)

f (W )

f (W ) = e0.05039W

f (M)

f (W)f (M)R = 0.208

f (M) = 91.9e–0.1386M 1 + M 5.31 / 4.93 x 107

B = 4RA

S = { exp(2.72(0.434 lnB)0.647)B

B > 1

B < 1

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

∈ ≤≥∞W (0,65)

∈ ≤≥∞H (5,70)

∈ ≤≥∞T (5,45)

∈ ≤≥∞A (0,1)

f (A) = e0.987 ln(10A)

f (W) = e0.0234W

f (M) = e–0.0345H + 0.0338T

F = 2e–0.45 + 0.987 ln(10A)–0.0345H + 0.0338T + 0.0234W

f (M) = 27.3M–2.1

F = 1.275e0.987 ln(10A)e–0.0345H + 0.0338Te0.0234W

F = f (A,M,W ) = 1.275f (A)f (M )f (W )

M = 5.658 + 0.04651H + 0.0003151H 3T–1 – 0.1854T 0.77

5 < H < 70

10 < T < 41

42.5 – 1.25T < H < 94.5 – 1.35T

Class FFDI FFBT FWI-Canada

FWI-Camden

Low <5 <20 <5 <12

Moderate 5-12 21-40 5-8 12-24

High 12-24 41-140 9-16 24-47

Very High 24-50 141-240 17-29 47-94

Extreme >50 >240 >29 >94

Table 1. Fire danger index ranges for fire danger rating class-es. Ranges for FFDI, FFBT, and FWI-Canada are the values set in the definition of each index. Ranges for FWI-Camden were derived from weather observa-tions made at Camden.


in McArthur (1967) but have been determined from the FFDI meter by Griffiths (1999). The FWI calculates fuel availability, called ‘relative intensity’ by van Wagner (1987), from long term drought and duff moisture content. Long term drought is calculated using the drought code, in a manner similar to KBDI. Duff moisture content is calculated in a similar man-ner to fuel moisture using the duff moisture code, changes in which depend on rainfall, temperature, humidity, and day length. The equations for fuel availability, drought code, and duff moisture are given by van Wagner (1987). The FFBT does not use fuel availability in the fire danger calculation, although the effect of rainfall on its fuel moisture model acts to reduce fire danger after rain in a similar manner. Some of the principles used in these models are question-able. For example, rain affects fuel availability but not fuel moisture in the FFDI. However, because moisture and fuel availability are measurable quantities, the structures of the indices are independent of the sub-models and these could conceivably be changed at a future date if they are found to perform poorly.

Comparison of index structures

By examining the response of fire danger rating indices to changes in wind, fuel moisture, and fuel availability it is possible to understand how the indices differ. The response of each index to its inputs can be visualised by plotting fire danger as a function of one input while holding the others constant. For example, the response function of the FFDI to wind is defined as

…15

where X is the response function, F is FFDI (Eqn 8), and A0 , M0 , and W0 are constant values of fuel availability index, moisture, and wind speed at which X is normalised to equal 1. Similar functions are defined for X(M) and X(A), and for the FWI and FFBT using Eqns 5 and 14. Because the FFDI

and r is the ratio of the wind speed at 2 m height in the forest to the standard 10 m wind speed. Different values of r may be used to calculate fire danger for different forest types. The study in which these equations were derived (Beck 1995) used a reference forest with five years since the last fire, and a value of r = 5 corresponding to 60 per cent crown cover and flat terrain in Northern Jarrah forest. Valid ranges for windand fuel moisture are .................. and . Fuel avail-ability is not used in the calculation. The fixed ranges for the FFBT rating classes are shown in Table 1.

Fuel moisture and fuel availability models

McArthur included a simple table predicting fuel moisture as a function of temperature and relative humidity in the de-scription of the FFDI (McArthur 1967). This model is imple-mented implicitly using the temperature and relative humid-ity wheels on the FFDI circular slide rule. For the present study Viney’s (1992) equation, Eqn 12, was used. The FWI predicts fuel moisture using a moisture index, the fine fuel moisture code (FFMC). Day to day changes in the FFMC are calculated as a function of temperature, relative humidity, rainfall, and wind speed. FFMC is converted to fuel moisture by a scaling function. The equations for the FFMC are given by van Wagner (1987). The FFBT uses book-keeping meth-ods to predict fuel moisture, M, in the morning as a function of the previous day’s afternoon M and rainfall or overnight relative humidity. Afternoon M is predicted from morning M and a drying function determined from afternoon air tem-perature and relative humidity. Equations are given in Beck (1995). The FFDI meter calculates fuel availability, called ‘drought factor’ by McArthur (1967), from soil moisture deficit, time since last rain and rainfall amount. Soil moisture deficit is calculated using the Keetch-Byram drought index (KBDI, Keetch and Byram 1968) or the soil dryness index (SDI, Mount 1972). The structure and climatology of the KBDI and SDI across Australia have been reviewed by Finkele et al. (2006). Equations for the fuel availability calculation were not given

∈ ≤≥∞W (0,67)

∈ ≤≥∞W (0,55)

∈ ≤≥∞M (3,∞)

∈ ≤≥∞M (3,17)

∈ ≤≥∞A (0,1)

X(W ) =F(A = A0,M = M0,W)

F(A = A0,M = M0,W = W0)

∈ ≤≥∞W (0,67)

∈ ≤≥∞W (0,55)

∈ ≤≥∞M (3,∞)

∈ ≤≥∞M (3,17)

∈ ≤≥∞A (0,1)

X(W ) =F(A = A0,M = M0,W)

F(A = A0,M = M0,W = W0)

∈ ≤≥∞W (0,67)

∈ ≤≥∞W (0,55)

∈ ≤≥∞M (3,∞)

∈ ≤≥∞M (3,17)

∈ ≤≥∞A (0,1)

X(W ) =F(A = A0,M = M0,W)

F(A = A0,M = M0,W = W0)

0 10 20 30 40 50 60

0.0

0.2

0.4

0.6

0.8

1.0

Wind speed (km h−1)

Res

pons

e fu

nctio

n

a)

0 5 10 15

0.0

0.2

0.4

0.6

0.8

1.0

Fuel moisture (%)

Res

pons

e fu

nctio

n

b)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fuel Availability

Res

pons

e fu

nctio

n

c)

0 10 20 30 40 50 60

0.0

0.2

0.4

0.6

0.8

1.0

Wind speed (km h−1)

Res

pons

e fu

nctio

n

a)

0 5 10 15

0.0

0.2

0.4

0.6

0.8

1.0

Fuel moisture (%)

Res

pons

e fu

nctio

n

b)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Fuel Availability

Res

pons

e fu

nctio

n

c)

Fig. 1 Response of fire danger to (a) wind speed, (b) fuel moisture, and (c) fuel availability, calculated using Eqn 15. Black line is FFDI, black shading is FFBT, and grey shading is FWI.


The response of all three indices to changing wind speed is approximately exponential, as expected from the forms of Eqns 1, 11, and 14. The FFDI is least sensitive to wind and the FFBT most sensitive over the ensemble of M and A values. At zero wind speed, the FFDI is 28 per cent of the reference value, and the averages of the FWI and FFBT ensembles are 14 per cent and 1 per cent respectively. There is greater vari-ation in the response of the FWI compared to the FFBT, due to the inclusion of A in the FWI. Fire danger decreases with increasing fuel moisture in all systems, with the curves following approximately the power law or exponential decay curves of the underlying equa-tions. The FFDI is most sensitive to M, while the FWI is least sensitive. At M = 10%, FFDI drops to 8 per cent of the refer-ence value, compared to 20 per cent for the FFBT and 54 per cent for the FWI. At M = 17%, FFDI drops to 3 per cent of the reference value, the FFBT to 8 per cent, and the FWI to 28 per cent. As with wind, there is greater spread in the FWI ensemble compared to the FFBT due to the inclusion of A in the FWI. Thus all the systems examined exhibit similar functional responses to changing M, W, and A: they are approximately linear with respect to A, increase exponentially with W, and drop off rapidly with M at low M and more slowly at higher M. However, the specific dependence on each variable varies greatly between systems. This results in a wide spread in the fire danger rating assigned by each system to a given set of M, W, and A, as is shown in the next section.

Comparison of index values

The interaction of the differences in structure can be exam-ined by comparing the index values over the range of fuel availability, fuel moisture and wind where the systems are valid. A comparison of FFDI, FWI, and FFBT for fuel avail-ability from zero to maximum, fuel moisture from 3 per cent to 17 per cent, and wind speed from 0 to 55 km h-1 is shown in Fig. 2. Because the numerical scales of the indices are ar-bitrary, the thresholds of the fire danger rating classes are

is a product of functions of A, M, and W (Eqn 8) there is a unique X(W) for any given W0 , independent of the choice of M0 and A0 , and similarly for X(M) and X(A). By choos-ing reference values of the indices defined by W0 = 55 km h-1, M0 = 3%, and A0 = 1, unitless response curves can be calculated for the FFDI. The shape of the curves (Fig. 1) on an arbitrary scale is independent of the choice of A0 , M0 , and W0 . Because FWI and FFBT are not simple products of functions of M, A, and W, there is not a unique X(W) in-dependent of M0 and A0 for a given W0 , and similarly for X(M) and X(A). It is thus necessary to calculate an ensemble of X functions for each variable to cover the full range of the other two variables, e.g. there are many X(W) that cover the range of possible combinations of M0 and A0 . Figure 1 shows the ensemble of response curves, X for the FWI using , , , and for the FFBT over the same ranges of M and W. The FFBT does not use A. The M, W, and A ranges are the widest span allowed in each vari-able such that the values are valid for all three indices. For the comparison shown in Fig. 1 to be valid there needs to be a linear relationship between the rating class ranges for the indices, so that a change in the response function can be interpreted as the same change in rating class for all three indices. Since the FFDI and FFBT use geometric spacing, a comparison is possible only if the FWI also uses a geometric spacing. This is the case for the values in Table 1 from van Wagner (1987). If FWI rating class ranges were assigned by a method which did not produce a geometric spacing then the comparison shown in Fig. 1 would not be valid. The FFDI exhibits a simple linear response to fuel avail-ability, with no fire danger when fuel availability is zero and maximum fire danger when all fuel is available to burn. Al-though it has the same end points, there is some spread in the FWI ensemble. FWI increases more rapidly than FFDI at low fuel availability; for example at A=0.1, FWI is 30 per cent of maximum while FFDI is only 10 per cent. Except for some combinations of W and M at low A, FWI is closer to its maximum than FFDI for a given fuel availability.

FFDI

FW

I

1 10 100

1

10

100

L M H V E

FFDI

FF

BT

1

10

100

1000

1 10 100

L M H V E

L

M

HV

E

FFBT

FW

I

1 10 100 1000

1

10

100

L M H V E

FFDI

FW

I

1 10 100

1

10

100

L M H V E

FFDI

FF

BT

1

10

100

1000

1 10 100

L M H V E

L

M

HV

E

FFBT

FW

I

1 10 100 1000

1

10

100

L M H V E

Fig. 2 (a) Comparison of FFDI and FWI for common fuel moisture, wind, and fuel availability values, (b) FFDI and FFBT, (c) FFBT and FWI. Vertical and horizontal lines are the boundaries between fire danger rating classes: Low, Moderate, High, Very high, and Extreme. Black points indicate A = 1, grey points indicate A < 1.

∈ ≤≥∞W (0,67)

∈ ≤≥∞W (0,55)

∈ ≤≥∞M (3,∞)

∈ ≤≥∞M (3,17)

∈ ≤≥∞A (0,1)

X(W ) =F(A = A0,M = M0,W)

F(A = A0,M = M0,W = W0)

∈ ≤≥∞W (0,67)

∈ ≤≥∞W (0,55)

∈ ≤≥∞M (3,∞)

∈ ≤≥∞M (3,17)

∈ ≤≥∞A (0,1)

X(W ) =F(A = A0,M = M0,W)

F(A = A0,M = M0,W = W0)

∈ ≤≥∞W (0,67)

∈ ≤≥∞W (0,55)

∈ ≤≥∞M (3,∞)

∈ ≤≥∞M (3,17)

∈ ≤≥∞A (0,1)

X(W ) =F(A = A0,M = M0,W)

F(A = A0,M = M0,W = W0)

a) b) c)


also shown for the FFDI and FFBT. Because the thresholds of the FWI are not fixed, these are not included. All three indices were correlated but there was consider-able scatter. The scatter in the FFDI vs FFBT comparison was not due only to the absence of fuel availability in the FFBT as there was also considerable scatter for points where fuel availability was at its maximum. Given that each point in Fig. 2b represents a particular set of measurable fuel and weath-er conditions, it is interesting that the FFDI and FFBT ratings differ widely as these were both designed for application in eucalyptus forest. Less scatter was seen in the comparison of FFDI and FWI. Inclusion of fuel availability in both indi-ces may have contributed to the lower amount of divergence than between FFDI and FFBT. As these systems were de-signed for different forest types, divergence in assessment of given conditions was not unexpected. For maximum fuel availability, there was a very good correlation between FFBT and FWI, such that FWI threshold values could easily be se-lected such that both systems gave the same rating for any given M and W values. For fuel availability values other than the maximum the non-inclusion of fuel availability in the FFBT resulted in more scatter. The differences in index values given to identical condi-tions by the three systems demonstrate that although each was constructed using the same underlying principles, the particular forms chosen for the equations resulted in widely diverging assessments of identical conditions. For opera-tional adoption, however, the systems would not usually be applied to identical M, W, and A values as done here because each system is used as a package with its own moisture and fuel availability models and using slightly different weather inputs. The next section examines the three indices in a real world case study.

A case study

In the previous section it was shown that for given fuel mois-ture, wind, and fuel availability conditions the FFDI, FFBT, and FWI were often very different. However, the sub-models

used to calculate fuel moisture and fuel availability also differ and the indices are calculated using weather observations at differing times of the day. The interaction of these three factors was examined using a case study. Daily fire danger indices were calculated using thirteen years of automatic weather station data from Camden airport in NSW, Austra-lia (34° 2’ S, 150° 41’ E). The AWS is located on the urban fringe in the Sydney sandstone basin, at an altitude of 74 m. Mean annual rainfall is 774 mm. Index values were calcu-lated using the temperature, wind, and humidity observa-tions specific to each system: 1500 local time values for the FFDI (McArthur 1967), 1200 local time values for the FWI (van Wagner 1978), and daily extreme values for the FFBT (Sneeuwjagt and Peet 1998). All indices use daily rainfall ob-servations. KBDI (Keetch and Byram 1968) was used in the calculation of drought factor for the FFDI. Overnight relative humidity count for the FFBT was calculated by numerical integration of relative humidity observations above 70 per cent (Sneeuwjagt and Peet 1998). FWI rating class ranges were determined using the method of van Wagner (1987). The lower boundary of the Extreme class was set to 94, so that the number of Extreme days in the data set was 5, the average of number of extreme days for the FFDI (6 days) and FFBT (4 days). To preserve the relationships shown in Fig. 1, the remaining class boundaries were then spaced geometri-cally (Table 1). A comparison of the indices shows considerable scatter (Fig. 3) but less than was seen in Fig. 2. This was due to dif-ferences in the weather and sub-models compensating for the difference in the index structures. For example, the FWI tended to predict higher M than the FFDI, compensating for the FFDI’s higher sensitivity to M. Also, the lack of a drought index in the FFBT was compensated for by the fuel moisture model which allows very high values after rain, in contrast to the FFDI which has M constrained to below 17 per cent at all times. The overall mass of observations fell along the line of equal ratings and 96 per cent of observations were within one rating class difference for all three indices. The same

FFDI

FW

I

1 10 100

1

10

100

L M H V E

L

M

H

V

Ea)

FFDI

FF

BT

1

10

100

1000

1 10 100

L M H V E

L

M

HV

E

b)

FFBT

FW

I

1 10 100 1000

1

10

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L M H V E

L

M

H

V

Ec)

FFDI

FW

I

1 10 100

1

10

100

L M H V E

L

M

H

V

Ea)

FFDI

FF

BT

1

10

100

1000

1 10 100

L M H V E

L

M

HV

E

b)

FFBT

FW

I

1 10 100 1000

1

10

100

L M H V E

L

M

H

V

Ec)

Fig. 3 Case study using observations from Camden AWS. (a) FFDI and FWI, (b) FFDI and FFBT, (c) FFBT and FWI. Vertical and horizontal lines are the boundaries between fire danger rating classes: Low, Moderate, High, Very high, and Extreme.


rating class was assigned for 62 per cent of observations. Figure 3 shows that FWI rating class ranges can be chosen to give the same ratings as the FFDI and FFBT. However, in a comparison of the FFDI and FWI using daily extrema in weather observations from a network of Australian stations, Finkele and Mills (2006) found that least-squares fitted linear relationships between FFDI and FWI were site specific. Thus a universal scaling is not possible; rating class ranges have to vary with climate.

Discussion

Fire danger encompasses all those factors which determine ignition, spread, suppression difficulty and damage caused by fires. As such, fire danger index is not a physical quantity that can be measured with any instrument and must be in-terpreted as expert judgements of the effects of weather con-ditions on fire danger. Assessment of the indices must also be an expert judgement of how well each system is suited to fire management in a given location. However, fire danger is related to fire behaviour. Fires which are intense and fast moving are more difficult to suppress and likely to do more damage than slower, less intense fires. So while there need not be a strict correspondence between fire danger and fire behaviour, the fire danger indices should reflect our under-standing of fire behaviour. Since the development of the fire danger indices, under-standing of the fire behaviour in forests has changed signifi-cantly. Measurements from experimental fires in eucalyptus have shown the effect of wind on rate of spread increases as a power law with exponent of 1 or less (Gould et al. 2007), rather than the exponential increase used in the three fire danger indices (Fig. 1). Discussing the implications of simi-lar experimental findings for grass fires, Cheney and Gould (1995) argued that although rate of spread was directly pro-portional to wind speed (Cheney et al. 1993), fire danger should increase exponentially because ‘due to spotting, fan-ning smouldering combustion, and erratic fire behaviour... it may well be that suppression difficulty increases exponen-tially as wind speed increases’. Gould et al. (2007) also found that fuel arrangement was a better predictor of fire behaviour than simply fuel load but that the two measures were correlated. Burrows (1999b) did not observe a significant relationship between fuel load and rate of spread in experimental fires in eucalyptus forest. These results contrast with the assumption of the FFDI and FWI that rate of spread is proportional to surface fuel load, expressed as fuel availability (McArthur 1967, van Wagner 1987). As was the case with wind speed, there are good rea-sons to expect fire danger to increase with fuel availability since intensity increases as a greater proportion of the litter fuel is burnt and other fuel components such as bark and coarse fuels burn more readily. That fire danger decreases as fuel moisture increases is in

agreement with experimental observations (Burrows 1999a, 1999b, Gould et al. 2007). It is known that pine fuels remain flammable at higher moisture contents than eucalyptus for-est (Cheney 1985, Woodman and Rawson 1982). Thus, fire danger should drop more rapidly with increasing moisture content in eucalyptus forest than in pine forest and so the FWI is possibly more suited to the pine forests for which it was developed, and similarly the FFBT and FFDI to eucalyp-tus forest (Fig. 1). Finally, while there need not be a strict correspondence between fire danger index and fire behaviour, the fuel avail-ability and moisture sub-models must be accurate. If either of these models incorrectly predict the state of the fuel then the rating system that uses the sub-models cannot be expected to give a good assessment of fire danger. Any future studies that seek to assess fire danger indices against quantifiable outcomes (e.g. area burned or number of fires) should treat the sub-models as well as the indices. Failure to do so may result in erroneous conclusions about the adequacy of the indices. If any of the sub-models are found to perform poor-ly, it is possible to replace them with better models without needing to modify the fire danger indices in any way.

Conclusions

This study has examined the structure and predictions of three fire danger rating indices: the Forest Fire Danger In-dex, the Forest Fire Behaviour Tables, and the Fire Weather Index. Despite differences in presentation, all three indices calculate fire danger in a similar manner and provide the same type of information to the fire manager. There are differences in the specifics of each index which meant that for a given combination of wind speed, drought, and fuel moisture the indices differed widely in their assessment of fire danger. However, when the indices, including their fuel availability and moisture sub-models, were applied in a real world case study there was closer agreement in their predic-tions. Qualitative consideration of the factors contributing to fire danger and fire behaviour suggest that the structures of the indices are physically plausible.

Acknowledgments

Comments by my CSIRO colleagues Andrew Sullivan and Miguel Cruz and from the anonymous reviewers helped to improve the original manuscript.

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