program intended as a standard for processing the equations in their most accurate ..... unless r 0> 2.8; that is, in
4. 3. 2. 5. 6. 7.
THE CANADIAN FORESTRY SERVICE GOVERNMENT OF CANADA
SERVICE CANADIEN DES FORETS GOUVERNEMENT DU CANADA
The Canadian Forestry Service is the principal source of federal expertise in forestry and has been designated as the government's lead agency for forestry matters. Its general objective is to promote the wise management and use of Canada's forest resources for the economic, social and environmental benefit of Canadians.
Le Service canadien des forets (SCF) reunit la majorite des specialistes federaux en foresterie; il a ete designe comme I'organisme officiel du gouvernement responsable du secteur forestier. Son objectif general est de promouvoir I'amenagement et I'utilisation judicieux des ressources forestieres du Canada pour Ie plus grand bien economique, social et environnemental des Canadiens.
The following are the main functions of the CFS: 1,
Coordination of federal policies for the promotion of better resource management and forest industry development. Provision of scientific and technological leadership in forestry through research and development.
Voici les principales fonctions du SCF: 1.
2.
Provision and analysis of national and international statistics and information as a basis for policy formulation. Development and certification of codes and standards for wood product performance. Protection of Canada's forests from foreign pests.
5.
Fostering the potential use of the forest resource for energy. Contributing to the environmental objectives of the Government of Canada.
6. 7.
Coordonner leg politiques federales afin de favoriser I'amelioration de la gestion des ressources et I'expansion de I'industrie forestiere. Fournir une orientation scientifique et technologique dans Ie domaine de la foresterie, par la recherche et Ie developpement.3. Fournir et analyser leg statistiques et I'informalion nationales et internationales qui serviront a etablir leg politiques.4. Mettre au point et homologuer des codes et des normes en matiere de rendement des produits du bois. Proteger leg forets canadiennes en luttant contre leg ravageurs etrangers. Parrainer I'utilisation eventuelle des ressources forestieres pour la production d'energie. Adherer aux objectifs environnementaux du gouvernement federal.
Canadian Forestry Service programs are coordinated with those of other forestry agencies through a variety of mechanisms, including the Canadian Council of Forestry Ministers, the Forest Sector Strategy Committee, management committees for Federal-Provincial Forestry Development programs, national and regional Research Advisory Commit-tees, and various technical committees for specific program areas.
Les programmes du SCF sont menes de concert avec ceux d'autres organismes forestiers par I'entremise de divers mecanismes dont Ie Conseil canadien des ministres des Forets, Ie Comite de la strategie forestiere, les comites de gestion des programmes federaux-provinciaux de developpementforestier, les comites nationaux et regionaux consultatifs sur la recherche, de meme que divers comites techniques axes sur des domaines de programmes specifiques.
The Canadian Forestry Service is comprised of a headquarters unit, six forestry centres, and two national institutes. The forestry centres are responsive to regional priorities and maintain close liaison with the respective provincial government forestry departments and other clients. They also participatein, and frequently lead, national programs. The national institutes provide the focus for programs of national scope.
Le SCF comprend une administration centrale, six centres de foresterie et deux instituts nationaux. Les centres de foresterie doivent repondre aux imperatifs regionaux et entretenir une liaison etroite avec leg ministeres provinciaux des Forets. lis participent egalement a des programmes nationaux dont ils assument frequemment la direction. Les instituts nationaux sont leg foyers des programmes d'envergure nationale.
C.E. Van Wagner and T.L. Pickett Petawawa National Forestry Institute
Canadian Forestry Service Government of Canada Forestry Technical Report 33
Ottawa 1985
@Minister of Supply and Services Canada 1985 ISBN 0-662-13906-2 Cat. No. Fo64-33/1985E Additional copies of this publication are available at no charge from: Canadian Forestry Service Place Vincent Massey, 3rd Floor Ottawa, Ontario K1A 1G5 A microfiche edition of this publication may be purchased from: Micromedia Ltd. 158 Pearl Street Toronto, Ontario M5H 1L3 Cette publication est aussi disponible en franl;ais so us Ie titre Equations et programme FORTRAN de /'Indice Foret-Meteo de la methode canadienne. First printing 1985 Second printing 1987
Abstract. Resume.. 11
CONTENTS Page IV
.
IV
Introduction. Symbols in the Equations
3
Equations and Procedures.
5
Description of Program.
9
Symbols in the Program
Program F-32.
12
Sample of Input. .
16
Sample of Output
17
References
III
.18
ABSTRACT Improved official equations are presented for the 1984 version of the Canadian Forest Fire Weather Index System. The most recent mathematical refinements serve to further rationalize the Fine Fuel Moisture Code and render it more compatible with other developments in the Canadian Forest Fire Danger Rating System. The effect of these changes is so slight that no problems are anticipated in converting from the previous version to this new one. Also given is a FORTRAN program intended as a standard for processing the equations in their most accurate mathematical
form.
RESUME Ce rapport presente, en complement au systeme de l'lndice canadien foret-meteo, des equations connues qu'on a retouchees. Ces precisions mathematiques veulent rendre I'indice du combustible leger plus rationnel et davantage compatible avec les nouveaux developpements que conna!t la Methode canadienne d'evaluation des dangers d'incendie de foret. II s'agit de changements mineurs qui ne devraient pas faire probleme advenant qu'une equation de la version anterieure soit a convertir. Le programme FORTRAN se veut une base pour traiter des equations dans Ie plus pur langage mathematique.
1\/
3. 2. 4. 5.
INTRODUCTION The present report is a companion to the fourth edition of the Tables for the Canadian Forest Fire Weather Index System (Canadian Forestry Service 1987). The equations on which this new edition is based are presented here. Also included is a computer program incorporating the mathematical routines leading to the Fire Weather Index (FWI). It is written in FORTRAN 77 to run on a DEC PDP-11/44. With proper modification it could be handled by many smaller computers. The report is a replacement of Information Report PS-X-58 (Van Wagner and Pickett 1975'), which listed equations for the 1976 version of the Fire Weather Index (FWI) System. The development and structure of the FWI System were described originally by Van Wagner (1974) in Canadian Forestry Service Publication 1333, butthe mathematics in that paper are partly obsolete. Publication 1333 has now been replaced by Forestry Technical Report 35 (Van Wagner 1987). The 1976 version of the FWI System listed the following mathematical changes from the original 1970 version:
1
Change in equation giving the equilibrium moisture content (EMC) during a wetting cycle in the Fine Fuel Moisture Code (FFMC), to eliminate an anomaly at very high relative humidity
(RH); Replacement of the original temperature correction in the FFMC with separate temperature effects on EMC and drying rate; Increase in the amount of rain discarded in the Drought Code (DC) from 1.524 mm to 2.8 mm; . Change in the buildup function, f(D), at Buildup Index (BUI) values over 80, in order to cause the FWI to level off in extreme drought. Note: Further acronyms and symbols are defined in accompanying lists. The additional mathematical changes in the present version further rationalize the structure of the FFMC. This code has worked adequately, but new developments in the Canadian Forest Fire Danger Rating System (CFFDRS), of which the FWI System is a part, create a need for a) realistic conversions from code value to actual fuel moisture, b) a common basis for the standard daily FFMC and its round-the-clock hourly version (Van Wagner 1977) and, c) ready modification for special purposes. Accordingly, the new FFMC incorporates the following alterations: 1,
A new moisture scale, the FF-scale, with a higher maximum possible moisture content (250% instead of 101%);
2.
A new rain-effect equation that operates on moisture content rather than on code value;
3.
An adjusted drying rate that operates on the moisture content as expressed by the new moisture scale, but results in the same rate of change in code value as before; A variable wetting rate when the EMC is higher than the initial moisture content, in place of the fixed rate used previously, and; An adjustment of the fine fuel moisture function, f(F), in the Initial Spread Index (IS I), to fit the new higher moisture conversion scale.
1C.E. Van Wagner is a research scientist, and T.L. Pickett is a computer programmer at the Petawawa National Forestry Institute, Chalk River, Ontario KOJ 1JO.
1
These changes have been accomplished with very little difference in the output of the system of equations. That is, the resulting codes and indexes will be sufficiently similar for daily use of the system to continue uninterrupted and for the statistical continuity of annual records to be pre-
served. As before, the computer program is set up for the calculation at one time of an entire season's output for one station only. Its primary purpose is to illustrate the programming of the equations in order to give the purest possible mathematical output, with no artificial constraints or limits other than those required by the nature of the equations. It is intended to serve as a standard of comparison by which the output of any other program may be tested. This 1984 version (as well as the previous version) includes the computation of the Daily Severity Rating (DSR), as described by Van Wagner (1970). The DSR is a function of the FWI specifically designed for averaging, either for any desired period of time at a single location, or as an area average of any number of locations. The FWI itself, on the other hand, is not considered suitable for averaging, and should be used as its single daily value only. The DSR averaged over a whole season, for example, would be called the Seasonal Severity Rating (SSR) and could be used for comparing fire weather from year to year, or fire climate from place to place.
2
SYMBOLS IN THE EQUATIONS All quantities used in the numbered equations are represented in the following list by single letters, sometimes with subscripts. The symbols are arranged in groups according to their place in the whole. All moisture contents are percentages based on dry weight. Noon refers to standard time.
WEATHER -noon
temperature,
°C
-noon
relative humidity, %
-noon
wind speed,
km/h
-effective
rainfall, FFMC
-effective
rainfall, DMC
-effective
rainfall, DC
FINE FUEL MOISTURE CODE (FFMC)
-fine
fuel moisture content after rain
-fine
fuel moisture content after drying
-fine
fuel EMC for drying
-fine
fuel EMC for wetting
-
-intermediate -log
step in, calculation of kd
drying rate, FFMC, log1om/day
-intermediate -log
step in calculation of kw
wetting
-previous
rate, log10m/day
day's FFMC
-FFMC
DUFF MOISTURE CODE (DMC)
-duff
moisture content after rain
-duff
moisture content after drying
-log
drying
-effective -slope -previous -DMC
-DMC
3
rate in DMC,
log1oM/day
day length in DMC, hours variable in DMC rain effect day's DMC after rain
. .
DROUGHT CODE (DC)
-DC FIRE BEHAVIOR INDEXES (ISI, BUI, FWI) f(W)
-wind
f(F)
-fine
SEVERITY
4
function
fuel moisture function
RATING
2. 6. 8.
EQUATIONS AND PROCEDURES FINE FUEL MOISTURE CODE (FFMC) mo =
147.2 (101 -Fo)/(59.5
+ Fo)
(1)
rf
= r 0 _ 05.,
mr
=
mo + 42.5
mr
=
mo + 42.5 rf (e-1OO/(251-moI)(1-e-6.93ir')+O.0015
ro > 0.5 rf (e-100/(251-mo)X1 -e-6.93/r,), (mo -150)2
Ed = 0.942 HO.679+ 11e(H-100)/10 +0.18
(21.1-T)(1-e-O.115H)
Ew
(21.1 -T)(1
ko
~ kl
=
0.618
HO.753 + 10e (H-100)/10 +0.18
=
0.424 [1-(H/100)1.7]
=
ko x 0.581 eO.O365T
, k1
+ 0.0694 WO.51-
100
=
m
= Ed + (mo -Ed)
x 10-~
m
=
x
F
= 59.5 (250-m)/(147.2
-(Ew
( ~)8] 100
eO.O365T
-mo)
mo:5
150
(3a)
mo>
150
(3b) (4) (5) (6a) (6b)
kw
Ew
X 0.581
+0.0694 Wo.s [1-(H/100)81
[
= 0.424 1-(~)1.7]
-e-O.115H)
rfo.s,
(2)
(7a) (7b) (8)
10-kw
(9)
+ m)
(10)
The FFMC is calculated as follows:
1.
Previous day's F becomes Fo. Calculate
mo from F 0 by Equation
1.
3a. If ro > 0.5, calculate rf by Equation 2. b. Calculate mr from rf and mo by Equation 3a or 3b. (i) If mo :5 150, use Equation 3a. (ii) If mo > 150, use Equation 3b. c. Then, mr becomes the new mo'
4.
Calculate Ed by Equation 4.
5a, If mo > Ed, calculate kd by Equations 6a and 6b. b. Calculate m by Equation 8. If mo < Ed, calculate Ew by Equation 5. 7a. If mo < Ew, calculate kw by Equations 7a and 7b. b. Calculate m by Equation 9. If Ed 2: mo 2: Ew, let m = mo.
9.
Calculate F from m by Equation 10. This is today's FFMC.
There are two restrictions in the use of these equations: 1) Equation 3 (a or b) must not be used when ro ~ 0.5 mm; that is, in dry weather the rainfall routine must be omitted. 2) m has an upper limit of 250; that is, when Equation 3 (a or b) yields mr > 250, let mr = 250.
5
DUFF MOISTURE CODE (DMC) re
M
0
ro> 1.5
=
O.92ro
-1.27,
=
20 + e(5.6348-PJ43.43)
(11) (12)
b
= 100/(0.5 + 0.3 Po),
Po .$; 33
(13a)
b
=
14 -1.3
33 65
(13c)
Mr
= Mo + 1000re/(48.77
In Po'
=
244.72
K
=
1.894 (T + 1.1) (100 -H)
p
= Po (or Pr) + 100K
Pr
-43.43
+ bre)
(14)
In (Mr -20)
(15) Lex 10-6
(16)
(17)
The DMC is calculated as follows 1
Previous
2a. b. c. d. e.
If ro > 1.5, calculate re by Equation 11. Calculate Mo from Po by Equation 12. Calculate b by the appropriate one of Equations 13a, 13b, or 13c Calculate Mr by Equation 14. Convert Mr to P r by Equation 15. P r becomes new Po.
3,
Take Le from Table 1 below.
4
Calculate K by Equation 16.
5
Calculate P from Po (or Pr) by Equation 17. This is today's DMC.
day's P becomes
Po'
There are three restrictions on the use of the DMC equations: 1) Equations 11 to 15 are not used unless r 0 > 1.5; that is, the rainfall routine must be omitted in dry weather. 2) P r cannot theoretically be less than zero. Negative values resulting from Step 2e above must be raised to zero. 3) Values of T less than -1.1 must not be used in Equation 16. If T < -1.1, let T = -1.1. Table 1 Effective
day-lengths
(Le) for DMC
DROUGHT CODE (DC)
6
-1.27,
r> 2.8
=
O.83ro
00
=
800e-DJ400
(19)
Or
=
00
(20)
Dr
=
400 In(800/Qr)
v
= 0.36 (T + 2.8) + ~
(22)
D
=
(23)
rd
+ 3.937r d
Do (or Dr) + Q.5V
(18)
(21 )
5. f(W) FIRE 8>1 S
The DC is calculated as follows:
1.
Previous day's 0 becomes Do.
2a. b. c. d.
If ro > 2.8, calculate rd by Equation 18. Calculate 00 from Do by Equation 19. Calculate Or by Equation 20. Convert Or to Dr by Equation 21. Dr becomes new Do'
3.
Take 4 from Table 2 below.
4.
Calculate V by Equation 22. Calculate D from Do (or Dr) by Equation 23. This is today's DC.
There are four restrictions on the use of the DC equations: 1) Equations 18 to 21 are not used unless r 0> 2.8; that is, in dry weather the rainfall routine must be omitted. 2) Dr cannot theoretically be less than zero. Negative values resulting from Step 2d above must be raised to zero. 3) Values of T less than -2.8 must not be used in Equation 22. If T < -2.8, let T = -2.8. 4) V cannot benegative. If Equation 22 produces a negative result, let V = O.
Table 2 Day-length factors (LJ for DC
-1.6
INITIAL SPREAD =
-1.6
-1.6
INDEX (ISI)
eOO5039W
(24)
f(F)
= 91.ge-O.1386m[1 +mS.31/(4.93 X 107)]
(25)
R
= 0.208 f(W) f(F)
(26)
BUILDUP
INDEX (BUI)
u
= 0.8 PO/(P + 0.40),
u
= P -[1
P s 0.40
(27a)
P > 0.40
(27b)
1(0) = O.626Uo.809 + 2,
U:s;80
(28a)
f(O) = 1000/(25 + 108.64 e-O.O23U),
U > 80
(28b)
WEATHER
B
-O.8D/(P
+ O.4D)][O.92 + (O.O114P)1.7],
INDEX (FWI)
= 0.1 R 1(0)
(29)
InS = 2.72 (0:434 In 8)0-647,
= B,
7
(30a) B:51
(30b)
2. 3. 4. 6.
The ISI, BUI, and FWI are calculated as follows: 1,
Calculate f(W) and f(F) by Equations 24 and 25. Calculate R by Equation 26. This is today's 151. Calculate U by Equation 27a if P :5 0.40, or by Equation 27b if P > 0.40. This is today's
BUI. Calculate f(O) by Equation 28a for values of U up to 80. If U > 80, use Equation 28b.
5.
Calculate B by Equation 29. If B > 1, calculate S from its logarithm, given by Equation 30a. S = B according to Equation 30b. S is today's FWI.
If B s 1, let
DAILY SEVERITY RATING (DSR) DSR
8
=
0.0272
(FWI)1.77
(31 )
DESCRIPTION
OF PROGRAM
The computer program presented here descends from one written by Simard (1970) at the former Forest Fire Research Institute. That program was designed to process weather data from many stations for a whole season. There was provision for missing data and for limits to guard against abnormal weather data. It was a complex program requiring, at the time, considerable computer capacity. Simard's program was simplified by Engisch and Walker (1971) to handle one season's verified weather data for one station only, eliminating all unnecessary limits. Kean (1975) subsequently revised this program, incorporating several newly developed mathematical changes. However, the decision to convert to metric weather measurements rendered his version obsolete. Information Report PS-X-58 (Van Wagner and Pickett 1975) included the metric successor to Kean's program. The program listed in this report incorporates the mathematical changes described earlier, but is similar in usage to the one in PS-X-58. To operate this program, enter first the starting month and the number of days of data in that month. For example, if the starting month is April and the first day is April 13, there will be data for 18 days in month 4, and the entry will be 418. Then enter the daily weather observations in order: temperature (OC), relative humidity (%), wind (km/h), and rain (mm). Temperature and rain are entered to the first decimal place; relative humidity and wind are entered in whole numbers. The option of entering weather data in Imperial units is provided, but the output converts them to metric. The standard starting values of the three fuel moisture codes, namely FFMC 85, DMC 6, and DC 15, are incorporated in the program. However, the option of entering any desired starting values is also provided. The output is listed in twelve columns: date (month and day), the four kinds of weather data, the three fuel moisture codes (FFMC, DMC, DC), the three fire behavior indexes (ISI, BUI, FWI), and the Daily Severity Rating (DSR). The computer stops automatically after the last day's weather. The program includes no limits on the input data other than those needed to prevent mathematical anomalies. All moisture codes are carried from day to day in precise floating-point format, as are all intermediate quantities leading to the daily FWI. The output is thus in the purest possible mathematical form and constitutes a reference against which calculations from other computer programs or from the FWI System Tables (Canadian Forestry Service 1984) may be compared. The main uses of this standard program 1 are for development work on the FWI System, and for reference purposes as described previously. Operational programs designed for processing daily weather observations from many stations throughout a fire season will naturally have different input and output arrangements. Two points warrant comment. The first is the degree of precision necessary when printing out the daily codes and indexes. The standard program rounds all codes and indexes to the nearest tenth, and prints them out to one decimal place. However, whole-number (i.e., integer) output is, no doubt, adequate for most operational purposes. In certain cases, the first decimal may be desirable for the FFMC (especially above 90), and for the ISI (especialy below 10). The DSR is given to two decimal places, and is best used in that form. The second comment refers to the precision with which the three moisture codes (FFMC, DMC, and DC) are carried over from day to day. The standard program carries over each day's code values in full floating-point format, equivalent to about seven significant figures (four or five decimal places). However, if computer storage capacity is a limiting factor, something less than perfect accuracy in output may be acceptable in operational use. Trials were made at three reduced levels of the precision to which the three moisture codes are carried over from day to day: 1) two decimals, 2) one decimal, and 3) integers. The results of two seasons' tests, as percentage of error-days in the output of each code and index, are listed in Table 3.
1Designated Canadian
9
Program F-32 (January 28, 1986). Enquiries may be directed to the Petawawa National Forestry Institute, Forestry Service, Chalk River, Ontario KOJ 1JO
2.
Table 3 Percent of days in which whole-number output of the FWI System components is in error at three levels of precision in the carryover of moisture codes from day to day. Compared with standard floating-point precision.
2-decimal carryover % of days in error by 1
Component
1-decimal carryover % of days in e rror by 1
Integer carryover (no decimals) % of days in error by 1
2
3
1 or more
1.6 8.2
Conclusions
1
1.4
to be drawn from Table 3 are:
Carrying over the moisture codes with two decimal places provides nearly perfect accuracy of output except for occasional one-integer errors in the DC, which are of little
consequence. Carrying over one decimal place may be precise enough for some operational use. For example, one-integer errors would occur in the DMC on about one day in 25, in the FFMC on about one day in 50, and in the FWI on about one day in 200. 3.
Carrying over the moisture codes as integers produces a generally inaccurate output, and is not recommended.
Of all the six components, the DC is the only one to exhibit an anomalous pattern in Table 3. Because the DC has limited power of self-correction in the mathematical sense compared with the FFMC and DMC, it tends to slip out of tune by one digit and to remain so for days on end. Considerably more sampling would be needed to establish its average pattern. The standard program for the FWI System is listed in the following pages, followed by samples of input and output.
10
=
SYMBOLS IN THE PROGRAM WEATHER
relativehumidity,o~ -wind,
km/h
R,RA -rain,
mm
FINE FUEL MOISTURE CODE (FFMC)
-today's
-EMC
FFM
final moisture content
for wetting
-intermediate
value of X
-log
wetting
dryin[or
-today's
rate
FFMC
DUFF MOISTURE CODE (DMC)
PO
-starting
RK
-drying
or yesterday's DMC factor
EL(J) -effective
-DMC
day-length for month J
after rain
WM I -initial
moisture content
WMR -moisture
B
-function
content after rain in rain effect
DROUGHT CODE (DC)
FL(J) -day-length
-DC
factor for month J
after rain
FIRE BEHAVIOR INDEXES (ISI, BUI, FWI)
-ISI
-intermediate
11
form of FWI
READS
PROGRAM F-32 c c c c c
PROGRAM NO.:
F-32
STANDARD1984 VERSION OF CANADIAN FOREST FIRE WEATHERINDEX SYSTEMAS OF 28-JANUARY-1986. WRITTEN IN FORTRAN77.
c c c
c c c c
WEATHER DATA IN EITHER ENGLISH OR METRIC UNITS AND PRINTS OUT IN METRIC ONLY. CODESAND INDEXES OUTPUT ALL TO ONE DECIMAL PLACE. DAILY SEVERITY RATING OUTPUT TO TWO DECIMAL PLACES.
c c c c c
LMON = LENGTH OF MONTHS EL = DMC DAY-LENGTH FACTORS FL = DC DAY-LENGTH FACTORS DIMENSION LMON(12), EL(12), FL(12),AST(2),TITLE(20) LOGICAL*l DAT(9),YES,YES1,ANS,ANS1 LOGICAL *1 INFMT(40) TYPE 5 5 FORMAT(' INPUT FILENAME: eg: SAMPLE.DAT ' ,$) ACCEPT 10, INFMT10 FORMAT(40A1) INFMT(40)=0 OPEN(UNIT=l,NAME=INFMT,TYPE='OLD',READONLY) OPEN(UNIT=2,STATUS='NEW',NAME='F320UT.DAT') DATA LMON /31,28,31,30,31,30,31,31,30,31,30,31/ DATA EL /6.5,7.5,9.0,12.8,13.9,13.9,12.4,10.9,9.4,8.0,7.0, *6.0/ DATA FL /-1.6,-1'.6,-1.6,
c c c c
20 -METRIC
c c c
FORMAT, 25 -ENGLISH
O
FORMAT
IN STATION & YEAR. READ(1,30) TITLE 30 FORMAT(20A4) THIS
SECTION ALLOWS FOR INITIAL
VALUES OF FFMC, DMC,
FO=85.0 PO=6.0 DOT=15.0 TYPE 35 35 FORMAT(' FFMC=85.0, DMC=6.0, DC=15.0; * INITIAL STANDARDVALUES? [Y/N] '$) ACCEPT lO,ANSl IF(ANS1.EQ.ANS) GO TO 55 TYPE,40
12
.4,-1.6,-1.6/
20 FORMAT(F4.1,214,F5.1) 25 FORMAT(F4.0,214,F5.2)
c c
.9,3.8,5.8,6.4,5.0,2.4,
DATA AST /' ','*'/ DATA ANS /'Y'/ TYPE 15 15 FORMAT(//lX,'ENTER VIA KEYBOARDEITHER 0 OR 1 '/lX' * IF DATA IS IN METRIC UNITS'/lX' OR 1 IF DATA IS IN * ENGLISH UNITS') READ(5,*) IUNIT
DC TO BE OPTIONAL
DO YOU WISH TO USE THESE
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FINE FUEL MOISTURE CODE 110 WMO=(147.2*(101-FO))/(59.5+FO) IF(R.GT.0.5) GO TO 115 GO TO 125 115 RA=R-.5 IF(WMO.GT.150.) GO TO 120 WMO=WMO+42.5*RA*EXP(-100./(251.-WMO))*(1.-EXP(-6.93/RA)) GO TO 125 120 WMO=(WMO+42.5*RA*EXP(-100./(251.-WMO))*(1.-EXP(-6.93/RA)))+ *(0.0015*(WMO-150. )**2)*RA**.5 125 IF(WMO.GT.250.) WMO=250. ED=0.942*(H**0.679)+(11.*EXP((H-100.)/10.))+0.18*(21.1-T) **(1.-1./EXP(0.115*H)) IF(WMO-ED) 130,135,140 130 EW=.618*(H**.753)+(10.*EXP((H-100.)/10.))+.18*(21.1-T) **(1.-1./EXP(0.115*H)) IF(WMO.LT.EW) GO TO 145 135 WM=WMO GO TO 150 140 Z=0.424*(1.-(H/100.)**1.7)+(0.0694*(W**0.5))*(1.-(H/100.)**8) x=z*(0.581*(EXP(0.0365*T))) WM=ED+(WMO-ED)/10.**X GO TO 150 145 Z=.424*(1.-( (. -. )**1.7)+( .O694*(W**.5) )*(1.-«100.-H) */100.)**8) x=z*( .581*(EXP( .0365*T))) WM=EW-(EW-WMO)/10.**X 150 FFM=(59.5*(250.-WM))/(147.2+WM) IF(FFM.GT.101.) GO TO 155 ,,' ,. 155 160
c c c
IF(FFM) 160,165,165 FFM=101. 165 GO TO FFM=O.O
A ' I ;"' ., ~ '.;. '" '"r,..' \ !;:;,;~. ., ., ,\
DUFF MOISTURE CODE 165 IF(T+1.1.GE.0.) T=-l.l
GO TO 170
170 RK=1.894*(T+1.1)*(100.-H)*(EL(J)*0.0001) 175 IF(R.GT.1.5) GO TO 180
180
185 190 195 200 205 210
14
12
PR=PO GO TO 205 RA=R RW=0.92*RA-1.27 WMI=20.0+280./EXP(0.023*PO) IF(PO.LE.33.) GO TO 185 IF(PO-65.) 190,190,195 B=100./(0.5+0.3*PO) GO TO 200 B=14.-1.3*~.LOG(PO) GO TO 200 B=6.2*ALOG(PO)-17.2 WMR=WMI+(1000.*RW)/(48.77+B*RW) PR=43.43*(5.6348-ALOG(WMR-20.» IF(PR.GE.O.) GO TO 210 PR=O.O DMC=PR+RK
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SAMPLE OF INPUT FWI TEST DATA APRIL 13 TO MAY 31 4 Indicates 418 17.
42
25
20. 8.5 6.5 13. 6. 5.5 8.5 9.5 7. 6.5 6. 13. 15.5 23.
21 40 25 34 40 52 46 54 93 71 59 52 40 25
25 17 6 24 22 6 16 20 14 17 17 4 11 9
18. 14.5 14.5 15.5 21. 23. 23. 27. 28. 23.5 16. 11.5 16. 21.5 14. 15. 20. 14. 20. 19.5 25.5 10. 19. 26. 30. 25.5
41 51 69 42 37 32 32 33 17 54 50 58 54 37 61 30 23 95 53 30 51 38 27 46 38 67
12.
53'
2811.8
21. 13. 9.
38 70 78
8 20 24
4
16
39
9
19.
11 .5
15.5
46
-April
13
16
-April
30
20 16 11 8 8 16 14 12 27 20 22 12.2 20 16 9 22 0.2 27 11 3 16.4 4 2.8 16 20 6.0 24 16 11 4.2 22 19 12.6
-May 1
0.4
9.0 1.0
3.8 1.4
~::~;
18\36 ~:~::~ ;
Temperature
°C
Relative
Humidity %
16
18 indicates
2.4
Wind km/h
Rain mm
starting
month, In this case April.
no. of days in starting
month.
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REFERENCES Canadian Forestry Service. 1987. Tables for the Canadian Forest Fire Weather Index System. Environ. Can., Can. For. Serv., For. Tech. Rep. 25 (4th ed.). 48 p. Engisch, R.L.; Walker, J.D. 1971. PDP-8L version of Simard's Fire Weather Index Program. Environ. Can., Can. For. Serv., Petawawa Forest Exp. Sta., Intern. Rep. PS-23. 10 p. Kean, W.A. 1975. A PDP-8L program for calculating the Fire Weather Index. Environ. Can., Can. For. Serv., Petawawa Forest Exp. Sta., Info Rep. PS-X-57. 12 p. Simard, A.J. 1970. Computer program to calculate the Canadian Forest Fire Weather Index. Environ. Can., Can. For. Serv., Forest Fire Res. Inst., Intern. Rep. FF-12. 18 p. Van Wagner, C.E. 1970. Conversion of Williams' severity rating for use with the Fire Weather Index. Environ. Can., Can. For. Serv., Petawawa Forest Exp. Sta., Info Rep. PS-X-21. 5 p. Van Wagner, C.E. 1974. Structure of the Canadian Forest Fire Weather Index. Environ. Can., Can. For. Serv., Pub. No. 1333. 44 p. Van Wagner, C.E. 1977. A method of computing fine fuel moisture content throughout the diurnal cycle. Environ. Can., Can. For. Serv., Petawawa Forest Exp. Sta. Info Rep. PS-X-69. 15 p. Van Wagner, C.E. 1987. Development and structure of the Canadian Forest Fire Weather Index System. Can. For. Serv., For. Tech. Rep. 35. 37 p. Van Wagner, C.E.; Pickett, T.L.1975. Equations and Fortran IV program for the 1976 metric version of the Forest Fire Weather Index. Can. For. Serv., Petawawa Forest Exp. Sta., Info Rep. PSX-58. 20 p.
18
