United States 

Department of 

Agriculture The National FireDanger

Forest Service 

Pacific Southwest Rating System: Forest and Range 

Experiment Station 

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Jack D. Cohen John E. Deeming 
The Authors: 

at the time of the work reported herein were assigned to the National Fire-Danger 

Rating System Research Unit, Intermountain Forest and Range Experiment Station, 

Missoula, Mont. JACK D. COHEN, a research forester, earned a bachelor of science 

degree (1973) in forest science at the University of Montana, and a master of science 

degree (1976) in biometeorology at Colorado State University. He joined the Pacific 

Southwest Station staff in 1982, and is now assigned to the Chaparral Prescribed-Fire 

Research Unit, stationed at the Forest Fire Laboratory, Riverside, Calif. JOHN E. 

DEEMING, a research forester, received his bachelor of science degree in forestry 

(1959) at Utah State University. He headed the National Fire-Danger Rating System 

Research Unit from 1975 until 1978, when he joined the Pacific Northwest Forest and 

Range Experiment Station. He is now in charge of that Station's research unit studying 

culture of forests of Eastern Oregon and Washington, stationed at the Silviculture 

Laboratory, Bend, Oreg. 

Acknowledgments: 

The work reported herein was done while we were assigned to the Intermountain 

Forest and Range Experiment Station's Northern Forest Fire Laboratory at Missoula, 

Montana. We were aided materially by Robert E. Burgan. Other researchers who 

contributed to the updating of the National Fire-Danger Rating System and their 

contributions were from the Intermountain Station, Missoula, Montana--Richard C. 

Rothermel, Frank A. Albini, and Patricia L. Andrews, who assisted in adapting the 

current fire modeling technology, including the addition of 1000-hour fuels and 

herbaceous to 1-hour transfer; Hal E. Anderson and James K. Brown, who worked on 

fuels and fuel models; Donald F Fuquay, and Donald J. Latham, who worked on the 

lightning-caused fire occurrence index; North Central Forest Experiment Station, 

East Lansing, Michigan --Von J. Johnson, William A. Main, and Craig A. Johnson, 

who worked on human-caused fire occurrence index; and the Rocky Mountain Forest 

and Range Experiment Station, Fort Collins, Colorado-- Michael A. Fosberg, who 

worked on fuel moisture models; and R. William Furman and Glen F. Brink, who 

collected fire weather data needed to develop the system. 

Cover: Four climate classes in the United States are associated with different vegetation 

moisture contents, which affect fire spread and fire danger rating. 

Publisher: 

Pacific Southwest Forest and Range Experiment Station 

P.O. Box 245, Berkeley, California 94701 

May 1985 
The National Fire-Danger 

Rating System: 

basic equations 

Jack D. Cohen 

CONTENTS 

Introduction .........................................................................1

Calculating Moisture Content ............................................1

Equilibrium Moisture Content ...........................................1

Environmental Parameters .................................................2

Data Available ...............................................................2

Data Unavailable ...........................................................2

Models of Dead-Fuel Moisture ..........................................3

Fuels: 1-Hour Timelag ..................................................3

Fuels: 10-Hour Timelag ................................................4

Fuels: 100-Hour Timelag ..............................................4

Fuels: 1000-Hour Timelag ............................................5

Fuels: Wet or Ice Covered .............................................5

John E. Deeming 

Models of Live-Fuel Moisture ..................................... 6

Herbaceous Fuels ..................................................... 6

Shrub Fuels .............................................................. 8

System Components and Indexes ................................. 9 

Models of Fire Characteristics ..................................... 9

Preliminary Calculations .......................................... 9

Spread Component ................................................. 10 

Energy Release Component ................................... 11 

Burning Index ........................................................ 12 

Models of Fire Occurrence ........................................ 12 

Ignition Component ............................................... 12 

Human-Caused Fire Occurrence Index .................. 13

Lightning-Caused Fire Occurrence Index .............. 13

Fire-Load Index ...................................................... 14 

Appendix-Parameters for Fuel Models ...................... 15 

References ..................................................................... 16 
GLOSSARY 

AA: Intermediate variable in stick age correction equation. 

AD: Exponent in surface area weighted optimum reaction 

velocity (GMAOP) equation. 

ADE: Exponent in loading weighted optimum reaction velocity (GMAOPE) equation. 

AGE: Number of days since fuel moisture sticks were set out. 

AMBVP: Ambient vapor pressure. 

ANNTA: Parameter in linear herbaceous moisture content equation that is used in transition period for annual vegetation. 

ANNTB: Parameter in linear herbaceous moisture content equation that is used in transition period for annual vegetation. 

ATAN: Trigonometric inverse tangent function of (). 

B: Wind effect exponent in PHIWND equation. 

BB: Intermediate variable in stick age correction equation. 

BDYBAR: Seven-day running average of BNDRYT values for calculating MC1000. 

BETBAR: Packing ratio. 

BETOP: Optimum packing ratio, surface area weighted. 

BETOPE: Optimum packing ratio, loading weighted. 

BI: NFDRS Burning Index. 

BNDRY1: Average boundary moisture condition of first 16 hours 

of 24-hour forecast period. Applies to predicted 10-hour 

timelag moisture content. 

BNDRY2: Average boundary moisture condition of last 8 hours of 

24-hour forecast period. Applies to predicted 10-hour 

timelag moisture content. 

BNDRYH: Weighted 24-hour average moisture condition for 100-

hour timelag moisture content calculation (MC100). 

BNDRYT: Weighted 24-hour average moisture condition for 1000-

hour timelag moisture content calculation (MC1000). 

C: Intermediate variable in UFACT equation for calculating wind factor (PHIWND). 

CC: Intermediate variable in stick age correction equation. 

CELS: Temperature in degrees Celsius. 

CGRATE: Cloud-to-ground lightning discharge rate. 

CHI: Intermediate variable used in ignition probability (P(I)) 

equation. 

CLIMAT: NFDRS climate class. 

CORR: Calculated difference between wet bulb saturation 

vapor pressure (SATVPW) and ambient vapor pressure 

(AMBVP). 

CURED: AFFIRMS user command to model herbaceous condition as cured. 

D: Depth of flaming zone (ft). 

DAYLIT: Hours between sunrise and sunset. 

DELL: Daily solar zenith angle in radians. 

DEDRT: Ratio (WTMCD/MXD) in calculation of ETAMD. 

DEDRTE: Ratio (WTMCDE/ MXD) in calculation of ETAMDE. 

DEPTH: Effective fuel-bed depth measured (ft). 

DIFF: Twenty-four hour change in MC1000. 

DWPT: Dewpoint temperature. 

E: Wind effect exponent in UFACT equation used for calculating wind factor (PHIWND). 

ELEV: Elevation of the observing station in feet. 

EMC: Equilibrium moisture content. 

EMCBAR: Average EMC, weighted by hours of day and night. 

EMCBR1: EMC calculated using average temperature and relative 

humidity from first 16 hours of 24-hour forecast period. 

EMCBR2: EMC calculated using average temperature and relative 

humidity from last 8 hours of 24-hour forecast period. 

EMCMAX: EMC calculated from minimum temperature 

(TMPMIN) and maximum relative humidity 

(RHMAX). 

EMCMIN: EMC calculated from maximum temperature 

(TMPMAX) and minimum relative humidity 

(RHMIN). 

EMCOBS: EMC calculated from observation time temperature 

(TMPOBS) and relative humidity (RHOBS). 

EMCPRM: EMC calculated using temperature and relative humidity at fuel-atmosphere interface (TMPPRM, RHPRM, 

respectively). 

ERC: NFDRS energy release component. 

ETAMD: Surface area weighted dead-fuel moisture damping coefficient. 

ETAMDE: Loading weighted dead-fuel moisture damping coefficient. 

ETAML: Surface area weighted live-fuel moisture damping coefficent. 

ETAMLE: Loading weighted live-fuel moisture damping coefficient. 

ETAMD: Dead-fuel mineral damping coefficient. 

ETASL: Live-fuel mineral damping coefficient. 

EXP: Exponential function of ( ). 

FAHR: Temperature in degrees Fahrenheit. 

F1: Proportion of dead-fuel surface area in 1-hour class, 

used as a weighting factor for ROS calculation. 

F10: Proportion of dead-fuel surface area in 10-hour class, 

used as weighting factor for ROS calculation. 

F100: Proportion of dead-fuel surface area in 100-hour class, 

used as weighting factor for ROS calculation. 

F1E: Proportion of dead-fuel loading in 1-hour class, used as 

weighting factor for ERC calculation. 

F10E: Proportion of dead-fuel loading in 10-hour class, used 

as weighting factor for ERC calculation. 

F100E: Proportion of dead-fuel loading in 100-hour class, used 

as weighting factor for ERC calculation. 

F1000E: Proportion of dead-fuel loading in 1000-hour class, 

used as weighting factor for ERC calculation. 

FCTCUR: Fraction of fuel model herbaceous fuel loading transferred to 1-hour fuel class. 

FDEAD: Proportion of total surface area in dead-fuel classes. 

FDEADE: Proportion of total loading in dead-fuel classes. 

FHERB: Proportion of live surface area in herbaceous class. 

FHERBE: Proportion of live loading in herbaceous class. 

FINSID: Fraction of total corridor (TOTWID) occupied by 

lightning-rain corridor. 

FL: Byram's flame length (ft). 

FLI: NFDRS fire-load index. 

FLIVE: Proportion of total surface area in live-fuel classes. 

FLIVEE: Proportion of total loading in live-fuel classes. 

FMF: Moisture content of 1-hour fuels inside rain area. 

FOTSID: Fraction of total corridor (TOTWID) occupied by 

lightning-rain corridor. 

FREEZE: AFFIRMS user command to model herbaceous condition as cured and woody condition as dormant. 

FWOOD: Proportion of live surface area in woody class. 

FWOODE: Proportion of live loading in woody class. 

GMAMX: Weighted maximum reaction velocity of surface area. 

GMAMXE: Weighted maximum reaction velocity of loading. 

GMAOP: Weighted optimum reaction velocity of surface area. 

GMAOPE: Weighted optimum reaction velocity of loading. 

GREEN: AFFIRMS user command to start modeled process of 

herbaceous greenup. 

GREN: Fraction of greenup period that has elapsed in calculation of MCHERB. 

GRNDAY: Number of days elapsed since greenup started. 

HD: Specified dead-fuel heat of combustion of fuel model. 
HERBGA: Parameter in equation for linear herbaceous moisture 

content in greenup period or when MCHERB is greater 

than 120 percent. 

HERBGB: Parameter in equation for linear herbaceous moisture 

content used in greenup period or when MCHERB is 

greater than 120 percent. 

HL: Specified live-fuel heat of combustion of fuel model. 

HN1: Heating number of 1-hour class. 

HN10: Heating number of 10-hour class. 

HN100: Heating number of 100-hour class. 

HNHERB: Heating number of herbaceous class. 

HNWOOD: Heating number of woody class. 

HTSINK: Heat sink term in ROS equation. 

I: Byram's fireline intensity (Btu/ft/s). 

IC: NFDRS ignition component. 

ICBAR: Area-weighted average ignition component for storm 

corridor. 

ICR: Ignition component calculated for inside rain corridor. 

IR: Surface area weighted reaction intensity, used for 

calculating ROS (Spread Component -- SC). 

IRE: Loading weighted reaction intensity, used for calculating energy release component (ERC). 

IRND: Round-off function of ( ). 

JDATE: Julian day of year, 1 to 366, derived from month and 

day. 

KELVIN: Temperature in degrees Kelvin. 

KTMP: Temperature factor in X1000 calculation. 

KWET: Wetting factor in X1000 calculation. 

LAL: NFDRS lightning activity level. 

LAT: Station latitude in degrees. 

LGTDUR: Duration of lightning at a point within affected area. 

LIVRT: Ratio (WTMCL/MXL) in calculation of ETAML. 

LIVRTE: Ratio (WTMCLE/ MXL) in calculation of ETAMLE. 

LOL NFDRS lightning-caused fire occurrence index. 

LRISK: NFDRS lightning risk. 

LRSF: Lightning-risk scaling factor. 

MC: Moisture content, expressed as percent dry weight. 

MC1: Calculated 1-hour timelag percent fuel moisture content. 

MC10: Percent moisture content of fuel stick (age corrected) or 

calculated percent moisture content for 10 - hour timelag. 

MC100: Percent moisture content for 100 - hour timelag. 

MC1000: Percent moisture content for 1000 - hour timelag. 

MC10P1: Predicted MC10 as of next morning of forecast period. 

MC10P2: Predicted MC10 for observation time of next day. 

MCHERB: Calculated herbaceous percent moisture content. 

MCHRBI: Maximum of 30 percent of MCHERB calculated day 

before greenup. 

MCH RBP: Potential herbaceous moisture content during greenup 

period. 

MCLFE: Dead-fuel moisture content, weighted by heating 

number, for calculation of live moisture of extinction 

(MXL). 

MCOI: NFDRS human-caused index of fire occurrence. 

MCWODI: Greater of PREGRN or MCWOOD calculated day 

before greenup. 

MCWODP: Potential moisture content of woody fuel during 

modeled greenup period. 

MCWOOD: Calculated moisture content of twigs and foliage of 

woody shrubs. 

MRISK: NFDRS human-caused risk. 

MXD: Specified dead-fuel moisture of extinction for fuel 

model. 

MXL: Calculated live-fuel moisture of extinction. 

P(I): Probability that a firebrand will produce a successful 

fire start in dead, fine fuels. 

P(F/ I): Probability that ignition will result in a reportable fire. 

PDUR1: Predicted rain duration for first 16 hours of 24-hour 

forecast period. 

PDUR2: Predicted rain duration for last 8 hours of 24-hour 

forecast period. 

PERTA: Parameter in equation for linear herbaceous moisture 

content used in transition period for perennial 

vegetation. 

PERTB: Parameter in equation for linear herbaceous moisture 

content used in the transition period for perennial 

vegetation. 

PHI: Station latitude in radians. 

PHISLP: Multiplier for slope effect in ROS equation. 

PHIWND: Multiplier for wind effect in ROS equation. 

PM1000: MC1000 calculated for previous 7th day. 

PNORM1: Scaling factors in P(I) calculation that cause P(I) to 

PNORM2 equal 100 when MC1 is 1.5 percent and zero when MC1 

PNORM3 is 25 percent. 

PPTAMT: Amount of precipitation. 

PPTDUR: Duration of precipitation. 

PREGRN: Modeled moisture content of woody shrubs when 

dormant. 

QIGN: Calculated heat of ignition used for calculating P(I). 

RAIDUR: Duration of rain at a point within lightning-rain 

corridor. 

RH: Relative humidity. 

RHMAX: Maximum relative humidity for 24-hours. 

RHMIN: Minimum relative humidity for 24-hours. 

RHOBAR: Particle density of weighted fuel. 

RHOBED: Bulk density of fuel bed. 

RHOBS: Relative humidity of afternoon observation time. 

RHOD: Particle density of dead-fuel. 

RHOL: Particle density of live-fuel. 

RHPRM: Relative humidity estimated for fuel-atmosphere 

interface. 

ROS: Forward rate of spread of flaming front (ft/min). 

SA1: Surface area of 1-hour class fuels. 

SA10: Surface area of 10-hour class fuels. 

SA100: Surface area of 100-hour class fuels. 

SADEAD: Surface area of dead-fuel classes. 

SAHERB: Surface area of herbaceous fuel class. 

SALIVE: Surface area of live-fuel classes. 

SATVPD: Saturation vapor pressure for dry bulb temperature 

(TMPOBS). 

SATVPN: Saturation vapor pressure for minimum temperature 

(TMPMIN). 

SATVPW: Saturation vapor pressure for wet bulb temperature 

(TMPWET). 

SATVPX: Saturation vapor pressure for maximum temperature 

(TMPMAX). 

SAWOOD: Surface area of woody fuel class. 

SC: NFDRS spread component. 

SCM: Specified spread component (SC) of fuel model when 

all fire starts become reportable fires. 

SCN: Percent actual SC is to specified SCM (SC/SCM*100). 

SD: Silica-free mineral content of dead fuels. 

SG1: Specified surface area-to-volume ratio for 1-hour class 

of fuel model. 

SG10: Specified surface area-to-volume ratio for 10-hour class 

of fuel model. 

SG100: Specified surface area-to-volume ratio for 100-hour 

class of fuel model. 

SGBRD: Characteristic surface area-to-volume ratio of dead 

fuel, surface area weighted. 

SGBRDE: Characteristic surface area-to-volume ratio of dead 

fuel, loading weighted. 

SGBRL: Characteristic surface area-to-volume ratio of live 

fuel, surface area weighted. 
SGBRLE: Characteristic surface area-to-volume ratio of live fuel, 

loading weighted. 

SGBRT: Characteristic surface area-to-volume ratio of fuel bed, 

surface area weighted. 

SGBRTE: Characteristic surface area-to-volume ratio of fuel bed, 

loading weighted. 

SGHERB: Specified surface area-to-volume ratio for herbaceous 

class of fuel model. 

SGWOOD: Specified surface area-to-volume ratio for woody class of 

fuel model. 

SIN: Trigonometric sine function of ( ). 

SL: Proportion of silica-free mineral content of live fuels. 

SLPFCT: Coefficient in PHISLP equation. 

SQRT: Square-root function of ( ). 

STD: Proportion of inert mineral content of dead fuels. 

STL: Proportion of inert mineral content of live fuels. 

STMDIA: Width of corridor affected by rain-lightning. 

STMSPD: Translational speed of storm in miles per hour. 

TAN: Trigonometric tangent function of ( ). 

TAU: Calculated residence time of flaming front (min). 

TEMP: Dry-bulb temperature. 

TLA: Intermediate value in daylength calculation. 

TLA1: Intermediate value in daylength calculation. 

TMPMAX: Twenty-four hour maximum dry-bulb temperature. 

TMPMIN: Twenty-four hour minimum dry-bulb temperature. 

TMPOBS: Dry-bulb temperature of afternoon observation time. 

TMPPRM: Temperature estimated for fuel-atmosphere interface. 

TMPWET: Wet-bulb temperature. 

TOTWID: Total width of lightning-only and lightning-rain 

corridor. 

UFACT: Wind-effect multiplier in PHIWND equation. 

W1: Fuel model specified 1-hour class fuel loading. 

W10: Fuel model specified 10-hour class fuel loading. 

W100: Fuel model specified 100-hour class fuel loading. 

W1000: Fuel model specified 1000-hour class fuel loading. 

W1N: Net fuel loading of 1-hour class. 

W10N: Net fuel loading of 10-hour class. 

W100N: Net fuel loading of 100-hour class. 

W1P: One-hour fuel loading and transferred herbaceous 

loading (WHERBC). 

WDEADN: Net loading of dead fuels, surface-area weighted. 

WDEDNE: Net dead fuel loading. 

WETRAT: Rainfall rate set by climate class (CLIMAT). 

WHERB: Herbaceous fuel loading of fuel model. 

WHERBC: Amount of herbaceous loading transferred to 1-hour 

class. 

WHERBN: Net fuel loading of herbaceous class. 

WHERBP: Amount of herbaceous loading left after transfer to 1-

hour fuel loading. 

WLIVEN: Surface area weighted net loading of live fuels. 

WLIVNE: Net live-fuel loading. 

WNDFC: Fuel model specified wind reduction factor. WNDFC is 

calculated under certain conditions. 

WOODGA: Parameter in linear woody moisture content equation 

used for calculating MCWODP and MCWOOD. 

WOODGB: Parameter in linear woody moisture content equation 

used for calculating MCWODP and MCWOOD. 

WRAT: Ratio of dead-to-live heating numbers for calculation of 

live moisture of extinction (MXL). 

WS: Ten-minute average 20 ft windspeed for 10 minutes in 

miles per hour. 

WT: Weight of fuel sticks in grams. 

WTMCD: Surface area weighted dead-fuel moisture content. 

WTMCDE: Loading weighted dead-fuel moisture content. 

WTMCL: Surface area weighted live-fuel moisture content. 

WTMCLE: Loading weighted live-fuel moisture content. 

WTOT: Total fuel loading. 

WTOTD: Total dead-fuel loading. 

WTOTL: Total live-fuel loading. 

WWOOD: Specified woody shrub loading fuel model. 

WWOODN: Net fuel loading of woody class. 

X1000: Independent variable in herbaceous fuel moisture 

models. 

YLOI: Previous day's LOI. 

YM1000: MC1000 calculated previous day. 

YMC10: Initial or current value of 10-hour timelag moisture 

content for calculating MC10P1. 

YMC100: MC100 value calculated previous day. 

YX1000: XI000 calculated previous day. 

ZETA: No-wind propagating flux ratio in rate-of-spread 

(ROS) calculation. 
T he National Fire-Danger Rating System (NFDRS) 

provides indexes for measuring fire potential in wildlands. It is used by all Federal and many State natural 

resource management agencies. Data from fire-danger 

rating stations throughout the United States are processed 

through the interactive, time-share computer program 

AFFIRMS (Helfman and others 1980) or are computed 

manually each day. Fire weather stations record data on 

the 10-day fire weather record (NWS Form D-9b). 

The concept of fire-danger rating and various methods 

of rating fire-danger have been around for decades. The 

analytical approach that is the basis for the current 

NFDRS began in 1968 with the establishment of a 

National Fire-Danger Rating research work unit. After 4 

years of development and field trials, the 1972 NFDRS 

(Deeming and others 1972) became operational. A review 

and update was planned at that time. 

In 1974, the Chief of the Forest Service, U.S. Department of Agriculture, chartered a technical committee to 

direct the updating of the NFDRS. A research work unit 

was chartered and actual work started in 1975. The update 

work was completed in November 1977, with implementation in May 1978. The results were reported in two publications: one describes the basic system and revisions (Deeming and others 1977); the other explains how to calculate 

manually fire-danger ratings using the NFDRS (Burgan 

and others 1977). A third publication summarizes the technical development of the NFDRS (Bradshaw and others 

1983). 

This report documents the mathematical equations 

required to calculate fire-danger indexes in the National 

Fire-Danger Rating System. The equations are in the 

coded format of FORTAN and BASIC computer languages. They are described in the order processed in the 

computer program AFFIRMS (Helfman and others 1980) 

and FIREFAMILY (Main and others 1982), except for 

equations used to calculate equilibrium moisture content. 

CALCULATING MOISTURE 

CONTENT 

The equilibrium moisture content (EMC) is fundamental to all fuel moisture computations in the NFDRS. The 

EMC, itself a computed value, represents a steady state 

moisture content of dead woody material. This steady state 

is achieved under constant conditions for a sufficiently 

long adjustment period. Steady-state conditions do not 

occur under normal circumstances and, therefore, do not 

represent the woody moisture contents. The EMC offers 

the basis for calculating the various moisture contents 

considered by the NFDRS. 

Equilibrium Moisture Content 

Equilibrium moisture contents can be derived from dry 

bulb temperature and relative humidity by calculating the 

equilibrium moisture content (EMC). 

The following equations for EMC are the regression 

equations developed by Simard (1968) on the basis of 

tables in the Wood Handbook (U.S. Forest Products 

Laboratory 1955, revised 1974). Temperatures are expressed in degrees Fahrenheit, and the EMC is expressed as 

percent moisture content. All variables are explained in the 

glossary. 

Relative Humidity Less Than 10 Percent: 

EMC = 0.03229 + 0.281073 

* RH - 0.000578 * TEMP * RH (1a) 

in which 

RH is a relative humidity. 

TEMP is a dry bulb temperature. 

Relative Humidity Equal to or Greater Than 10 Percent 

but Less Than 50 Percent: 

EMC = 2.22749 + 0.160107 

* RH - 0.014784 * TEMP (1b) 

Relative Humidity Equal to or Greater Than 50 Percent: 

EMC = 21.0606 + 0.005565 * RH ** 2 

- 0.00035 * RH * TEMP - 0.483199 * RH (1c) 

With these equations, the EMC's can be evaluated for (1) 

observation time, (2) the time of maximum temperatureminimum relative humidity, and (3) the time of minimum 

temperature-maximum relative humidity: 

EMCOBS = f(TMPOBS, RHOBS) 

EMCMIN = f(TMPMAX, RHMIN) 

EMCMAX = f(TMPMIN, RHMAX) 

in which 
TMPOBS is the dry bulb temperature at the afternoon 

observation time. 

TMPMIN is the 24-hour minimum dry bulb temperature. 

TMPMAX is the 24-hour maximum dry bulb temperature. 

RHOBS is the relative humidity at the afternoon observation time. 

RHMIN is the 24-hour minimum relative humidity. 

RHMAX is the 24-hour maximum relative humidity. 

Environmental Parameters 

Data Available 

Calculating fuel moisture contents requires a set of 

environmental moisture and temperature variables that 

must be measured or derived. The variables are these: 

• Dry bulb temperature and relative humidity at the 

afternoon observation time; 

• Maximum and minimum dry bulb temperatures and 

relative humidities for the 24-hour period ending at the 

afternoon observation time; and 

• Duration of precipitation during this same 24-hour 

period. 

Operationally, the first and third items are required; 

measurements to obtain the second item are optional. Historical fire-weather records before 1972 typically do not 

include the second and third items, although they were 

often collected for 1972 or a later date. These parameters 

are calculated, derived, or assigned values. 

The dry bulb temperature (TMPOBS) is observed 

directly and reported in degrees Fahrenheit or degrees 

Celsius. The relative humidity (RHOBS) may be reported 

directly, or derived from the dry and wet bulb temperature 

(TMPOBS and TMPWET) or from the dry bulb temperature and dewpoint (TMPOBS and DWPT). The psychometric equations used for these operations are from the 

Smithsonian Meteorological Tables (1949). For these calculations, the temperatures are converted to degrees Kelvin 

by these equations: 

KELVIN = CELS + 273.16 

KELVIN = (FAHR + 459.69) * 5/9 

in which 

KELVIN is the temperature in degrees Kelvin. 

FAHR is the temperature in degrees Fahrenheit. 

CELS is the temperature in degrees Celsius 

The Moisture Variable Is Dewpoint Temperature: 

RHOBS = 100.0 

* EXP(-7482.6 / (DWPT + 398.36) + 15.674) / 

EXP(-7482.6 / (TMPOBS + 398.36) + 15.674) 

The Moisture Variable Is Wet Bulb Temperature: In this 

situation, the calculation is a bit more complicated. First, 

calculate the saturation vapor pressures for the wet and dry 

bulb temperatures (SATVPW and SATVPD). 

(dry bulb) SATVPD = EXP(1.81 + 

(TMPOBS * 17.27 - 4717.31) / (TMPOBS - 35.86)) 

(wet bulb) SATVPW = EXP(1.81 + (TMPWET 

* 17.27 - 4717.31) / (TMPWET - 35.86)) 

Now calculate an intermediate variable (CORR) to correct for station elevation. 

CORR = 6.6 * 10**-4.* (1.0 + (0.00115 

* (TMPWET - 273.16)) * TMPOBS - TMPWET) 

* (1013.09 / EXP(ELEV / 25,000.0)) 

in which ELEV is the elevation of the observing station in 

feet. For stations in Alaska, add 200 ft to the actual station 

elevation to adjust for generally lower surface atmospheric 

pressures. 

Now, the ambient vapor pressure in millibars (AMBVP): 

AMBVP = SATVPW – CORR 

Relative humidity in percent: 

RHOBS = 100.0 * (AMBVP / SATVPD) (2) 

Data Unavailable 

Relative Humidity---The most common situation observed 

is a report that includes TMPOBS, a humidity variable 

(DWPT, RHOBS or TMPWET), and maximum and minimum temperatures (TMPMAX and TMPMIN). Unfortunately, the 24-hour extreme relative humidity data were 

not collected and, therefore, are not available from pre1972 reports, and are often not available from post-1972 

reports. 

When the 24-hour extreme temperatures are reported but 

the relative humidities are not, it is assumed that the 

specific humidity at observation time was conserved for the 

preceding 24-hour period. 

Ambient Vapor Pressure: 

Rearranging equation (2): 

AMBVP = (RHOBS * SATVPD) / 100.0 (3) 

Saturation Vapor Pressure for the 24-Hour Maximum and 

Minimum Temperatures: 

(max temp) SATVPX = EXP(1.81 + (TMPMAX 

* 17.27-4717.31) 

/ (TMPMAX - 35.86)) 

2 
(min temp) SATVPN = EXP(1.81 + (TMPMIN 

* 17.27 - 4717.31) 

/ (TMPMIN - 35.86)) 

24-Hour Maximum and Minimum Relative Humidities: 

RHMAX = 100.0 * (AMBVP / SATVPN) 

RHMIN = 100.0 * (AMBVP / SATVPX) 

Relative Humidity and Temperature--When neither temperature nor relative humidity 24-hour extremes are reported, we estimate EMCMAX and EMCMIN directly. 

(These data are needed only to obtain values of 

EMCMAX and EMCMIN, the 24-hour extremes of 

EMC.) First, we assume that: 

EMCMIN = EMCOBS 

EMCMAX is assigned a value according to the following 

scheme: 

NFDRS 

climate class: Defaulted EMCMAX 

1or 2 15 percent 

3 or 4 23 percent 

These values were judged to be typical of nighttime 

recovery values for moderately severe fire-danger situations. 

Precipitation--In pre-1972 fire-weather reports, precipitation duration (PPTDUR) was not reported, but precipitation amount (PPTAMT) was. So by assuming a rainfall 

rate (WETRAT), a pseudo-duration can be calculated as 

follows: 

PPTDUR = IRND((PPTAMT / WETRAT) + 0.49) 

in which 

IRND indicates that the quantity in parentheses is a 

rounded integer. 

PPTDUR cannot be greater than 8 hours. 

WETRAT is a function of climate class as follows: 

NFDRS WETRAT 

climate class: Inches/hour 

1 or 2 0.25 

3 or 4 0.05 

One-quarter inch per hour was judged typical of dry 

areas (NFDRS climate classes 1 and 2) where the precipitation during the fire season comes usually in the form of 

moderately intense rain showers. In wetter areas, climate 

classes 3 and 4, the precipitation is typically much lighter 

and more or less continuous. PPTDUR, if estimated by this 

method, is not allowed to exceed 8 hours. 

Models of Dead-Fuel Moisture 

Fire-danger rating considers two major groups of fuels; 

live and dead. The live fuels are further classified into 

annual herbaceous, perennial herbaceous, and lesser 

woody plants (shrubs and young trees). The 1-, 10-, 100-, 

and 1000-hour timelag classes represent the dead 

fuels. 

The movement of water vapor between dead-fuel elements and the atmosphere is controlled by the vapor pressure gradient that exists between the two mediums. This 

gradient is proportional to the difference between the moisture content of the fuel element and the EMC corresponding to the temperature and relative humidity of the air in 

immediate contact with the fuel element. The dead-fuel 

moisture calculations are those developed and documented 

in Fosberg and Deeming (1971); Fosberg (1971); and Fosberg and others (1981). 

Fuels: 1-Hour Timelag 

The response of 1-hour timelag fuels to changes in the 

environmental conditions is so rapid that only the potential 

moisture content, which is equivalent to the EMC at the 

fuel-atmosphere interface, is required. The first task is to 

estimate the relative humidity and dry bulb temperature of 

the air in immediate contact with the fuel elements 

(TMPPRM and RHPRM). The approach, based on work 

by Byram and Jemison (1943), consists of correcting the 

dry bulb temperature and relative humidity values existing 

at instrument height (4.5 ft) according to the intensity of 

the insolation (amount of sunshine). Time of year or variables affecting insolation other than cloudiness are not considered. The amount of cloudiness is indicated by the stateof-weather code. The temperature correction is added (° F); 

the relative humidity correction is a multiplier. 

Corrections 

State-of-weather Temperature Relative humidity 

code: ° F 

0 + 25 * 0.75 

l + 19 * 0.83 

2 + 12 * 0.92 

3 + 5 * 1.00 

Boundary Layer EMC: 

From equations (1a), (1b), or (1c) 

EMCPRM = f(TMPPRM, RHPRM) 

When Fuel Moisture Sticks Are Not Used: 

MC1 = 1.03 * EMCPRM 

When Fuel Moisture Sticks Are Used: 

MC1 = (4.0 * EMCPRM + MC10) / 5.0 

in which MC10 is the 10-hour timelag fuel moisture. 

3 
This method was developed for the California wildland 

fire-danger rating system (U.S. Dep. Agric., Forest Serv. 

1958, revised 1968). 

If It Is Raining at the Afternoon Observation Time: 

MC1 = 35.0 

Fuels: 10-Hour Timelag 

If an Observation Is Being Processed and Fuel Sticks 

Are Being Used: 

MC10 = Fuel Stick Moisture Content (age corrected) 

Because fuel sticks lose weight as they weather, a correction to the measured, apparent moisture content is required. The correction for weathering used in the NFDRS 

is based on work done by Haines and Frost (1978) as 

modified by Deeming. A linear model that uses the number 

of days the sticks have been exposed to the elements and 

the climate class of the station where the sticks are located 

are the independent variables. 

MC10=AA*CC+BB*CC* (WT - 100.0) 

in which 

WT is the weight of the fuel sticks in grams. 

AA = 0.5 * AGE / 30.0 

BB = 1.0 + (0.02 * AGE / 30.0) 

CC = CLIMAT / 4.0 

AGE is the number of days since the sticks were set out. 

CLIMAT is the NFDRS climate class. 

If an Observation Is Being Processed and Fuel Sticks 

Are Not Being Used: 

MC10 = 1.28 * EMCPRM 

in which EMCPRM is the same value used in the calculation of MC 1. 

If a Forecast Is Being Processed and Stick Moisture 

Content Is Predicted Directly: AFFIRMS allows the fireweather forecaster to predict stick moisture content directly. A method of making such a prediction was not 

developed as an integral part of the NFDRS. If this practice is to be used, existing methods such as that by Cramer 

(1961) are suggested. 

If a Forecast Is Being Processed and MC10 Is To Be 

Calculated: In this situation the model is considerably 

more complex requiring two computational steps on the 

basis of work by Fosberg (1977). A fire-weather forecast 

includes predictions of the minimum temperature and 

maximum relative humidity for the next 24 hours, the state 

of weather, temperature, and relative humidity at observation time the next day, and precipitation durations for (a) 

the first 16 hours of the 24-hour period, and (b) the last 8 

hours of the 24-hour period. 

4 

The model first predicts the MC10 as of 0600 the next 

morning (MC10P1), with the current day's MC10 as the 

initial value (YMC 10). With MC l OP I as the initial value, it 

predicts the potential MC10 at observation time the next 

afternoon (MC10P2). 

Average Boundary Values for Periods 1 and 2 are these: 

BNDRY1 = ((16.0 - PDURI) * EMCBR1 

+ (2.7 * PDUR1 + 76.0) * PDUR1) / 16.0 

BNDRY2 = ((8.0 - PDUR2) * EMCBR2 

+ (2.7 * PDUR2 + 76.0) * PDUR2) / 8.0 

in which 

PDUR1 and PDUR2 are the predicted durations of 

precipitation, in hours, for periods 1 and 2. 

EMCBR1 and EMCBR2 are the EMC values calculated 

with the average temperatures and average relative 

humidities predicted for periods 1 and 2. (The temperatures and relative humidities at observation time the 

current day and predicted for observation time the 

next day are corrected for insolation before being 

averaged with the predicted maximum relative humidity and minimum temperature.) 

Moisture Content of the 10-Hour Fuels as of the End of 

Period 1: 

MC10P1 = YMC10 - (BNDRY1 - YMC10) 

* (1.0 - 1.1 * EXP(-1.6)) 

in which YMC10 is the initial value of the 10-hour fuel 

moisture as of observation time. 

Moisture Content of the 10-Hour Fuels as of the End of 

Period 2: 

MC10P2 = MC10P1 - (BNDRY2 - MC10P1) 

* (1.0 - 0.87 * EXP(-0.8)) 

MC10 = MC10P2 

Fuels: 100-Hour Timelag 

Because of the slow response of the 100-hour and the 

1000-hour classes of fuels to changes in environmental 

conditions, we use an EMC that represents the average 

drying-wetting potential of the atmosphere for the preceding 24-hour period. The 24-hour average EMC is 

denoted as EMCBAR, a weighted average of EMCMAX 

and EMCMIN. Weighting is done on the basis of hours of 

daylight and hours of darkness that are functions of latitude and date. 

Duration of Daylight: 

PHI = LAT * 0.01745 

in which 

LAT is the station latitude in degrees. 

DECL = 0.41008 * SIN((JDATE-82) * 0.01745) 
in which 

JDATE is the Julian date. 

DECL is the solar declination in radians. 

DAYLIT = 24 * (1. - ACOS(TAN(PHI) 

* TAN(DECL))/3.1416) 

in which DAYLIT is the number of hours between sunrise 

and sunset. 

Weighted 24-Hour Average EMC: 

EMCBAR = (DAYLIT * EMCMIN + 

(24.0 - DAYLIT) * EMCMAX) / 24.0 

Weighted 24-Hour Average Boundary Condition: 

BNDRYH = ((24.0 - PPTDUR) * EMCBAR 

+ PPTDUR * (0.5 * PPTDUR + 41.0)) / 24.0 

in which PPTDUR is the hours of precipitation reported 

(predicted) for the 24-hours. 

100-Hour Timelag Fuel Moisture: The model used in the 

manual version of the 1978 NFDRS to calculate the 100-

hour timelag fuel moisture differs from this model in two 

ways: (1) daylength is not considered, and (2) the 24-hour 

average EMC is a function of the simple averages of the 

24-hour temperature and relative humidity extremes. 

MC100 = YMC100 + (BNDRYH - YMC100) 

* (1.0 - 0.87 * EXP(-0.24)) 

in which YMC100 is the MC100 value calculated the previous day. 

Initializing YMC100 at the Beginning of a Computational Period: 

YMC100 = 5.0 + (5.0 * CLIMAT) 

Fuels: 1000-Hour Timelag 

Weighted 24 Hour Average Boundary Condition: 

BNDRYT = ((24.0 - PPTDUR) * EMCBAR + 

PPTDUR * (2.7 * PPTDUR + 76.0)) / 24.0 

Seven Day Running Average Boundary Condition: 

BDYBAR = (BNDRYT(1) + ...............+ BNDRYT(7)) / 7.0 

in which ( ) denotes a day in the 7-day series. It is necessary, 

therefore, to maintain a 1 x 7 array of BNDRYT values. 

1000-Hour Timelag Fuel Moisture: The model used in 

the manual version of the 1978 NFDRS to calculate the 

1000-hour timelag fuel moisture differs from this model in 

the following ways: (1) daylength is not considered, (2) the 

24-hour average EMC is a function of the simple averages 

of the 24-hour temperature and relative humidity extremes, 

and (3) BNDRYT is calculated daily, but BDYBAR and 

MC1000 are calculated only every seventh day. 

MC1000 = PM1000 + (BDYBAR - PM1000) 

* (1.00 - 0.82 * EXP(-0.168)) 

in which PM 1000 is the MC 1000 calculated for the seventh 

previous day. 

It is necessary, therefore, to maintain a 1 x 7 listing of 

MC1000 values: 

BNDRYT and MC1000 array 

1 2 3 4 5 6 7 

Xa Xb Xc Xd Xe Xf Xg Xh 

(next day) 

Xb Xc Xd Xe Xf Xg Xh Xi 

When a new value is added to the BNDRYT or MC 1000 

(Xh) arrays, the existing values are moved one position 

down the array. The value for the oldest day of the 7-day 

series (Xa) is replaced by the value for the next most recent 

day (Xb) and so on through the entire array. The latest 

BNDRYT and MC1000 values (Xi) are placed in the seventh position of the arrays. 

Initializing the MC1000 and BNDRYT Arrays at the 

Beginning of a Computational Period: 

MC1000 (n) = 10.0 + (5.0 * CLIMAT) 

BNDRYT (n) = 10.0 + (5.0 * CLIMAT) 

in which (n) denotes cells 1 through 7 in the two arrays. 

Fuels: Wet or Ice-Covered 

Rather than complicate the component models of the 

NFDRS with intricate logic, these conditions were judged 

better dealt with by rules. The wildfire potential is zero 

when the ground fuels are wet or covered with ice or snow. 

The expected data must be provided to the computer 

(AFFIRMS), however, and the 100- and 1000-hour fuel 

moisture calculations must continue without interruption. 

The logic of the rules is not difficult to accept: 

• No wildfire potential exists when ice, snow, or both 

are present. 

• Free water affects fuels in essentially the same way, 

whether it comes in the various forms of precipitation or 

from the thawing of ice or snow. 

• When precipitation is frozen or fuels are covered with 

ice, snow, or both, and there is no thaw, fuel moistures 

respond as if the relative humidity were 100 percent 

(McCammon 1974). 

Raining, Snowing, and Thawing, or Fuels Wet (Observation and Forecast): 

1. Set SC, ERC, BI, IC, MCOI, LOI, and FLI to Zero 

(0). 

2. Record MC1 as 35 percent. 

3. Record MC10 as 35 percent for the predicted value 

and for the observed value if sticks are not used: if sticks are 

5 
used, shake off the water and weigh as usual for the 

observed value. 

4. Calculate the 100- and 1000-hour fuel moistures as 

usual. 

Snowing or Fuels Covered by Ice, Snow, or Both, No 

Thaw (Observation and Forecast): 

1. Set SC, ERC, BI, IC, MCOI, LOI, and FLI to zero 

(0). 

2. Record MC1 as 35 percent. 

3. Record MC10 as 35 percent for the predicted value 

and for the observed value if sticks are not used; if sticks are 

used, shake off the snow and weigh as usual for the 

observed value. 

4. Calculate the 100- and 1000-hour fuel moistures as 

usual except use zero (0) for PPTDUR and 100 percent for 

both RHMAX and RHMIN. 

Fuels Covered by Ice, Snow, and Thawing: 

1. Set SC, ERC, BI, IC, MCOI, LOI, and FLI to zero 

(0). 

2. Record MC1 as 35 percent. 

3. Record MC10 as 35 percent for the predicted value 

and for the observed value if sticks are not used: if sticks are 

used, shake off the snow and weigh as usual for the 

observed value. 

4. Calculate the 100- and 1000-hour fuel moistures as 

usual except use the duration of the thaw during that 

24-hour period for PPTDUR and 100 percent for both 

RHMAX and RHMIN. 

Models of Live-Fuel Moisture 

For a more complete description of the live-fuel moisture models, refer to the publication by Burgan (1979). 

Essentially, two live-fuel moisture models are contained 

in the NFDRS: 

1. Herbaceous fuel moisture model with variations for 

annual and perennial types; 

2. Woody shrub fuel moisture model. 

Herbaceous Fuels 

The loading of the herbaceous fuels is a fuel model 

parameter just as the 1-hour timelag fuel loading is a fuel 

model parameter. The user specifies the herbaceous type as 

annual or perennial and the NFDRS climate class of the 

observation site. Those parameters control the rate at 

which the model passes through these five stages: 

1. pregreen (MCHERB 30 percent or less) 

2. greenup 

3. green (MCHERB greater than 120 percent) 

4. transition (MCHERB 30 to 120 percent) 

5. cured or frozen (MCHERB 30 percent or less) 

in which MCHERB is the moisture content of the herbaceous plants. 

6 

In late summer or fall herbaceous plants die or are killed 

back by frost. They remain, in either state, waiting for the 

warmth and moisture of spring before starting another 

growth cycle. When the herbaceous plants are in the pregreen stage, the model assumes their moisture content 

responds to the environment the same as the moisture 

content of the 1-hour fuels. The model accounts for this by 

transferring the entire loading of herbaceous plants to the 

1-hour fuel class. 

When greenup is declared by the user in spring, the 

herbaceous moisture content is initially at 30 percent. The 

loading of the herbaceous fuel is then reclaimed from the 

1-hour dead-fuel class as the herbaceous moisture content 

increases to 120 percent. The length of the greenup period 

depends on the NFDRS climate class of the observation 

site being 1 week for class 1, 2 weeks for class 2, 3 weeks for 

class 3, and 4 weeks for class 4. 

If greenup is complete, the MCHERB is 120 percent, the 

model has reached the green stage. The moisture content of 

perennials is allowed to increase or decrease as the available moisture increases or decreases. The moisture content 

of annuals can only remain the same or decrease once the 

greenup process is complete. The maximum value of 

MCHERB is 250 percent. 

When MCHERB falls below 120 percent, the herbaceous vegetation enters transition; that is, the curing process begins. As MCHERB decreases below 120 percent, the 

herbaceous loading is transferred to the 1-hour fuel class-­

the reverse of what occurred during greenup. When 

MCHERB falls to 30 percent, the loading of herbaceous 

fuel is zero. During transition, perennial plants are allowed 

to pick up moisture, but annual plants are not. 

If MCHERB decreases to 30 percent, the plants are 

considered cured. Perennial plants are allowed to recover 

and "re-green" on their own if moisture conditions improve. Once cured, however, annuals stay cured until the 

user declares "GREEN." 

The user can force the model to cure the herbaceous 

plants by specifying either "CURED" or "FROZEN." The 

herbaceous moisture prediction model responds identically to these two declarations. ("FROZEN" forces shrubs 

into dormancy, however). In this situation, both annuals 

and perennials remain cured until the next greenup is 

declared. 

Equations for the model through the pregreen, greenup, 

green, transition, and cured-frozen stages are these: 

Pregreen Stage--This stage is best described as that existing in late winter before new growth appears. The herbaceous plants are "straw-brown," having been killed by low 

moisture or freezing temperatures the previous year. The 

pregreen stage is set up in AFFIRMS only if a "FROZEN" 

command has been entered or if there has been a break in 

the data of at least 60 days. In milder climates, such as the 

Southeast, Gulf Coast, or Southwest, a killing freeze may 

not occur. So in those areas, if AFFIRMS is run year-long, 
the pregreen state should be forced during the winter with a 

"FROZEN" command. 

The following model settings are made for the pregreen 

stage: 

MCHERB = MC1 

W1P = W1 + WHERB 

in which 

W1 is the fuel model 1-hour fuel loading. 

WHERB is the fuel model herbaceous fuel loading. 

W1P is the pregreen 1-hour fuel loading. 

Greenup Stage--When the greenup process is begun the 

model settings are these: 

MCHERB = MCHRBI 

W1P=W1+ WHERB 

X1000 = MC1000 

GRNDAY = 0 

in which 

MCHRBI is the maximum of 30 percent or MCHERB 

calculated the day before to the greenup. 

W1P is the pregreen 1-hour fuel loading. 

X1000 is the independent variable in the herbaceous fuel 

moisture models 

GRNDAY is the number of days elapsed since 

greenup started. 

MCHERB is a function of X1000, the herbaceous plant 

type, and the NFDRS climate class. With the start of 

greenup, X1000 is set equal to MC1000. From that point 

on, the X1000 is calculated as follows: 

DIFF = MC1000 - YM1000 

X1000 = YX1000 + (DIFF * KWET * KTMP)

in which 

YM1000 is the MC1000 calculated the previous day. 

YX1000 is the X1000 calculated the previous day. 

DIFF is the 24-hour change in MC1000. 

KWET is the wetting factor. 

KTMP is the temperature factor. 

in which 

If MC1000 is greater than 25 percent, KWET = 1.0. 

If MC1000 is less than 26 percent and greater than 9 

percent, KWET = (0.0333 * MC1000 + 0.1675). 

If MC1000 is less than 10 percent, KWET = 0.5. 

If DIFF is less than or equal to 0.0, KWET = 1.0. 

If (TMPMAX + TMPMIN) / 2.0 is less than or equal 

to 50°F, KTMP = 0.6; otherwise, a value of 1.0 is used. 

Next needed is the moisture content that herbaceous 

fuels would have if the greenup period were over; this we 

call MCHRBP (P for Potential). MCHRBP is linearly 

related to X 1000, but the constants of the relationship are 

functions of the NFDRS climate class. 

MCHRBP = HERBGA + HERBGB * X1000 

in which the constant and coefficient are determined by the 

NFDRS climate class. 

NFDRS 

Climate class: HERBGA HERBGB 

1 - 70.0 12.8 

2 -100.0 14.0 

3 -137.5 15.5 

4 -185.0 17.4 

The length of the greenup period, in days, is seven times 

the NFDRS climate class. The fraction of greenup period 

that has elapsed must be calculated so that the loading of 

the herbaceous fuel can be calculated. 

GREN = GRNDAY / (7.0 * CLIMAT) (4) 

in which GRNDAY is the number of days since the greenup 

sequence was started. 

During greenup, MCHERB is phased up. 

MCHERB = MCHRBI 

+ (MCHRBP - MCHRBI) * GREN 

The fraction of the fuel model herbaceous fuel loading 

transferred to the 1-hour class is FCTCUR. 

FCTCUR = 1.33 - 0.0111 * MCHERB (5) 

in which FCTCUR cannot be less than 0.0 nor more than 

1.0. 

The actual amount of fuel transferred can now be 

calculated. 

WHERBC = FCTCUR * WHERB (6) 

The I-hour and herbaceous fuel loadings, W1P and 

WHERBP, therefore, become: 

W1P = W1 +WHERBC (7) 

WHERBP = WHERB - WHERBC (8) 

Green Stage--At the end of the greenup period 

GREN = 1.0; therefore, MCHERB = MCHRBP. If it has 

been exceptionally dry during the greenup period, X1000 

will be low, and MCHRBP may not reach 120 percent. 

When this situation occurs, the green stage is bypassed and 

the model goes directly into transition. As long as 

MCHRBC is greater than 120 percent, however, 

MCHERB (for both perennials and annuals) is calculated 

by the linear equation and constants determined by the 

climate class (see tabulation of HERBGA AND HERBGB 

above). 

7 
MCHERB = HERBGA + HERBGB * X1000 

in which MCHERB is not allowed to exceed 250 percent. 

Transition Stage--When MCHERB drops below 120 percent, these transition equations are used: 

For annuals: 

MCHERB = ANNTA + ANNTB * X1000 

For perennials: 

MCHERB = PERTA + PERTB * X1000 

in which 

MCHERB cannot exceed 150 or be less than 30 percent if 

plants are perennials. 

MCHERB cannot be higher than MCHERB calculated 

the previous day if plants are annuals. 

The constant and coefficient for the equations are 

determined by the NFDRS climate class as follows: 

NFDRS Annuals Perennials 

climate class: ANNTA ANNTB PERTA PERTB 

1 -150.5 18.4 11.2 7.4 

2 -187.7 19.6 -10.3 8.3 

3 -245.2 22.0 -42.7 9.8 

4 -305.2 24.3 -93.5 12.2 

For both herbaceous types, the model causes fuel to be 

transferred back and forth between the herbaceous and 

1-hour classes as MCHERB fluctuates between 30 and 120 

percent. Equations 5, 6, 7, and 8 are used to calculate the 

amount of fuel moving back and forth between classes. 

Cured or Frozen Stage--If curing occurs by way of normal, seasonal drying (MCHERB drops to 30 percent without intervention by the user), these equations are used: 

For annuals: 

MCHERB = MC1 

For perennials: 

MCHERB = PERTA + PERTB * X1000 

in which MCHERB cannot be less than 30 percent nor more 

than 150 percent if the plants are perennials. 

Perennials are treated no differently than they are in the 

transition stage unless the user forces curing with a FROZEN or CURED command. If that is the situation, the 

equation for MCHERB for perennials becomes: 

MCHERB = MC1 

In automated systems such as AFFIRMS and FIREFAMILY, once curing has taken place, the herbaceous 

moisture content of annual plants is displayed with the 

same value as the moisture content of the I-hour fuels. If 

the perennial designation has been used, the herbaceous 

moisture content will remain at 30 percent until moisture 

conditions improve or FROZEN or CURED has been 

declared. Operationally, a killing freeze is declared by the 

user. With historical fire-weather data, FIREFAMILY 

handles freezing as follows: the user designates on a lead 

card the earliest date that a killing frost is plausible. FIREFAMILY, for observations after that date, will then set the 

FROZEN flag: 

1. The first time a minimum temperature (TMPMIN) 

25° F or less occurs; or 

2. The fifth day that a minimum temperature falls in the 

range 26° to 32° F. 

Shrub Fuels 

The prediction model for woody fuel moisture is much 

simpler than that for herbaceous fuel moisture. Only four 

stages in the annual growth cycle are recognized, and loadings between fuel classes are not transferred. The four 

stages of the model are: 

1. pregreen (MCWOOD = PREGRN) 

2. greenup 

3. green (MCWOOD greater than PREGRN) 

4. frozen (MCWOOD = PREGRN) 

in which 

MCWOOD is the predicted moisture content of the 

twigs and foilage [sic] of the shrubs. 

PREGRN is the moisture content of shrubs when 

dormant. 

Pregreen Stage--This stage is analagous to the pregreen 

stage of the herbaceous fuel moisture model. 

MCWOOD = PREGRN 

in which PREGRN is 50 for NFDRS climate class 1, 60 for 

class 2, 70 for class 3, or 80 percent for class 4. 

Greenup Stage--MCWOOD is a function of MC1000 and 

the NFDRS climate class. During greenup, as in the herbaceous fuel moisture model, MCWOOD increases to its 

potential value over a period equal to seven times the 

climate class of the observation site. 

The first step is the calculation of the potential woody 

fuel moisture 

MCWODP = WOODGA + WOODGB * MC1000 

in which the constant and coefficient are determined by the 

NFDRS climate class. 

NFDRS 

climate class: WOODGA WOODGB 

1 12.5 7.5 

2 -5.0 8.2 

3 -22.5 8.9 

4 -45.0 9.8 

8 
The fraction of the greenup period that has elapsed, 

GREN, is calculated by equation 4. The woody fuel moisture during greenup is then calculated by this equation: 

MCWOOD = MCWODI 

+ (MCWODP - MCWODI) * GREN 

n which MCWODI is the greater of PREGRN or the 

MCWOOD calculated the day previous to greenup. 

Green Stage--After greenup, GREN = 1.0 and 

MCWOOD = MCWODP, and, therefore, MCWOOD can 

be calculated by the linear equation and constants from the 

preceding table. 

MCWOOD = WOODGA + WOODGB * MC1000 

in which MCWOOD cannot be less than the appropriate 

PREGRN value or greater than 200 percent. 

Frozen Stage--This is the same as the pregreen stage, but is 

included to provide consistency between the discussions of 

the herbaceous and woody moisture models. 

The model for woody fuel moisture does not respond to 

CURED if and when it is declared by the user. The types of 

shrubs considered here are not deciduous, therefore, no 

condition analogous to herbaceous cured exists. Shrubs 

will go into dormancy if the weather is cold enough, however, so the model for woody fuel moisture responds to 

FROZEN by setting MCWOOD to the appropriate 

PREGRN value. MCWOOD will not change until the next 

greenup. 

SYSTEM COMPONENTS AND 

INDEXES 

The NFDRS spread and energy release components (SC 

and ERC) are taken from Rothermel (1972) as modified by 

Albini (1976). The burning index (BI) is based on Byram's 

flame-length model (Byram 1959). The ignition and the 

two occurrence models were developed for the NFDRS, as 

was the fire load index (FLI). The SC, ERC, and BI relate to 

the characteristics of fire. These models will be dealt with first. 

Models of Fire Characteristics 

Preliminary Calculations 

All fuel loadings are converted to pounds per square foot 

by multiplying the tons per acre value by 0.0459137 (lbacre)/(ton-ft2

). Fuel model characteristics are listed in the 

appendix. 

Total Dead and Live-Fuel Loadings: 

(dead) WTOTD = W1P + W l0 + W100 + W1000 

(live) WTOTL = WHERBP + WWOOD 

in which 

W1P is the 1-hour timelag fuel loading in addition to the 

portion of the live herbaceous loading that has cured. 

W 10, W100, and W1000 are the loadings of the 10-, 

100-, and 1000-hour timelag fuels specified in the fuel 

model. 

WHERBP is the herbaceous fuel loading remaining. 

WWOOD is the loading of the woody shrub plants specified in the fuel model. 

Total Fuel Loading: 

WTOT = WTOTD + WTOTL 

Net Fuel Loading of Each Fuel Class: 

(1-hour) W1N = W1P * (1.0 - STD) 

(10-hour) W10N = W10 * (1.0 - STD) 

(100-hour) W100N = W100 * (1.0 - STD) 

(herbaceous) WHERBN = WHERBP * (1.0 - STL) 

(woody) WWOODN = WWOOD * (1.0 - STL) 

in which STD and STL are the fractions of the dead and 

live fuels made up of inert, noncombustible minerals. A 

value of 0.0555 is used for both. 

Bulk Density of the Fuel Bed: 

RHOBED = (WTOT - W1000) / DEPTH 

in which DEPTH is the effective fuel bed depth measured 

in feet. 

Weighted Fuel Density: 

RHOBAR = ((WTOTL * RHOL) 

+ (WTOTD * RHOD)) / WTOT 

in which 

RHOL and RHOD are the live and dead-fuel particle 

densities. 

A constant value of 32 lb/ft

3

 is used. 

Packing Ratio: 

BETBAR = RHOBED/ RHOBAR 

Mineral Damping Coefficient of Live and Dead Fuels: 

(dead) ETASD = 0.174 * SD**(-0.19) 

(live) ETASL = 0.174 * SL**(-0.19) 

9 
in which SD and SL are the fractions of the dead and live 

fuels made up of silica-free, noncombustible minerals. A 

constant value of 0.01 is assumed for both SD and SL. 

Heating Numbers of Each Fuel Class: 

(1-hour) HN1 = W1N * EXP(-138.0 / SG1) 

(10-hour) HN10 = W10N * EXP(-138.0 / SG10) 

(100-hour) HN 100 = W100N 

* EXP(-138.0 / SG100) 

(herbaceous) HNHERB = WHERBN 

* EXP(-500.0 / SGHERB) 

(woody) HNWOOD = WWOODN 

* EXP(-500.0 / SGWOOD) 

in which SG1, SG10, SG100, SGHERB, and SGWOOD 

are the surface-area-to-volume ratios of the 1-, 10-, 100-

hour herbaceous and woody fuels specified in the fuel 

model. 

Because the surface-area-to-volume ratio of the 1000-

hour fuel class is so low (8.0 ft-1), its influence is minimal 

and is omitted to simplify the computation. No net 1000-

hour fuel loading is computed for the same reason. 

Ratio of Dead-to-Live Fuel Heating Numbers: 

WRAT = (HN1 + HN10 + HN100) 

/ (HNHERB + HNWOOD) 

Spread Component 

In this model, the influence each fuel class has on the 

result is determined by the fraction of the total surface area 

of the fuel complex contributed by that fuel class. 

Surface Area of Each Fuel Class: 

(1-hour) SA1 = (W1P/RHOD) * SG1 

(10-hour) SA10 = (W10/RHOD) * SG10 

(100-hour) SA100 = (W100/RHOD) * SG100 

(herbaceous) SAHERB = (WHERB/ RHOL) 

* SGHERB 

(woody) SAWOOD = (WWOOD/RHOL) 

* SGWOOD 

Total Surface Area of Dead and Live Fuels: 

(dead) SADEAD = SA1 + SA10 + SA100 

(live) SALIVE = SAHERB 

+ SAWOOD 

Weighting Factors of Each Fuel Class: 

(1-hour) F1 = SA1/SADEAD 

(10-hour) F10 = SA10/SADEAD 

(100-hour) F100 = SA100/SADEAD 

(herbaceous) FHERB = SAHERB/SALIVE 

(woody) FWOOD = SAWOOD/SALIVE 

Weighting Factors of Dead and Live Fuels: 

(dead) FDEAD = SADEAD/(SADEAD + SALIVE) 

(live) FLIVE = SALIVE/(SADEAD + SALIVE) 

Weighted Net Loadings of Dead and Live Fuels: 

(dead) WDEADN = (Fl * WIN) + (F10 * W10N) 

+ (F100 * W100N) 

(live) WLIVEN = (FWOOD * WWOODN) 

+ (FHERB * WHERBN) 

Dead and Live Fuel Characteristic Surface-Area-to-Volume Ratios: 

(dead) SGBRD = (Fl * SG1) + (F10 * SG10) 

+ (F100 * SG100) 

(live) SGBRL = (FHERB * SGHERB) 

+ (FWOOD * SGWOOD) 

Characteristic Surface-Area-to-Volume Ratio: 

SGBRT = (FDEAD * SGBRD) + (FLIVE * SGBRL) 

Optimum Packing Ratio: 

BETOP = 3.348 * SGBRT**(-0.8189) 

Maximum Reaction Velocity: 

GMAMX = (SGBRT** 1.5) / (495.0 

+ 0.0594 * SGBRT**1.5) 

Optimum Reaction Velocity: 

GMAOP = GMAMX*(BETBAR/BETOP)**AD 

* EXP(AD * (1.0 - BETBAR / BETOP)) 

in which AD = 133.0 * SGBRT**(-0.7913) 

No Wind Propagating Flux Ratio: 

ZETA = EXP((0.792 + 0.681 * SGBRT**0.5) 

* (BETBAR + 0.1)) / (192.0 + 0.2595 * SGBRT) 

Weighted Dead-Fuel Moisture Content for Live-Fuel 

Extinction Moisture: 

MCLFE = ((MC1 * HN1) + (MC10 * HN10) 

+ (MC100 * HN100)) / (HN1 + HN10 + HN100) 

Moisture of Extinction of Live Fuels: 

MXL = (2.9 * WRAT * (1.0 - MCLFE/MXD) 

- 0.226) * 100.0 

in which 

10 
MXD is the moisture of extinction of the dead fuels 

from the fuel model.

MXL cannot be less than MXD. 

Weighted Moisture Content of Dead and Live Fuels:

(dead) WTMCD = (F1 * MC1) + (F10 * MC10) 

+ (F100 * MC100) 

(live) WTMCL = (FHERB * MCHERB) 

+ (FWOOD * MCWOOD) 

Moisture Damping Coefficients of Dead and Live Fuels: 

(dead) ETAMD = 1.0 - 2.59 * DEDRT + 5.11 

* DEDRT**2.0 - 3.52 

* DEDRT**3.0 

(live) ETAML = 1.0 - 2.59 * LIVRT + 5.11 

* LIVRT**2.0 - 3.52 * LIVRT**3.0 

in which 

DEDRT = (WTMCD / MXD) 

LIVRT = (WTMCL/MXL) 

ETAMD and ETAML cannot be less than zero or 

greater than 1.0.

Wind Effect Multiplier Coefficients and Exponents: 

B = 0.02526 * SGBRT**0.54 

C = 7.47 * EXP(-0.133 * SGBRT**0.55) 

E = 0.715 * EXP(-3.59 * 10.0**(-4.0) * SGBRT) 

UFACT = C * (BETBAR/BETOP)**(-E) 

Wind Effect Multiplier: 

PHIWND = UFACT * (WS * 88.0 * WNDFC)**B 

in which 

WS is the 10-minute average 20-ft windspeed in mph. 

WNDFC is the fuel model wind reduction factor. 

The effect of high winds is limited: 

If (WS * 88.0 * WNDFC) is greater than (0.9 * IR), 

then (0.9 * IR) replaces (WS * 88.0 * WNDFC). Then the 

equation becomes 

PHIWND = UFACT * (0.9 * IR)**B 

Slope Effect Multiplier Coefficient: 

SLPFCT = 5.275 * (TAN(slope angle))**2.0 

in which 

NFDRS slope class: Slope angle SLPFCT 

1 12.67° 0.267 

2 17.63° 0.533 

3 24.23° 1.068 

4 32.46° 2.134 

5 41.99° 4.273 

Slope Effect Multiplier: 

PHISLP = SLPFCT * BETBAR**(-0.3) 

Reaction Intensity: 

IR = GMAOP * ((WDEADN * HD * ETASD 

* ETAMD) + (WLIVEN * HL * ETASL * ETAML)) 

in which HD and HL are the heat values for dead and live 

fuels specified in the fuel model, Btu/lb. 

Heat Sink: 

HTSINK = RHOBED * (FDEAD 

* (F1 * EXP(-138.0/SG1) * (250.0 + 11.16 * MC1) 

+ Fl0 * EXP(-138.0/SG10) * (250.0 + 11.16 * MC10) 

+ F100 * EXP(-138.0/SG100) * (250.0 + 11.16 * MC100))) 

+ (FLIVE * (FHERB * EXP(-138.0/SGHERB) 

* (250.0 + 11.16 * MCHERB) + FWOOD 

* EXP(-138.0/SGWOOD) 

* (250.0 + 11.16 * MCWOOD))) 

Rate of Spread: 

ROS = IR * ZETA 

* (1.0 + PHISLP + PHIWND)/HTSINK (ft/ min) 

Spread Component: 

SC = IRND(ROS) 

Energy Release Component 

In this model the influence of each fuel class is deterined by the fraction of the total fuel loading contributed 

by that class. As a result, the conditions of the larger fuels 

have more influence on the fire-danger. 

Weighting Factors of Each Fuel Class: 

(1-hour) F1E= WIP/WTOTD 

(10-hour) F10 = 10/WTOTD 

(100-hour) F100E = W100/WTOTD 

(1000-hour ) FI000E = W1000/WTOTD 

(herbaceous) FHERBE = WHERBP/ WTOTL 

(woody) FWOODE = WWOOD/WTOTL 

Weighting Factors of Dead and Live Fuels: 

(dead) FDEADE = WTOTD/ WTOT 

(live) FLIVEE = WTOTL/ WTOT 

Net Loadings of Dead and Live Fuels: 

(dead) WDEDNE = WTOTD * (1.0-STD) 

(live) WLIVNE = WTOTL * (1.0-STL) 

11 
Dead and Live Fuel Characteristic Surface-Area-toVolume Ratios: 

(dead) SGBRDE = (FIE * SG1) + (FLOE * SG10) 

+ (FC100E * SG100) 

+ (FI000E * SG1000) 

(live) SGBRLE = (FWOODE * SGWOOD) 

+ (FHERBE * SGHERB) 

Characteristic Surface-Area-to-Volume Ratio: 

SGBRTE = (FDEADE * SGBRDE) 

+ (FLIVEE * SGBRLE) 

Optimum Packing Ratio: 

BETOPE = 3.348 * SGBRTE**(-0.8189) 

Maximum Reaction Velocity: 

GMAMXE = SGBRTE**1.5/(495.0 

+ 0.0594 * SGBRTE**1.5) 

Optimum Reaction Velocity: 

GMAOPE = GMAMXE 

* (BETBAR/BETOPE)**ADE*EXP(ADE 

* (1.0 - BETBAR/BETOPE)) 

in which ADE = 133.0 * SGBRTE**(-0.7913) 

Weighted Moisture Contents of Dead and Live Fuels: 

(dead) WTMCDE = (F1E * MC1) + (F10E * MC10) 

+ (F100E * MC100) 

+ (F1000E * MC1000) 

(live) WTMCLE = (FWOODE * MCWOOD) 

+ (FHERBE * MCHERB) 

Moisture Damping Coefficients of Dead and Live Fuels: 

(dead) ETAMDE = 1.0 - 2.0 * DEDRTE 

+ 1.5 * DEDRTE**2.0 

- 0.5 * DEDRTE**3.0 

(live) ETAMLE = 1.0 - 2.0 * LIVRTE 

+ 1.5 * LIVRTE**2.0 

- 0.5 * LIVRTE**3.0 

in which 

DEDRTE = (WTMCDE/MXD) 

LIVRTE = (WTMCLE/ MXL) 

ETAMDE and ETAMLE cannot be less than zero or 

greater than 1.0 

Reaction Intensity: 

12 

IRE = GMAOPE * ((FDEADE * WDEDNE * HD 

* ETASD * ETAMDE) + (FLIVEE * WLIVNE 

* HL * ETASL * ETAMLE)) 

Residence time of the Flaming Front: 

TAU = 384.0/ SGBRT 

The surface area weighted surface area-to-volume ratio, 

SGBRT, is used rather than the mass weighted form 

(SGBRTE). The mass weighted residence time produced 

unrealistic results. 

Energy Release Component: 

ERC = IRND(0.04 * IRE * TAU) 

The 0.04 scaling factor has the units ft

2

/ Btu. As such, a 

unit value of ERC is equivalent to 25 Btu of available energy 

per square foot. 

Burning Index 

The BI is numerically equivalent to 10 times the predicted flame length, in feet. The equation developed by 

Byram (1959) is used with some liberties, enabling us to use 

parameters that are outputs from Rothermel's fire spread 

model. 

Byram's equation: 

FL = 0.45 * I**0.46 (ft.) 

in which I is the fireline intensity, Btu/ft-sec 

but I = IRE * D/60.0, Btu/ft-sec 

in which D = ROS * TAU, ft 

so I = (ROS/60.0) * IRE * TAU, Btu/ft-sec 

but ROS = SC and IRE * TAU = 25.0 * ERC 

therefore FL = 0.45 * ((SC/60.0) * (25.0 * ERC))**0.46 

and FL = 0.301 * (SC * ERC)**0.46 

Burning Index: 

BI = IRND(3.01 * (SC * ERC)**0.46) 

If the fuels are wet or covered by snow or ice at observation time, the BI is set to zero. 

Models of Fire Occurrence 

Ignition Component 

The IC consists of two parts: (1) the probability that a 

firebrand will produce a successful fire start in dead, fine 

fuels, P(I); and (2) the probability that a reportable fire will 

occur, given an ignition P(F/ I). 

P(I) is a function of the amount of heat required to 

produce an ignition (QIGN) which, in turn, is a function of 

the 1-hour fuel moisture, MC1. P(I) is scaled such that it is 

100 when MC1 = 1.5 percent and zero when MC1 = 25.0 

percent. Three scaling factors are used for this purpose: 
PNORM1 = 0.00232 

PNORM2 = 0.99767 

PNORM3 = 0.0000185 

Heat of Ignition: 

QIGN = 144.5 - (0.266 * TMPPRM) - (0.00058 

* TMPPRM**2.0) - (0.01 * TMPPRM * MC1) 

+ (18.54 * (1.0 - EXP(-0.151 * MC1))) + 6.4 * MC1) 

in which TMPPRM is the estimated observation time dry 

bulb temperature of the air in immediate fuel contact, in 

degrees Celsius. 

Intermediate Calculations: 

CHI = (344.0 - QIGN) / 10.0 

in which, if (CHI**3.6 * PNORM3) is equal to or less than 

PNORMI, then P(I) and the IC are set to zero. 

Probability of Ignition: 

P(I) = (CHI**3.6 * PNORM3 

- PNORMI) * 100.0/PNORM2 

in which P(I) is limited to the range of values from 0 to 100. 

P(F/ I) is a function of the spread component for that 

fuel model normalized to the value the spread component 

would have under a specific set of severe burning conditions (slope class 1; 20-ft wind 20 mph; herbaceous vegetation cured; woody vegetation moisture content at the pregreen level; and the 1-, 10-, and 100-hour fuel moistures 3.0 

percent.) This function was derived empirically by Main 

and others (1982). 

Normalized Rate of Spread: 

SCN = 100.0 * SC/SCM 

in which SCM is, in the developers' best judgment, the SC 

for which all ignitions become reportable fires. An SCM 

was calculated for each fuel model and is included as a fuel 

model parameter. 

Probability of a Reportable Fire: 

P(F/I) = SCN**0.5 

Ignition Probability: 

IC = IRND(0.10 * P(I) * P(F/I)) 

in which the factor 0.10 is required to limit the range of IC 

to 0 to 100. 

Human-Caused FireOccurrence Index 

MCOI = IRND(0.01 * MRISK * IC) 

in which MRISK is the human-caused risk. See Deeming 

and others (1977) for details about its evaluation. 

Lightning-Caused Fire Occurrence Index 

For information about this model, see the publications 

by Fuquay and others (1979) and Fuquay (1980). The 

model assumes that a thunderstorm traversing an area 

forms a corridor aligned with the storm's track that 

receives both rain and lightning. Flanking the rainlightning corridor on both sides are areas subjected to 

lightning only. 

The width of the rain-lightning corridor affected 

(STMDIA), the total width of the lightning-only and 

lightning-rain corridors (TOTWID), and the discharge 

rate (CGRATE) for cloud-to-ground lightning are functions of the NFDRS lightning activity level (LAL): 

NFDRS CGRATE STMDIA TOTWID 

LAL strikes/min miles miles 

1 0.0 0.0 0.0 

2 12.5 3.0 7.0 

3 25.0 4.0 8.0 

4 50.0 5.0 9.0 

5 100.0 7.0 11.0 

6 (LRISK = 100, LOI = 100) 

Duration of Lightning at a Point Within the Affected 

Area: 

LGTDUR = -86.83 + 153.41 * CGRATE**0.1437. 

Fractions of the Area Occupied by the Lightning-Rain 

and Lightning-Only Corridors: 

(Lightning-rain) FINSID = ((STMDIA * STMSPD 

*LGTDUR) + (0.7854 

*STMDIA**2.0)) 

/((STMDIA * STMSPD 

*TOTWID) + (0.7854 

*TOTWID**2.0)) 

(Lightning-only) FOTSID = (1.0 - FINSID) 

Rain Duration at a Point Within the Lightning-Rain 

Corridor: 

RAIDUR = STMDIA/STMSPD 

in which STMSPD is the translational speed of the storm 

in miles per hour. For the NFDRS, a constant speed of 30 

mph is used. 

Moisture Content of the 1-Hour Fuels Within the Rain 

Area: 

FMF = MC1 + ((76.0 + 2.7 * RAIDUR) 

- MC1) * (1.0 - EXP(-RAIDUR)) 

The ignition component within the area affected by rain 

is calculated exactly as the IC except that FMF is used 

13
instead of MC1. The IC for the rain-affected corridor is 

denoted as ICR and is a significant deviation from the 

Fuquay model. As a simplification, it was decided to use 

the NFDRS IC function rather than the ignition probability function developed for the model. The difference was 

judged to be minor. Also, the LRSF was introduced to 

account for area-specific fuel conditions that affect the 

fire-starting efficiency of the lightning (Bradshaw and others 1983). 

Area Weighted Ignition Component: 

ICBAR = ((FINSID * ICR) + (FOTSID * IC))/ 100.0 

Lightning-Risk: 

LRISK = CGRATE * LRSF 

in which 

LRSF is the lightning risk scaling factor. See Deeming 

and others (1977) for a complete description. 

LRISK is limited to a numerical range of 0-100. 

Lightning-Caused Fire Occurrence Index Computation: 

If it is not lightning, or if it is raining at the time of the 

afternoon weather observation at the fire-weather station, 

14 

25 percent of the previous day's LOI is used to account for 

carry-over fires. 

LOI = IRND(0.25 * YLOI) 

in which YLOI is the previous day's LOI; 

otherwise 

LOI = IRND(10.0 * (LRISK * ICBAR) + 0.25 * YLOI) 

in which the multiplier 10.0 scales the LOI such that the 

expected number of lightning fires per million acres 

increases by 1.0 for every 10 points of LOI. The LOI is 

limited to a value range of 0 to 100. 

If LAL 6 is observed or predicted, the lightning risk 

(LRISK) and lightning-caused fire occurrence index (LOI) 

are set to 100. 

Fire Load Index 

FLI = 0.71 * SQRT(BI**2.0 + (LOI + MCOI)**2.0) 

in which the BIis limited to 100 as is the sum of LOI and 

MCOI. 
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APPENDIX--Parameters for fuel models 

Ratios and Fuel loadings1 

Fuel model 1-h2 10-h3 100-h4 1000-h5 Wood6 Herb7 

Depth 

(ft)8 

MXD 

(pct)9 

HD&HL 

(Btu/lb)10 SCM11 WNDFC12 

A 

B 

C 

D 

E 

F 

G 

H 

I 

J 

K 

L 

N 

O 

P 

Q 

R 

S 

T 

U 

Western grasses 

(annual) 

California 

chaparral 

Pine-grass 

savanna 

Southern rough 

Hardwood litter 

(winter) 

Intermediate 

brush 

Short needle 

(heavy dead) 

Short needle 

(normal dead) 

Heavy slash 

Intermediate 

slash 

Light slash 

Western grasses 

(perennial) 

Sawgrass 

High pocosin 

Southern pine 

plantation 

Alaskan black 

spruce 

Hardwood litter 

(summer) 

Tundra 

Sagebrush-grass 

Western pines 

3000 

0.20 

700 

3.50 

2000 

0.40 

1250 

2.00 

2000 

1.50 

700 

2.50 

2000 

2.50 

2000 

1.50 

1500 

12.00 

1500 

7.00 

1500 

2.50 

2000 

0.25 

1600 

1.50 

1500 

2.00 

1750 

1.00 

1500 

2.00 

1500 

0.50 

1500 

0.50 

2500 

1.00 

1750 

1.50 

109 

4.00 

109 

1.00 

109 

1.00 

109 

0.50 

109 

2.00 

109 

2.00 

109 

1.00 

109 

12.00 

109 

7.00 

109 

2.50 

109 

1.50 

109 

3.00 

109 

1.00 

109 

2.50 

109 

0.50 

109 

0.50 

109 

0.50 

109 

1.50 

30 

0.50 

30 

0.25 

30 

1.50 

30 

5.00 

30 

2.00 

30 

10.00 

30 

6.00 

30 

2.00 

30 

3.00 

30 

0.50 

30 

2.00 

30 

0.50 

30 

0.50 

30 

1.00 

8 

12.0 

8 

2.00 

8 

12.00 

8 

5.50 

8 

2.50 

8 

2.00 

8 

1.00 

8 

0.50 

1250 

11.50 

1500 

0.50 

1500 

3.00 

1500 

0.50 

1250 

9.00 

1500 

0.50 

1500 

0.50 

1500 

2.00 

1500 

7.00 

1500 

0.50 

1200 

4.00 

1500 

0.50 

1200 

0.50 

1500 

2.50 

1500 

0.50 

3000 

0.30 

2500 

0.80 

1500 

0.75 

2000 

0.50 

2000 

0.50 

2000 

0.50 

2000 

0.50 

2000 

0.50 

1500 

0.50 

2000 

0.50 

1500 

0.50 

2000 

0.50 

2000 

0.50 

0.80 15 8000 

4.50 15 9500 

0.75 20 8000 

2.00 30 9000 

0.40 25 8000 

4.50 15 9500 

1.00 25 8000 

0.30 20 8000 

2.00 25 8000 

1.30 25 8000 

0.60 25 8000 

1.00 15 8000 

3.00 25 8700 

4.00 30 9000 

0.40 30 8000 

3.00 25 8000 

0.25 25 8000 

0.40 25 8000 

1.25 15 8000 

0.50 20 8000 

300 

58 

32 

25 

25 

24 

30 

8 

65 

44 

23 

178 

167 

99 

14 

59 

6 

17 

73 

16 

0.6 

0.5 

0.4 

0.4 

0.4 

0.5 

0.4 

0.4 

0.5 

0.5 

0.5 

0.6 

0.6 

0.5 

0.4 

0.4 

0.4 

0.6 

0.6 

0.4 

1

For each fuel model, the top value is surface-area-to-volume ratio (ft

-1), 8

Effective fuel bed depth. 

and the bottom value is fuel loading (tons/acre). 9

Assigned dead fuel moisture of extinction. 2

1-hour timelag dead fuel moisture class. 10Dead and live fuel heat of combustion. 3

10-hour timelag dead fuel moisture class. 11Assigned spread component value when all ignitions become report- 4

100-hour timelag dead fuel moisture class. able fires. 5

1000-hour timelag dead fuel moisture class. 12Wind reduction factor from 20-foot standard height to the midflame 6

Live fine woody fuel class. height. 7

Live fine herbaceous fuel class. 

15 
REFERENCES 

Albini, Frank A. Estimating wildfire behavior and effects. Gen. Tech. 

Rep. INT-30. Ogden, UT: Intermountain Forest and Range Experiment Station, Forest Service, U.S. Department of Agriculture; 1976. 

92 p. 

Bradshaw, Larry; Deeming, John E.; Burgan, Robert E.; Cohen, Jack 

D. 1978 National Fire-Danger Rating System--technical documentation. Gen. Tech. Rep. INT 169. Ogden, UT: Intermountain Forest 

and Range Experiment Station, Forest Service, U.S. Department of 

Agriculture; 1983. 44 p. 

Burgan, Robert E. Estimating live-fuel moisture for the 1978 National 

Fire-Danger Rating System. Res. Pap. INT 226. Ogden, UT: Intermountain Forest and Range Experiment Station, Forest Service, U.S. 

Department of Agriculture; 1979. 17 p. 

Burgan, Robert E.; Cohen, Jack D.; Deeming, John E. Manually calculating fire-danger rating-- 1978 National Fire Danger Rating System. 

Gen. Tech. Rep. INT-40. Ogden, UT: Intermountain Forest and 

Range Experiment Station, Forest Service, U.S. Department of Agriculture; 1977. 51 p. 

Byram, George M. Combustion of forest fuels. In: Forest fire control 

and use. New York, NY: McGraw Hill Book Company; 1959: Chapter 

3, p. 61. 

Byram, George M.; Jemison, George M. Solar radiation and forest fuel 

moisture. J. Agric. Res. 67(4):149-176; 1943 August. 

Cramer, Owen P. Predicting moisture contents of fuel moisture indicator sticks. Res. Pap. PNW-41. Portland, OR: Pacific Northwest 

Forest and Range Experiment Station, Forest Service, U.S. Department of Agriculture; 1961. 17 p. 

Deeming, John E.; Burgan, Robert E.; Cohen, Jack D. The National 

Fire-Danger Rating System--1978. Gen. Tech. Rep. INT-39. 

Ogden, UT: Intermountain Forest and Range Experiment Station, 

Forest Service, U.S. Department of Agriculture; 1977. 63 p. 

Deeming, John E.; Lancaster, J. W.; Fosberg, Michael A.; Furman, 

William R.; Schroeder, Mark J. The National Fire-Danger Rating 

System. Res. Pap. RM-84. Fort Collins, CO: Rocky Mountain Forest 

and Range Experiment Station, Forest Service, U.S. Department of 

Agriculture; 1972, revised 1974. 165 p. 

Fosberg, Michael A. Moisture content calculations for the 100-hour 

timelag fuel in fire-danger rating. Res. Note RM-199. Fort Collins, 

CO: Rocky Mountain Forest and Range Experiment Station, Forest 

Service, U.S. Department of Agriculture; 1971. 7 p. 

Fosberg, Michael A. Forecasting the 10-hour timelag fuel moisture. 

Res. Pap. RM-187. Fort Collins, CO: Rocky Mountain Forest and 

Range Experiment Station, Forest Service, U.S. Department of Agriculture; 1977. 10 p. 

16 

Fosberg, Michael A.; Deeming, John E. Derivation of the 1- and 10-

hour timelag fuel moisture calculations for fire-danger rating. Res. 

Note RM-207. Fort Collins, CO: Rocky Mountain Forest and Range 

Experiment Station, Forest Service, U.S. Department of Agriculture, 

1971. 8 p. 

Fosberg, Michael A.; Rothermel, Richard C.; Andrews, Patricia L. 

Moisture content calculations for the 1000-hour timelag fuels. Forest 

Sci. 27(l):19-26; 1981. 

Fuquay, Donald M. Forecasting lightning activity level and associated 

weather. Res. Pap. INT-244. Ogden, UT: Intermountain Forest and 

Range Experiment Station, Forest Service, U.S. Department of Agriculture; 1980. 30 p. 

Fuquay, D. M.; Baughman, R. G.; Latham, D. J. A model for predicting 

lightning-fire ignition in wildlands fuels. Res. Pap. INT-217. Ogden, 

UT: Intermountain Forest and Range Experiment Station, Forest Service, U.S. Department of Agriculture; 1979. 22 p. 

Haines, Donald A.; Frost, John S. Weathering effects on fuel moisture 

sticks: corrections and recommendations. Res. Pap. NC-154. St. Paul, 

MN: North Central Forest Experiment Station, Forest Service, U.S. 

Department of Agriculture; 1978. 7 p. 

Helfman, Robert S.; Straub, Robert J.; Deeming, John E. User's guide to 

AFFIRMS: time-share computerized processing of fire-danger rating. 

Gen. Tech. Rep. INT-82. Ogden, UT: Intermountain Forest and Range 

Experiment Station, Forest Service, U.S. Department of Agriculture; 

1980. 159 p. 

Main, William A.; Straub, Robert J.; Paananen, Donna M. FIREFAMILY: fire planning with historic weather data. Gen. Tech. Rep. NC-73. 

St. Paul, MN: North Central Forest Experiment Station, Forest Service, U.S. Department of Agriculture; 1982. 31 p. 

McCammon, Bruce P. Snowpack influences on dead-fuel moisture. Fort 

Collins, CO: Colorado State University; 1974. Dissertation. 

Rothermel, Richard C. A mathematical model for fire spread predictions 

in wildland fuels. Res. Pap. INT-1 15. Ogden, UT: Intermountain Forest 

and Range Experiment Station, Forest Service, U.S. Department of 

Agriculture; 1972. 40 p. 

Simard, Albert J. The moisture content of forest fuels I. A review of basic 

concepts. Ottawa, ONT: Forest Fire Research Institute; 1968. Rep. 

FF-X-14. 47 p. 

Smithsonian Institution. Smithsonian meteorological tables. Smithsonian Miscellaneous Collection 114(6):527, Washington DC: Smithsonian Institution Press; 1949. 526 p. 

U.S. Department of Agriculture, Forest Service. The wildland fire-danger 

rating system. Berkeley, CA: Pacific Southwest Forest and Range 

Experiment Station, Forest Service, U.S. Department of Agriculture; 

1958, revised 1968. 108 p. 

U.S. Forest Products Laboratory. Wood handbook: Wood as an engineering material. Agric. Handb. 72. Washington, DC: U.S. Department of 

Agriculture; 1955, revised 1974. Paged by chapter. 
Cohen, Jack D.; Deeming, John E. The National Fire-Danger Rating System: basic 

equations. Gen. Tech. Rep. PSW-82. Berkeley, CA: Pacific Southwest Forest and 

Range Experiment Station, Forest Service, U.S. Department of Agriculture; 1985. 

16 p. 

Updating the National Fire-Danger Rating System (NFDRS) was completed in 

1977, and operational use of it was begun the next year. The System provides a guide to 

wildfire control and suppression by its indexes that measure the relative potential of 

initiating fires. Such fires do not behave erratically-- they spread without spotting 

through continuous ground fuels. Estimates of fire potential have a basis in the 

mathematical models used for fire behavior. The fire manager must select the fuel 

model that best represents the fuels in the protection area. Among the 20 fuel models 

available, not more than two or three are appropriate for any one area. This documentation of the 20 fuel models and their equations supplements previous reports on the 

System. The equations are presented in the coded format of FORTRAN and BASIC 

computer languages. 

Retrieval Terms: fire modeling, fire occurrence, fire-danger indexes, forest-fire hehavior, forest-fire risk, fuel moisture, fuel models.