United States
Department of
Agriculture The National Fire-Danger
Forest Service
Pacific Southwest Rating System:
Forest and Range
Experiment Station
General Technical basic equations
Report PSW-82
Jack D. Cohen John E. Deeming
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National Fire-Danger Rating System and Fuel Moisture Models, Study notes of Logic
The contributors and components of the National Fire-Danger Rating System (NFDRS), focusing on the models of dead-fuel moisture and live-fuel moisture. The NFDRS considers two major groups of fuels, live and dead, and uses potential moisture content, EMC, and weighted 24-hour average boundary condition for 100-hour and 1000-hour timelag fuels. The document also explains herbaceous fuel moisture model, woody shrub fuel moisture model, and fuel model characteristics.
What you will learn
- How does the NFDRS classify fuel moisture content?
- What are the herbaceous fuel moisture model and woody shrub fuel moisture model?
- What are the contributors to the National Fire-Danger Rating System?
- What are the models for dead-fuel moisture and live-fuel moisture?
- What are the fuel model characteristics in the NFDRS?
Typology: Study notes
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United States Department of
Agriculture The National Fire
Danger
Forest Service
Pacific Southwest Rating System:
Forest and Range Experiment Station
General Technical basic equations
Report PSW-
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
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 velo city (GMAOPE) equation. AGE: Number of days since fuel moisture sticks were set out. AMBVP: Ambient vapor pressure. ANNTA: Parameter in linear herbaceous moisture content equa tion that is used in transition period for annual vegeta tion. ANNTB: Parameter in linear herbaceous moisture content equa tion that is used in transition period for annual vegeta tion. 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 cal culating 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 calcu lating 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 condi tion 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 cal culating 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 humid ity at fuel-atmosphere interface (TMPPRM, RHPRM, respectively). ERC: NFDRS energy release component. ETAMD: Surface area weighted dead-fuel moisture damping co efficient. ETAMDE: Loading weighted dead-fuel moisture damping coeffi cient. ETAML: Surface area weighted live-fuel moisture damping coef ficent. ETAMLE: Loading weighted live-fuel moisture damping coeffi cient. 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 trans ferred 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 condi tion 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 calcula tion 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 calcu lating 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 con- tent. MC10: Percent moisture content of fuel stick (age corrected) or calculated percent moisture content for 10 - hour time- lag. 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 MC 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.
T
he National Fire-Danger Rating System (NFDRS) provides indexes for measuring fire potential in wild- lands. 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. Depart ment 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 implementa tion in May 1978. The results were reported in two publica tions: one describes the basic system and revisions (Deem ing 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 tech nical 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 lan guages. 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 fundamen tal 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 ex- pressed 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.
- 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.
- 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 temperature- minimum 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 tempera ture. TMPMAX is the 24-hour maximum dry bulb tempera ture. RHOBS is the relative humidity at the afternoon obser vation 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. His torical 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 tempera ture and dewpoint (TMPOBS and DWPT). The psycho- metric equations used for these operations are from the Smithsonian Meteorological Tables (1949). For these cal culations, the temperatures are converted to degrees Kelvin by these equations:
KELVIN = CELS + 273. KELVIN = (FAHR + 459.69) * 5/
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.
- 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 cor rect for station elevation.
CORR = 6.6 * 10*-4. (1.0 + (0.
- (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 min imum temperatures (TMPMAX and TMPMIN). Unfor tunately, the 24-hour extreme relative humidity data were not collected and, therefore, are not available from pre- 1972 reports, and are often not available from post- 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))
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.
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 correc tion to the measured, apparent moisture content is re quired. 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=AACC+BBCC* (WT - 100.0)
in which WT is the weight of the fuel sticks in grams. AA = 0.5 * AGE / 30. BB = 1.0 + (0.02 * AGE / 30.0) CC = CLIMAT / 4. 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 calcula tion of MC 1.
If a Forecast Is Being Processed and Stick Moisture Content Is Predicted Directly: AFFIRMS allows the fire- weather forecaster to predict stick moisture content di rectly. A method of making such a prediction was not developed as an integral part of the NFDRS. If this prac tice 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 observa tion 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.
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) * EMCBR
- (2.7 * PDUR1 + 76.0) * PDUR1) / 16. BNDRY2 = ((8.0 - PDUR2) * EMCBR
- (2.7 * PDUR2 + 76.0) * PDUR2) / 8.
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 tempera tures 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 humi dity 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 = MC10P
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 pre- ceding 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 lati tude and date. Duration of Daylight:
PHI = LAT * 0.
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.
Weighted 24-Hour Average Boundary Condition:
BNDRYH = ((24.0 - PPTDUR) * EMCBAR
- PPTDUR * (0.5 * PPTDUR + 41.0)) / 24.
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 pre vious day.
Initializing YMC100 at the Beginning of a Computa tional 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.
Seven Day Running Average Boundary Condition:
BDYBAR = (BNDRYT(1) + ...............+ BNDRYT(7)) / 7.
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 sev enth 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 (Obser- vation and Forecast):
- Set SC, ERC , BI, IC, MCOI, LOI, and FLI to Zero (0).
- Record MC1 as 35 percent.
- Record MC10 as 35 percent for the predicted value and for the observed value if sticks are not used: if sticks are
the pregreen state should be forced during the winter with a "FROZEN" command. The following model settings are made for the pregreen stage:
MCHERB = MC 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 = MC 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 - YM 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 * X
in which the constant and coefficient are determined by the NFDRS climate class.
NFDRS Climate class: HERBGA HERBGB 1 - 70.0 12. 2 -100.0 14. 3 -137.5 15. 4 -185.0 17.
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, X 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).
MCHERB = HERBGA + HERBGB * X
in which MCHERB is not allowed to exceed 250 percent.
Transition Stage-- When MCHERB drops below 120 per- cent, these transition equations are used:
For annuals:
MCHERB = ANNTA + ANNTB * X
For perennials:
MCHERB = PERTA + PERTB * X
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. 2 -187.7 19.6 -10.3 8. 3 -245.2 22.0 -42.7 9. 4 -305.2 24.3 -93.5 12.
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 nor mal, seasonal drying (MCHERB drops to 30 percent with- out intervention by the user), these equations are used:
For annuals:
MCHERB = MC
For perennials:
MCHERB = PERTA + PERTB * X
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 FRO- ZEN or CURED command. If that is the situation, the equation for MCHERB for perennials becomes:
MCHERB = MC
In automated systems such as AFFIRMS and FIRE- FAMILY, 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. FIRE- FAMILY, for observations after that date, will then set the FROZEN flag:
- The first time a minimum temperature (TMPMIN) 25° F or less occurs; or
- 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 load ings between fuel classes are not transferred. The four stages of the model are:
- pregreen (MCWOOD = PREGRN)
- greenup
- green (MCWOOD greater than PREGRN)
- 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 her baceous 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 * MC
in which the constant and coefficient are determined by the NFDRS climate class.
NFDRS climate class: WOODGA WOODGB 1 12.5 7. 2 -5.0 8. 3 -22.5 8. 4 -45.0 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) * SG (10-hour) SA10 = (W10/RHOD) * SG (100-hour) SA100 = (W100/RHOD) * SG (herbaceous) SAHERB = (WHERB/ RHOL)
- SGHERB (woody) SAWOOD = (WWOOD/RHOL)
- SGWOOD
Total Surface Area of Dead and Live Fuels:
(dead) SADEAD = SA1 + SA10 + SA (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-Vol ume 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.
- 0.0594 * 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.
in which
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.
- DEDRT**2.0 - 3.
- DEDRT**3. (live) ETAML = 1.0 - 2.59 * LIVRT + 5.
- LIVRT2.0 - 3.52 * LIVRT3.
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 * SGBRT0. C = 7.47 * EXP(-0.133 * SGBRT0.55) 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.
in which
NFDRS slope class: Slope angle SLPFCT 1 12.67° 0. 2 17.63° 0. 3 24.23° 1. 4 32.46° 2. 5 41.99° 4.
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 deter ined 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)
PNORM1 = 0.
PNORM2 = 0.
PNORM3 = 0.
Heat of Ignition:
QIGN = 144.5 - (0.266 * TMPPRM) - (0.
* 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.
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 * PNORM
- PNORMI) * 100.0/PNORM
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 condi tions (slope class 1; 20-ft wind 20 mph; herbaceous vegeta tion cured; woody vegetation moisture content at the pre- green level; and the 1-, 10-, and 100-hour fuel moistures 3. 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. 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 Fire Occurrence 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 rain- lightning 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 func tions of the NFDRS lightning activity level (LAL):
NFDRS CGRATE STMDIA TOTWID LAL strikes/min miles miles 1 0.0 0.0 0. 2 12.5 3.0 7. 3 25.0 4.0 8. 4 50.0 5.0 9. 5 100.0 7.0 11. 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. STMDIA2.0)) /((STMDIA * STMSPD TOTWID) + (0. TOTWID2.0)) (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
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 probabil ity 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 oth ers 1983). Area Weighted Ignition Component:
ICBAR = ((FINSID * ICR) + (FOTSID * IC))/ 100.
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,
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(BI2.0 + (LOI + MCOI)2.0)
in which the BIis limited to 100 as is the sum of LOI and MCOI.