United States 

Department of 

Agriculture 

Forest Service 

Intermountain 

Research Station 

Ogden, UT 84401 

Research Paper 

INT-359 

February 1986 

Modeling Moisture 

Content of Fine 

Dead Wildland Fuels: 

Input to the BEHAVE Fire 

Prediction System 

Richard C. Rothermel 

Ralph A. Wilson, Jr. 

Glen A. Morris 

Stephen S. Sackett 

This file was created by scanning the printed publication.

Errors identified by the software have been corrected;

however, some errors may remain.
THE AUTHORS 

RICHARD C. ROTHERMEL received his bachelor of 

science degree in aeronautical engineering from the 

University of Washington in 1953 and his master's 

degree in mechanical engineering from Colorado State 

University, Fort Collins, in 1971. He served in the U.S. 

Air Force as special weapons aircraft development 

officer from 1953 to 1955. Upon his discharge he was 

employed at Douglas Aircraft Co. as a designer and 

trouble shooter in the armament group. From 1957 to 

1961 Rothermel was employed by the General Electric 

Co. in the aircraft nuclear propulsion department at 

the National Reactor Testing Station in Idaho. In 1961 

he joined the Intermountain Fire Sciences Laboratory, 

Missoula, MT, where he has been engaged in research 

on the mechanisms of fire spread. He was project 

leader of the fire fundamentals research work unit 

from 1966 until 1979 and is currently project leader of 

the fire behavior research work unit at the fire 

sciences laboratory. 

RALPH A. WILSON, JR. is a research physicist 

assigned to the fire behavior research work unit at the 

Intermountain Fire Sciences Laboratory, Missoula, MT. 

His undergraduate studies were at Willamette University, Salem, OR (B.A. 1956), with graduate work from 

1956 to 1960 at University of Oregon (M.A. 1958). He 

worked in infrared detectors and optics at Naval 

Ordnance Test Station, China Lake, CA, from 1957 to 

1964. He worked with the Forest Service's airborne 

infrared forest fire surveillance project at Intermountain Fire Sciences Laboratory, 1964 to 1975. 

GLEN A. MORRIS holds a bachelor's degree in mathematical statistics from the Unive-rsity of Washington 

and a master of science degree in mathematics from 

the University of Wisconsin. His function has been 

programming and mathematics in connection with aircraft structures at the Boeing Company and navigation 

systems at AC Electronics in Milwaukee, WI. He came 

to the Forest Service in Missoula, MT, in 1970 to provide similar support to research on lightning and 

forest fires and is at present providing that support for 

the fire behavior research work unit. 

STEPHEN S. SACKETT is a research forester (fire) stationed at the Forestry Sciences Laboratory in 

Flagstaff, AZ. He is a research scientist with the fire 

effects portion of the Management of Southwestern 

Forests and Woodlands research work unit of the 

Rocky Mountain Forest and Range Experiment Station. 

Sackett received an associate of science degree in 

forestry at Olympic Junior College, Bremerton, WA, in 

1958, and a B.S. degree in agricultural economics in 

1962 and an M.S. degree in forest economics in 1964 

from the University of Wisconsin. He joined the staff 

at the Southern Forest Fire Laboratory in 1964 with 

the fire use research work unit. Sackett transferred to 

the Forestry Sciences Laboratory in Tempe, A"£. , in 

1974 with the forest fuels research project of the 

Rocky Mountain Forest and Range Experiment Station. 

In 1984, Sackett was relocated to Flagstaff, AZ, to continue his research in prescribed fire effects in southwestern ponderosa pine forests. 

RESEARCH SUMMARY 

A method for predicting the time-dependent nature 

of fine fuel moisture is badly needed to support fire 

behavior prediction systems used in fire management. 

Of the models available, none met all the requirements 

of the BEHAVE fire behavior prediction system. The 

Canadian Fine Fuel Moisture Code (FFMC) came 

closest to meeting our needs and was selected as a 

base model. Improvements to the FFMC were concentrated on providing a means of accounting for annual 

and diurnal variation due to solar heating of woody 

fuels. This was necessary because the FFMC was 

developed for fuels located within forest stands, a 

generally shaded condition. Solar heating raises the 

temperature of the fuel surface and lowers the relative 

humidity of the film of air surrounding the fuel particle. Formulas describing this near-fuel environment 

produce the temperature and relative humidity that are 

then used by FFMC to derive the moisture content. 

The solar intensity that drives the fuel temperature 

and relative humidity accounts for latitude, time of 

year, time of day, aspect, slope, elevation, 

atmospheric haze, and shade. Shade can be from 

clouds or overstory trees. Provisions are made to 

guide the user through tree descriptors necessary to 

determine expected amount of shade. 

Basic operation of the model will determine fine fuel 

moisture for early afternoon. Provisions are made for 

extending the prediction over the next 24 hours (day or 

night) by use of a diurnal code developed in Canada 

and adapted for this model. It uses prediction of 

weather conditions at sunset and sunrise to extend 

the model capabilities throughout the diurnal cycle. 

The model was tested against actual moisture data 

taken from general fuel types in Texas, Arizona, Idaho, 

and Alaska. It consistently proved to be a better 

predictor of moisture than currently operating 

procedures. 

ACKNOWLEDGMENTS 

We appreciate the efforts of the many individuals 

who contributed to this qiverse manuscript. Collecting 

field data on a regular basis over long periods is a 

tedious task. Fortunately, we found a rich source of 

data among scientists scattered over the west: Rod 

Norum (Alaska), Bob Clark and Henry Wright (Texas), 

Mick Harrington (Arizona), and Bill Frandsen and Larry 

Bradshaw (Idaho). 

We also thank AI Simard and Bill Main for the computer program of the Canadian Fine Fuel Moisture 

Code, and Marty Alexander for the latest references to 

Canadian publications. 

Finally, thanks to Charlie Van Wagner for his 

friendly consultation. 
CONTENTS 

Page 

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

Review and Discussion ......................... 1 

Objectives .................................... 3 

Model Logic arid Equations ..................... 4 

Initialization ............... ............... 5 

Elevation Correction . . . . . . . . . . . . . . . . . . . . . . .. 7 

Solar Heating. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7 

Shade .................................... 14 

Fuel level Windspeed ...................... 19 

Canadian Standard Daily Fine Fuel Moisture 

Code (FFMC) ............................ 21 

Canadian Hourly Fine Fuel Moisture Code .... 21 

Diurnal Predictions ......................... 21 

Validation ..................................... 24 

Purpose of Validation ...................... 24 

Daily Version Validation (Objective No.1) ..... 25 

Initialization Validation (Objective No.2) ...... 31 

Validation of Diurnal Capability (Objective 

No.3) ................................... 32 

References .................................... 38 

Nomenclature ................................. 42 

List of Equations ....................... 0 0 0 0 ••• 44 

Appendix A: Canadian Standard Daily Fine Fuel 

Moisture Code (FFMC) ......... 0 0 0 0 • 0 0 •••• 0 0 •• 46 

Explanation 0 •••••••••••••••• 0 •••• 0 0 •••• 0 0 0 46 

Appendix B: Canadian Hourly Fine Fuel Moisture 

Code 00 ••••••••••• 0 ••••••••• 0.00. 0 ••••• 0 •••• 47 

Appendix C: Correction for Initial Shade Conditions 

in FFMC ... 00 •• 00000 •• 0 ••• 0., o. 0 0 0 •••• 0. 0 ••• 48 

Appendix D: Sunrise and Sunset Determination .... 48 

Appendix E: Methods of Estimation for Missing Model 

Inputs ... 0.0 ••• 0 ••• 0 •••••• 000 •• 0 ••••• 0 •••••• 49 

Internal Estimation of H2, H3, "0, HN and 

Other Humidities ... 0 •• 0 0 •• 0 •• 0 0 0 0 0 ••••• 0 • 50 

I nternal Estimation of T 2' T 3' 0'" TN -1 0 0 0 0 • 0 • 0 •• 50 

Internal Estimation of Mo 0000. 0 • 0 0 • 0 000 ••• 0 • 50 

External Estimation of Missing Inputs .. 0 0 •••• 51 

Appendix F: Formula Used for Humidity and Dew 

Point Calculations 0 0 0 • 0 0 • 0 0 0 0 •••••••••••••••• 51 

Appendix G: Summary of Validation Data . 0 ••••••• 52 

Modeling Moisture Content of 

Fine Dead Wildland Fuels: Input 

to the BEHAVE Fire Prediction System 

Richard C. Rothermel 

Ralph A. Wilson, Jr. 

Glen A. Morris 

Stephen S. Sackett 

INTRODUCTION 

The model described here was developed to predict fuel moisture content of 

fine fuels for use with the BEHAVE fire behavior prediction and fuel modeling 

system. BE HAVE is a computer system designed to aid fire managers and 

field personnel to assess fire situations and carry out operational planning 

(Andrews 1986; Burgan and Rothermel 1984). BEHAVE requires a model 

that will predict fine fuel moisture over a wide variety of conditions. We had 

planned to predict fine fuel moisture with the procedures developed for use by 

fire behavior officers (FBO's), described by Rothermel (1983); however, 

BEHAVE will be used over a wider range of conditions than the relatively dry 

situations encountered by FBO's on escaped fires. Consequently, a more robust 

model is needed. A review by Simard and Main (1982) of the available moisture 

models identified the Canadian Fine Fuel Moisture Code as the best choice. To 

use it. throughout the wide range of conditions found in this country, however, 

required modifications and additions. The major change was the method of 

accounting for drying of surface fuels by solar radiation. Other changes include 

a new method of initiating the model at any time of the season without a complete record of weather data prior to the startup time, and a method for 

integrating the daily code with a diurnal code for estimating fine fuel moisture 

at any time of the day or night. 

REVIEW AND DISCUSSION 

Fine fuel moisture is one of the primary factors controlling the behavior of 

wildland fires (Barrows 1951). Methods for predicting it have been sought for 

many years by those seeking means for rating fire behavior (Van Wagner 1974; 

Fosberg and Deeming 1971; Deeming and others 1972; Luke and McArthur 

1978; Rothermel 1983). Various methods have been under scrutiny for some 

time. Simard and Main (1982) recently published a comprehensive comparison 

of moisture prediction systems. Their analysis, based on fine fuels and litter 

from jack pine logging slash in Minnesota, concluded that: 

Predictions from the Canadian Forest Fire Weather Index (FWI) 

models and some meteorological elements were superior to the 

National Fire Danger Rating System (NFDRS) models for every 

fuel tested. It appears that the FWI models are well suited to moist 

climates, whereas the NFDRS models work better under dry 

conditions. 

In fairness, it should be pointed out that the NFDRS system is intended to 

indicate the worst-case condition, and Simard and Main's data did not include 

the 10-hour stick moisture measurement. This is an important element in the 

NFDRS system to account for seasonal changes. 
Because the FBO procedures (Rothermel 1983) are based in part on the 

NFDRS models, and because users of BEHAVE will not usually have 10-hour 

stick moisture data available, we decided to evaluate the Canadian Fine Fuel 

Moisture Code for use with BEHAVE. 

The Fine Fuel Moisture Code (FFMC) is a component of the Canadian Forest 

Fire Weather Index System (Canadian Forestry Service 1984). The literature is 

rich with descriptors of the Canadian Fire Weather Index and the moisture 

codes. We will not attempt to summarize it all here. Van Wagner (197-4) 

describes the evolution of the index: 

The FFMC was developed from concurrent weather and fuel moisture 

data obtained in pine stands at Petawawa, Ontario, by multiple correlation of present moisture content with current weather and previous 

day's moisture content. Although pine needles are relatively fast drying, they found that there was a substantial effect of the previous 

day's moisture content which meant that drying cannot be assumed 

to be instantaneous. Thus, the method of estimating fuel moisture is 

based on a known or previous value and adjustment to it according 

to weather during the intervening 24 hours. The rate of change is 

commensurate with atmospheric conditions imposed upon the fuel 

and the final equilibrium value. This code calculates a daily value of 

fine fuel moisture for the afternoon. 

The idea of yesterday's fuel moisture content affecting today's fine fuel moisture content may be hard to accept by those trained to equate fine fuels with 

I-hour time lags. However, recent information shows that some conifer needles 

have time lags as long as 30 hours (Anderson 1985). These fuels will not come 

close to equilibrium in a typical 24-hour diurnal cycle. 

Because the FFMC was developed from data taken beneath a canopy of jack 

pine trees, it cannot adequately account for drying of fuels exposed to the sun; 

a condition important to the fuels in a large part of the world. 

The effects of solar radiation on fuel moisture and fire hazard were recognized 

early in the present century (for example, Plumnler 1912). Gast and Stickel 

(1929) found that "diminution in the radiation intensity incident upon the duff 

reduces the rate at which the duff moisture content decreases during the day," 

and further suggested " ... the importance of a cloud 'weather eye' to patrolmen. By estimating cloudiness, the probable hazard can be estimated." 

Gisborne (1928) gives data for exposures to different totals of radiation and 

concludes that determining changes in moisture is of value only when the 

amount of shielding from sunlight is varied. Gisbome (1933) hypothesized a 

mechanism of wind and solar radiation to account for observations of dead 

wood lying on the ground being drier than in air. Again, Gisborne (1936), 

explaining the operation of his forest fire danger meter, referenced the work of 

Hornby (1935) who also emphasized exposure to sun and wind in fuel classification. Byram (1940) reported that his experiment showed excellent evidence that 

the effects of wind and sunshine on fuel moisture are not additive, but partially 

compensating; that the energy of sunshine seems to be a very powerful drying 

agent, and wind prevents some of this energy from being absorbed by the fuels; 

and, further, that the reflection factor of fuels has considerable effect on their 

moisture content when exposed to sunlight-black sticks absorbing more than 

2 
white, hence having lower moisture contents. Countryman (1977) found moisture variation under a ponderosa pine stand (Pinus ponderosa Laws.) to have 

significant variation within short distances-enough to offset ignition and fire 

behavior significantly. These variations were found to be caused primarily by 

solar radiation reaching some litter areas through openings in the crown canopy 

and cooling directly under the openings at night. Catchpole and Catchpole 

(1983) found that a large portion of the variation in spread rate of experimental 

grass fires in Australia (statistical variation between fires) could be attributed 

to the degree of cloud cover. 

In 1943 Byram and Jemison reported on a method they developed whereby 

radiation intensity could be determined for any season of year, hour of day, 

slope, and aspect. They established a relationship of solar radiation intensity to 

surface fuel moisture equilibria and rates of drying. Van Wagner (1969) used 

Byram and Jemison's model as a basis for investigating the effect of solar 

heating and wind on the surface temperature of jack pine needles and quaking 

aspen leaves. He obtained results similar to theirs with a slightly different 

mathematical form. The solar heating section of our model is an extension and 

application of Byram and Jemison's original idea. 

In the interim many authors have investigated solar irradiance on the terrestrial surface (Kimball 1919; Bates and Henry 1928; Okanoue 1957; Lee 1962; 

Loewe 1962; Kaufmann and Weatherred 1982; Running and Hungerford 1983). 

The correct solar;,terrestrial geometry varies among authors only in detail. 

Our customers will be oriented to local standard time; to measuring slope 

aspect clockwise from north; to measuring slope angle positive (up) in the sense 

opposite the slope aspect ... etc. 

We wish also to circumvent the popular concept of "equivalent slope" 

because of the geometric difficulties encountered when the shade trees are 

standing at tilted slant angles on that "equivalent horizontal slope." (See, for 

example, Okanoue, Lee, Kaufmann and Weatherred.) 

OBJECTIVES 

Our objectives in developing a new model are to predict the moisture of fine 

dead fuels with greater accuracy over a wider range of conditions and times 

than possible with the FBO procedures (Rothermel 1983). The main concerns 

with the FBO system are its inability to account for precipitation prior to the 

day of the fire and its tendency in northern latitudes to underestimate moisture 

values of fuels beneath a forest canopy. 

Simard and Main suggest at least five characteristics of a fuel and its 

environment that must be specified when developing a predictive model: 

1. Composition of the material (wood, needles, leaves, grass). 

2. Presence of surface layer (bark, wax). 

3. Thickness (diameter of wood). 

4. Location (on, off the ground). 

5. Environment (under a canopy, in the open). 

3 
A summary of the characteristics to be accounted for by this model is given 

below: 

1. The model will be applicable to fine dead fuels, needles, leaves, cured 

herbaceous plants, and dead stems less than one-fourth inch in diameter. 

2. The model should be sensitive to atmospheric moisture. This is the most 

common factor in all models wherein an equilibrium fuel moisture is determined 

based on air temperature and humidity and the fuel moisture is continually 

seeking this equilibrium value. (The influence of soil moisture on fuel moisture, 

perhaps through dew formation, is an important consideration for future 

revisions to this model.) 

3. The model should be sensitive to the drying effect of solar radiation. This 

requires a considerable amount of additional information. The amount of solar 

heating depends upon day length, sun angle, windspeed, and shade. These, in 

turn, depend upon time of year, latitude, slope, aspect, cloud cover, and 

overstory conditions. 

4. The model should be sensitive to precipitation occurring within 7 days 

preceding the fire. 

5. The model should be capable of predicting fuel moisture any time of the 

day or night. 

6. The model should be capable of accounting for elevation differences by 

adjusting temperature and humidity to fire locations above or below the 

position where they are measured. 

7. Inputs must be available to a knowledgeable person without requiring a 

previously assembled weather data file. 

B. Because the fuel moisture is intended for use in a fire behavior model 

(Rothermel 1972; Albini 1976), wherein fires are in fuels with moistures less 

than a specified moisture of extinction (usually less than 30 percent), attention 

will be concentrated on accuracy at the lower levels. 

9. The model should account for atmospheric haze. 

Considerations omitted at this time are: 

1. Differences in moisture because fuels are either standing (such as grass) or 

lying on the ground. 

2. Differences between freshly fallen and old litter. 

3. Differences caused by fuel coating, such as bark or wax. 

4. The effect of dew. 

5. The effect of moisture in the duff and soil beneath the litter layer. 

The reasons for omitting these influences at this time are threefold: (1 ) We do 

not have the necessary information to model the process; (2) every new model 

requires data from the user when applying the model, and it is not clear how 

some of these data would be known to the user; and (3) a necessity to derive a 

solution in a reasonable time, with a strong expectation that the planned 

improvements will make the model significantly better than present methods. 

MODEL LOGIC AND EQUATIONS 

A simplified model flow diagram is shown in figure 1. There are six major 

sections to the model: 

1. Initialization (accounting for previous weather). 

2. Current situation (time, site description, weather forecast). 

3. Correction for elevation. . 

4. Correction for solar heating (adjusting air temperature and relative 

humidity to fuel level). 

4 
Initialization 

INITIALIZATION 

mo CORRECTION CALCULATE EARLY CORRECTION 

f---I- FOR r--- FOR AFTERNOON FINE 

ELEVATION SOLAR FUEL MOISTURE 

HEATING 

CURRENT 

a WEATHER 

SITE ~ SITUATION DIURNAL 

ADJUSTMENT OF 

FUEL MOISTURE 

Figure 1.-Flow diagram of fine fuel moisture model. 

5. Calculation of early afternoon fine fuel moisture. 

6. Diurnal adjustment of fuel moisture. 

Briefly, the model shown in figure 1 is used as follows. It must be initiated 

by one of five options that appraise the weather for 3 to 7 days preceding the 

day on which a prediction is wanted. This is necessary to establish a reference 

moisture value for the day preceding the day on which a prediction is wanted. 

The five options are designed to accommodate the type of information the user 

might know about preceding weather events. 

The inputs describe the prediction day weather and site conditions. The elevation correction is designed to adjust the air temperature and humidityl from 

the elevation where they were measured to the elevation where the moisture 

content is wanted. If the fuel is exposed to the sun, a correction is made to predict the fuel surface temperature and the air moisture condition in immediate 

proximity to the fuel. The effect of turbulent mixing caused by wind at the fuel 

level is included. The adjusted temperature and humidity will determine the effect 

of atmospheric moisture on the fuel. These values are entered into the Canadian 

Fine Fuel Moisture Code, which then calculates the early afternoon fine fuel 

moisture. 

If moisture is needed at another time, additional data are requested from the 

user and the early afternoon moisture is use~ as a starting value for advancing 

.fuel moisture through to the time that a prediction is needed (projection time), 

which must not be later than 1200 of the next day. 

Details of the model components follow. 

The model requires a value for the 1400-hour fuel moisture for the day 

preceding the day for which you wish to make a prediction. This value is called 

the initial fuel moisture (mo) and the process of determining it is called initialization. Five options are provided for obtaining mo: 

1. mo is known. 

2. Weather records are available for several preceding days. 

3. Complete weather data are not available and it rained within the past 

week. 

4. It has not rained within the past week and weather conditions have been 

persistent from day to day. 

l'rhe term humidity is sometimes used rather than relative humidity; in this publication, humidity 

always means relative huhUdity. 

5 
5. It has not rained within the past week and weather conditions have been 

variable. 

These options do not exhaust all ways of initiating the model. As the user 

becomes familiar with the initialization process, it will be seen that these 

options can be adapted to needs and ~limates. For instance, option 3 may work 

very well even if there were no rain at the beginning of the period. 

Option 1 - mC' is known.-If the previous day's early afternoon fine fuel moisture is known from measurement or a previous calculation or an estimate, it 

may be used directly. 2 

Option 2 - weather records available.-If the standard NFDR early afternoon 

fire weather measurements are available for 3 to 7 preceding days, the following data are entered for early afternoon of each day: 

air temperature 

relative humidity 

amount of rain 

20-foot windspeed 

percent cloud cover 

The 1400-hour moisture for the first day of the series is obtained by iterating 

the first day's weather data with the sun-adjusted FFMC until an equilibrium 

solution is reached. Then the data from each subsequent day are used as per 

the normal procedures of the Canadian system. The final value of moisture calculated in this initialization process is used as mo. This tedious option can be 

avoided by most users. It is included for those who wish to be exact or test the 

system. 

Option 3 - complete weather data not available, and rain occurred.-If it has 

rained within the past week and if there has been no frontal passage since it 

rained, this option may be used. 

Rain can act as a triggering event, causing a major change in fine fuel moisture. The occurrence of rain is a logical choice for initiating a new moisture 

prediction. The occurrence of rain is also unique enough that a fire manager 

could be expected to know or be able to find out when the last rainfall occurred 

and be able to estimate how much. The assumption of no frontal passage is 

necessary to make calculations about the air mass between the time of rain and 

proj ection time. 

Enter: 

(1) How many days since it rained (2 to 7). 

(2) Amount of rain, inches. 

(3) The early afternoon temperature on the day it rained. 

(4) What has been the sky condition on the days since it rained? 

(a) clear 

(b) cloudy 

(c) partly cloudy. 

2If the NFDR lO-hour stick moisture is known, Simard (personal communication) has shown that 

fine fuel moisture can be calculated from the formula m =-8.74 + 2.90 (IO-h). This correlation was made in the Lake States; it is not known how well it works elsewhere. 

6 
, "~: . 

These will give cloud cover values of 10, 90, and 50 percent, respectively. 

(5) Today's (fuel moisture projection day) complete weather data (measured or 

forecast). 

On the day it rained, the model assumes humidity = 90 percent, cloud cover = 

90 percent, and windspeed = 5 mi/h if these values are not known. Early afternoon temperature and humidity on the days since it rained are reconstructed as 

follows: temperature is adjusted linearly between the day it rained and today. 

Today's dewpoint is calculated from today's temperature and humidity. Using 

the assumption of constant air mass since it rained, the humidity on each day 

is calculated from today's dewpoint and the linearly estimated temperature for 

each day. (Se~ appendix F for humidity calculation from dew point.) 

When fuel moisture on the day before it rained is unknown, it is set to 

equilibrium for conditions on the day it rained. Any error will be overcome by 

the rain and successive calculations. 

Option 4 - no rain within the past week and weather persistent.-Under these 

conditions, the fine fuel moisture will also persist from day to day. Today's 

early afternoon weather is iterated to find an equilibrium value. 

Option 5 - no data available and weather during the preceding week has been 

variable.-Here, none of the preceding four situations can be utilized, but an 

estimate can be made as follows: 

(1) Estimate yesterday's early afternoon weather conditions. 

(2) What was the general weather pattern before yesterday? 

(a) hot and dry 

(b) cool ~d wet 

(c) between (a) and (b). 

These will give initial fuel moisture values of 6, 76, and 16 percent respectively. 

These rough estimates will be adjusted twice, once by yesterday's estimated 

weather and once by today's measured or forecasted weather. 

Elevation Correction It is often impossible or impractical to measure the weather at the site where 

the fuel moisture estimate is needed. In mountainous terrain, the temperature 

and moisture of the atmosphere change with elevation. For a well-mixed 

atmosphere, the adiabatic lapse rate is used to adjust temperature and humidity according to elevation differences. The correction amounts to 3.5 of per 

1,000 feet for temperature and 101°F per 1,000 feet for the dewpoint. Both corrections decrease with elevation. This correction has lieen used by others dealing with mountain meteorology (Running and Hungerford 1983). 

Solar Heating 

The corrections should only be applied when there is good mixing, such as in 

the late morning and afternoon when inversions have broken, and at night if 

neither location lies within an inversion. 

If elevation differences are small, say less than 1,000 feet, the correction is 

ignored. 

Many fuels in the United States, particularly rangelands in the West and 

Southwest, are exposed to considerable solar heating. We wanted the moisture 

model for BEHAVE to be able to account for this, but not to underpredict 

7 
moisture, as the FBO model often does, in northern latitudes under a forest 

canopy. 

The physical basis of the problem is that, while some of the sun's energy is 

absorbed by the air, the solid fuel particles absorb heat more efficiently and 

consequently the fuel temperature can rise to a much higher temperature than 

the air temperature, which is measured 4Y2 feet above the surface in a shaded 

weather shelter (fig. 2). Furthermore, the warmer fuel temperature alters the 

microclimate near the fuel on the ground, particularly the humidity of the air 

surrounding the fuel. The relative humidity of the air adjacent to the fuel particles heated by the sun will be lower than the relative humidity in the instrument shelter. The overall effect is a lower fuel moisture than what would be calculated from the shelter measurements. 

Figure 2.-Environmental conditions influencing fuels sub· 

ject to solar heating are not measured by instruments in 

weather shelter. 

8 
Wind sweeping over the fuel confounds the problem. The moving air above 

the fuel will be cooler than the thin layer of air surrounding the fuel particles. 

Consequently, any turbulent mixing will tend to cool the air near the fuel, 

bringing it closer to the general air temperature and humidity. 

A solution began with the research on solar heating by Byram and Jemison 

(1943). They attacked the problem directly by constructing and using a weather 

synthesizer or artificial sun to determine the effect.of solar intensity and windspeed upon fuel temperature and moisture. From heat transfer considerations 

explained in the original text, Byram and Jemison developed an equation to be 

evaluated with data from the artificial sun apparatus. The difference in temperature between the air and the fuel is assumed to be directly proportional to the 

incident radiation intensity, I, and inversely proportional to the wind velocity, 

U, and two constants attributed to fuel conditions. 

Tf - Ta = I1(0.015Uh , + 0.026), (1) 

where 

Tf 

Ta 

I 

= temperature of fuel, of, 

= temperature of air, of, 

= radiation intensity, cal/cm2 • min, 

= wind velocity at fuel level, mi/h. 

The units are preserved from the original text. From Byram and Jemison's 

experimental data, the constants were evaluated to be 0.015 and 0.026, respectively. They emphasized that in fuel types in which loss of heat to the soil 

underlying the litter and loss to the air proceed at faster or slower rates than 

in the beds of hardwood leaf litter used in their investigation, other values 

would be needed in place of their constants. 

We agree, and after reviewing our verification data believe that these factors 

should be investigated in the next revision to this type of model. 

U sing vapor pressure arguments concerning the air temperature and moisture 

immediately adjacent to the fuel, Byram and Jemison develop a correction for 

relative humidity as a function of the fuel temperature and air temperature: 

Hf = Ha exp(-0.033(Tf - Ta)), (2) 

where H and T refer to humidity l:\l1d temperature, and the subscripts f and a 

refer to fuel and air. 

Equations 1 and 2 provide the means to adjust the air temperature and 

humidity to the fuel level and thus account for solar heating and wind cooling 

effects. To do this, however, we must have a means of determining the solar 

radiation intensity I as a function of the solar terrain slope geometry, and 

windspeed at the fuel level. 

Solar/Terrain Slope Geometry.-The development of the basic equations for 

the solar irradiance on a horizontal. surface neglecting the atmosphere is lost in 

antiquity (Milankovetch 1930; Frank and Lee 1966; Kaufmann and Weatherred 

1982 ... ). 

Using the particular construction of Byram and Jemison (fig. 3) 

I = (la/r2) sin A, 

9 

(3) 
.~ ., .. 

z: 

li 

.... 

N 

Figure 3. - Diagram of solar geometry. 

where Ia is irradiance at the earth's surface, perpendicular to the solar rays, 

and attenuated by intervening atmosphere, clouds, timber canopy, etc. The 

earth-sun (center of mass) distance, r, in units of its mean value varies from 

0.98324 (January 3) to 1.01671 (July 5) (see List 1958, table 169); thus r2 varies 

less than ± 3Y2 percent annually and may be neglected as having a much 

smaller effect on the solar intensity than unpredictable atmospheric absorption, 

for example. The solar altitude angle, A, is given by 

sin A = sin h * cos a cos c/> + sin a sin C/>, 

where 

h* = hour angle from the local 6 a.m.,3 

c/> = latitude, 

a = solar declination. 

(4) 

Because the inverse trigonometric functions are double valued in the complete 

cycle, 0 to 271", and because computer software does not return angular values in 

a consistent half cycle, we provide a redundant calculation of the solar azimuth 

3i.e., the hour angle, h* = (360/24)(t - 6.0), where t is scaled in fractions of hours and, for exam- ple, t = 13.5 represents 1330 military or 1:30 p.m. civil time. 

10 
to remove the double value ambiguity. (There is no ambiguity in the solar elevation angle, A, if it is understood that -7r/2 :s A :s 7r/2. There are situations, 

however, where the solar azimuth must range the full 27r circle.) 

Thus, from figure 3, 

tan. z = sin h* cos 0 sin cP - sin 0 cos cP , and 

cos h* cos 0 

cos z = cos h* cos olcos A. 

(5) 

(6) 

By simple ratios of equations 5 and 6, any function of solar azimuth, z, may 

be calculated over the full range 0 :s z :s 27r. 

Kaufmann and Weatherred (1982) give the analytic solution to List's tabular 

values of r and 0: 

r2 = 0.999847 + 0.001406 (0), 

o = 23.5 sin(0.9863(284 + NJ)) 

= solar declination in degrees, 

NJ = Julian date 

= Integer Value (31(Mo - 1) + Dy - 0.4Mo - 1.8 + e) 

1

2 if Mo = 1, 

_ 3 if Mo= 2, 

~ - 1 if Mo> 2 on leap years, 

o otherwise. 

(7) 

(8) 

Mo and Dy are the month and day, respectively, of the Gregorian calendar and 

Integer Value means round up or down to nearest integer. 

Irradiance on a slope (neglecting the small variation in r) is 

I = la sin t, (9) 

where angle A in equation 3 is replaced by t, the solar angle to the slope in the 

plane normal to the slope (fig. 4) and 

sin t = sin (A -1/;) (cos a)/cos 1/;, (10) 

where (A -1/;) is the solar angle to the slope in the local vertical plane and 1/; is 

the slope angle at the solar azimuth, z, 

tan 1/; = tan a sin(z - 13) (11) 

and angles A and z are determined from equations 4 and 5 (with equation 6 

where necessary), respectively. Note from figure 3 that the nodes of sin A 

(eq. 4) determine sunrise and sunset and that I = 0 for sin A < O. Note also 

that, for proper choice of slope and aspect (for example, (3 ::;: 0 and a > 0, a 

steep north slope) one may observe two "sunrises" and "sunsets" on the slope. 

11 
HORIZONTAL 

Figure 4. - Diagram of sun/slope geometry. 

Obscuration and Attenuation of Irradiance.-The irradiance, la' of equation 

9, on the forest floor is the product of the incident solar power density and the 

transmittance of the intervening media: 

la = IMTn' (12) 

where Tn is the net transmittance of clouds and trees discussed below, and 1M is 

the direct solar irradiance including atmospheric attenuation. 

The direct solar irradiance, 1M , may be written (see Kondratyev 1969, ch. 5, 

or Johnson 1960, ch. 4): 

(13) 

where 10 is the incident intensity or solar constant, 1.98 cal/cm2 -min (variously 

quoted as 10 = 1.84 to 1.98 cal/cm2 -min). 

p is the transparency coefficient (integral over all wavelengths). 

M, the optical air mass, is the ratio of the optical path length, lM' of radiation 

through the atmosphere at angle, A, to the path length, lzo' toward the zenith 

from sea level. Thus 

(14) 

12 
The air mass M is referenced to the optical path lzo at sea level. If one is 

working at a few thousand feet elevation, the zenith air mass optical path, lz' is 

significantly reduced (at 5 km elevation you are above half of the air mass!): 

lz = lzo el eo ' (15) 

where e is the absolute atmospheric pressure at the site and eo is the sea level 

pressure (1,000 mb). For an elevation, E, in feet above sea level, e is 

approximately 

e = eo exp (-0.0000448E). 

Thus, 

M = (el eo) csc A = exp( -0.0000448E) csc A, and (16) 

Ia = Io7npM. (17) 

Because of the earth's curvature, optical refraction by the air density gradient, 

etc., the exact csc A dependence of solar irradiance on solar altitude angle fails 

near the horizon, that is, for A < 10 degrees. But because the irradiation just 

after sunrise and before sunset is "small" and the probability of shading is 

very high, we will let the approximation stand for those small angles. 

Atmospheric transparency, p, is most notably dependent on absorption of 

radiation by differing amounts of atmospheric moisture and by atmospheric 

turbidity (haze). Even an empirical estimation of p requires knowledge (radiosonde measurement) of the vertical distribution of temperature, pressure, and 

relative humidity in addition to measures of dust-haze and particulates. Acquisition of such data is beyond the scope of the BEHAVE system. It is sufficient 

to say that Byram and Jemison used a constant p = 0.7, which they assumed 

was a "reasonable average for a thin layer of rather dense haze which is common at 2,000 feet during the fire season in the southern Appalachians," and 

that a 30-year mean value at Pavlovsk, Russia (Kondratyev 1969) was p = 

0.745, with extreme values of 0.710 (1914) and 0.770 (1909) and a typical annual 

(12-month) variation of Ap = ±0.02 (except for the 2-year period following the 

eruption of Katmai volcano (Alaska) in 1912 when the annual average transparency was 0.57). Similar data are presented in the other monographs on 

atmospheric transparency. The mean Kondratyev value represents a "clean forest atmosphe~e." On exceptionally clear days p may range as large as 0.8 and 

on very hazy days as small as 0.6, excluding direct interference from local 

smoke palls. The list below suggests a series of p values with qualitative 

descriptors for application by field observers. 

P 

0.8 

Qualitative description 

exceptionally clear atmosphere 

0.75 average clear forest atmosphere 

0.7 moderate forest (blue) haze 

0.6 dense haze 

13 
Shade The net cloud/tree transmittance from above is 

(18) 

where Tt is the transmittance of the timber canopy and Tc = (1 - Si100) is the 

transmittance of cloud cover. Sc is scaled in percent. 

Cloud Shade.-Cloud shade is familiar to users of the National Fire-Danger 

Rating System as a contribution to the state of the weather code. For this 

model the user can enter any percentage of cloud cover between 0 and 100. 

When working with the NFDRS state of weather code, convert to percent cloud 

cover according to the following: 

NFDRS Shade 

code range Input 

Pet Pet 

0 o - 10 5 

1 10 - 50 30 

2 50 - 90 70 

3 90 - 100 95 

Tree Shade.-Many authors have suggested that the Beer-Lambert exponential absorption model of solar radiation is applicable to forest plant communities and that the Leaf Area Index (LAI) may be the significant attenuation 

parameter (Monsi and Saeki 1953; Jordan 1969; Barbour and others 1980). 

Considerable work has been done to relate site productivity, habitat classification, and topographic distributions to LAI (see also Stage 1976; Pfister and 

others 1977; Zavitkovski 1976; Salomon and others 1976). Those relationships 

have not been satisfactorily established nor has LAI become a universally 

established mensurational parameter, so that we can use it in the present application. Instead, our site-specific approach to shade is an extension of the 

method suggested by Satterlund (1983). In the Satterlund approach the shadow 

area of an average tree on a unit surface area is calculated, then the fractional 

area of shadow cast by n trees is estimated. Because the tree crowns are not 

totally opaque we assume a Beer law attenuation and estimate the optical 

attenuation coefficient on the basis of shade tolerance and crown shape. 

We consider crowns of two general geometric shapes (fig. 5). Conifers are 

right circular cones; deciduous trees are assumed to be ellipsoids of revolution. 

The tree boles are totally opaque with a vertical cross section approximated by 

an inverted paraboloid of revolution. 

For a conifer tree (fig. 6A), we require the shadow area, Ah, projected on a 

horizontal reference plane by the sun at solar altitude, A, crown diameter, D, 

and length, L. (The unsubscripted A is the solar altitude angle while A with 

subscripts is a shadow area on the ground.) We have two cases: 

Ah = 7I"D2/4, for conifers, if tan A ;::: 2L/D, or (19) 

Ah = (71" - G)D2/4 + DL cot A sin G, if tan A < 2L/D (20) 

where 

cos G = (2 (L/D) cot A)-I. (21) 

14 
TREE CROWNS 

Fig~re 5;-Tree crown 

shape assumptions. 

h 

Figure 6A. -Conifer tree shadow configuration. 

15 
For deciduous trees (fig. 6B) with crown dimensions of L/2 and D/2 semi. 

axes, the height-to-width ratio is LID and Ah is 

Ah = 7rDl/(2 sin A) for deciduous, 

where 

I = r' sin(G' - A), 

tan G' = -(LID) cot A, and 

r' = (L/2)(sin2 G'+ (L/D)2 cos2 G')-Y2. 

(22) 

(23) 

(24) 

(25) 

Because the crowns are not opaque we assume an exponential attenuation 

function, exp(-JX), where the optical attenuation coefficients, J ft- 1, exclusive 

of the opaque tree boles, are estimated below from data on file at IFSL (USDA 

FS 1968). (In deciduous forests shade tolerance for present purposes may equal 

zero.) 

Crown Shade tolerance class 

type o 1 2 3 

Conifer 

Deciduous 

NA 

o 

D 

Figure 6S.-Deciduous tree shadow con· 

figuration. 

16 

0.13 

0.10 

0.16 

0.12 

L 

0.20 

0.20 
The intracrown path length, X (fig. 6e), is approximated: 

X = V/(Ah sin a) 

= 7r D2LI (12 Ah sin A) for conifers 

= 7rD2L/(6 Ah sin A) for deciduous 

(26) 

(27) 

If one adds the shadow of a parabolic tree bole of height h and diameter d (vertical cross section area 2/3 dh), the horizontal bole shadow Ab cast is 

Ab = (2/3) dh cot A (28) 

In the model we use the approximation dlh = 0.014 (ft/ft), then 

Ab = O.Od93 h2 cot A. The net "effective" tree shadow on the horizontal is 

Ah = Ab + Ah (1 - exp(-JX)) (29) 

Figure Be. -In tercro wn path length 

relationship. 

17 
For either tree type, the area Ah is the shadow projected to a horizontal reference plane. The shadow, however, is actually cast on the slope, S (fig. 6D), and 

the vertical projection of S onto a horizontal plane, As' is 

As = Ah(cos 'I/; sin A)/ sin(A + '1/;) (30) 

The fractional area N 1 shaded by one average tree per unit horizontal surface 

area, Au (usually ha or acres), is 

Nl = As/Au' (31) 

Then, assuming that the trees are independently distributed, the shadow of the 

nth tree is expected to add to the total shaded area an amount equal to the 

product of its relative shadow area, Nl' and the unshaded area, (1 - Nn- 1) by 

n -1 trees such that: 

N2 = Nl (1 - N1) + NIt 

N 3 = N 1 (1 - N 2) + N 2' 

Nn = Nl (1 - Nn- 1) + Nn-l' or 

Nn == 1 - exp(-nN1), 

where N n is the area shaded by n trees and 

Tt = 1 - Nn = exp(-nN1) 

(32) 

(33) 

approximates the expected fraction of direct beam solar radiation impinging on 

the moist fuel under the timber canopy in equation 18. 

Figure 6D.-Shadow relationship to slope. 

18 
Fuel Level 

Windspeed 

An alternative estimate of the number of trees per unit area, n, that is consistent with this rationale is as follows: Given the crown closure, C, and average tree diameter, D, then the vertically projected crown area, A;. of one tree is 

A; = 7rD2/4 

N{ = A~/Au' 

By definition, then 

N; = C = 1 - exp(-nN{) (34) 

n = -In(l - C)/N{ 

n = -4Au In(l - C)/7rD2 (35) 

One must caution that A~ is not the proper effective crown area, As' used in 

equation 31. A; is the total area within the crown perimeter while calculations 

of As (in eq. 31) must include the transparency of the particular crown type as 

developed above. 

A list of the equations and pertinent constants is given at the end of the 

text. 

Byram and Jemison's equation for calculation of surface fuel temperature 

(eq. 1) requires a value for the windspeed at the fuel surface. This is not a 

trivial correction; even though wind speeds close to the surface are low, Byram 

and Jemison's data show that the cooling effect can be pronounced. 

The standard height for measuring windspeed for fire applications in the 

United States is 20 feet above vegetation height (Fischer and Hardy 1976). 

Many authors have described how surface roughness reduces wind near the 

ground as shown in figure 7. Albini and Baughman (1979) developed a relationship that includes vegetation height, making it easy to adapt to fire situations. 

Their ratio of windspeed at vegetation height to that at 20 feet above the vegetation is given by: 

Uh , IU20+h , = 1Iln((20 + 0.36h ')/0.13h ') (36) 

where 

Uh , = windspeed at vegetation height, 

U20+h , = windspeed at 20 feet above vegetation, 

h' = vegetation height. 

Equation 36 gives reasonable answers as shown by the examples below: 

h' Uh ,/U20+h ' 

0.1 

.5 

1.0 

6.0 

0.0006 

.17 

.2 

.3 

For exposed conditions, the vegetation height windspeed is determined by 

multiplying the windspeed measured 20 feet above the vegetation by the ratio 

in equation 36. For unexposed (sheltered) conditions, a fraction called the wind 

adjustment factor is input to the model instead of the fuel depth. The wind 

adjustment factor times the canopy-top wind estimates a reduced wind near the 

fuel. 

For daytime application of the model, the only inputs required are the 20-foot 

windspeed and the fuel bed depth or wind adjustment factor. In the BEHAVE 

application fuel bed depth is already known from the fuel model and guides for 

determining the wind adjustment factor are given. 

19 
20 FT WIND 

MID-FLAME 

Figure 7.-Near·surface wind profile. 

For nighttime application in uneven terrain, downslope winds may need to be 

considered. Slope winds do not follow the log reduction pattern used in daytime. At night, if the slope is less than 5 percent, use the daylight procedures. 

If the slope is greater than 5 percent, and if the 20-foot windspeed is less than 

10 mi/h, let the vegetation height wind equal 4 mi/h (a reasonable assumption 

for downslope winds). If the windspeed is greater than 10 mi/h, consider the 

canopy closure; if the closure is less than 10 percent, use the daylight procedures. If the canopy closure is greater than 10 percent, assume the 20-foot 

winds are blocked and let the vegetation height wind equal 4 mi/h. 

The effect of wind on fine fuel moisture is also incorporated directly in the 

Canadian Fine Fuel Moisture Code. Van Wagner (1974) explains that wind 

affects the log drying rate, k, 

k = a + b (U20)0.5 (37) 

where U 20 is the windspeed at 20 feet. 

Consequently, windspeed in the Canadian code is directly related to the rate at 

which fuel moisture approaches equilibrium. 

The two wind corrections (eqs. 36 and 37) use windspeed measured at different heights. The fine fuel moisture code was calibrated to winds measured at 

the international standard height, 10 meters, in the open. The solar heating correction requires windspeed at the vegetation height. The U.S. standard established for NFDR stations is 20 feet. The ratio of windspeed at 10 m to 20 feet 

(6.1 m) can be calculated from equation 36 if the vegetation height is known. 

We assume the windspeed at 20 feet and 10 meters are the same in this model. 

20 
Canadian Standard 

Daily Fine Fuel 

Moisture Code 

(FFMC) 

Canadian Hourly 

Fine Fuel Moisture 

Code 

Diurnal Predictions 

The FFMC accepts initial fuel moisture, temperature, humidity, wind, and 

rain as inputs. In our model, the FFMC is used to calculate fine fuel moisture 

after the inputs are adjusted for elevation and solar heating. The version used 

in our model is the same as used by Simard and Main (1982). Like any large 

system, the FFMC has undergone many revisions. Work on the FFMC subsequent to the version we used is designed to provide consistency for table 

presentation and to give better moisture predictions' under very wet conditions, 

100 to 250 percent. It is not expected that these changes would affect our 

model significantly. The formulations of the FFMC we used are given in 

appendix A. 

The other major condition to be accounted for by this model is the capability 

to make a calculation of expected moisture content at any time of the day or 

night. As presently used, the Canadian standard daily FFMC is structured to 

give a moisture value for midafternoon with data collected at noon, local standard time. Fortunately, the Canadian Forestry Service has also investigated 

diurnal prediction. Muraro and others (1969) used litter data sampled from a 

dry lodgepole pine site near Prince George, BC, to produce tables for adjusting 

the FFMC for various times of the day or night. Van Wagner (1972) developed 

a new scale supplemented with data from a jack pine forest at Petawawa, and 

produced a single table for predicting FFMC based on time, initial FFMC, and 

relative humidity. 

Van Wagner (1977) developed a set of equations, similar to the standard daily 

FFMC, that would accept hourly weather data, thereby freeing the model from 

the restraint of the original data and a single value of humidity. Alexander and 

others (1984) programmed the equations so that hourly computations of the 

FFMC and other components of the Canadian Forest Fire Weather Index 

system could be made on a handheld calculator with weather measured or forecast hourly. The BEHAVE model, as will be shown, adds the capability of 

predicting the necessary weather elements over a 24-hour period. 

Unfortunately, weather forecasts on an hourly basis for extended periods are 

not readily available. It was necessary, therefore, to devise a way of estimating 

hourly weather frem a few forecasts at key times. This is done by initiating the 

diurnal predictions from the daily moisture prediction and weather data at 1400 

hours. This is supplemented with a forecast at the time when the prediction is 

needed and with estimates of weather data at sunset and sunrise if projection 

time is after sunset or sunrise. Temperature and relative humidity values at 

each hour are predicted from sinusoidal curves linking the 1400 weather to the 

projection time weather. No trend for wind or cloud cover can be justified, so 

linear interpolations are used. The model will not apply to days with precipitation after 1200 (noon). The model determines hourly values of the weather data 

needed and performs the adjustments for solar heating. If the user does not 

have a weather forecast, he/she can estimate the temperature at any of the key 

points and if the air mass :Q.as not changed, the model will estimate the humidity. This will be based on the dew point of the air at the last known condition 

(calculation shown in appendix). 

Beyond noon, the process will begin with a new 1400 fuel moisture calculated 

by the daily code. A discontinuity in a smooth-line moisture trend can occur 

between late morning predictions made by the morning code and early afternoon predictions made by the daily code. 

21 
Curves used to match weather conditions during each period of the day are 

described below. 

Early afternoon.-If the moisture is needed between 1200 and 1600, the daily 

value is sufficient and no adjustments are necessary. Personal discussions with 

Van Wagner confirm this view. 

Late afternoon.-In late afternoon, in addition to the 1400 weather, the user 

must supply a weather forecast at the projection time. The temperature and 

humidity are assumed to follow cosine curves as shown in figure 8. If sunset 

conditions are hotter and drier than 1400, the curves will arc in opposite forms. 

From figure 8 the temperature, T, at any time t can be expressed as: 

T = T14 + (T14 - Ts)(cos(90(t - 14)/(ts - 14)) - 1) (38) 

where T and t refer to temperature and time, respectively, and the subscripts 

are 14 = 1400 and s = sunset. 

Time of sunset is determined by an algorithm using latitude and date (see 

appendix D). The user enters a forecasted temperature at the projection time 

and equation 38 is used to determine a hypothetical temperature at sunset, (T s), 

which fixes the end point of the cosine curve. Equation 38 will then be used to 

calculate temperature for each hour between 1400 and the proj ection time. 

The humidity as shown in figure 8 is treated similarly with the following 

equation: 

H = H14 + (H14 - Hs )(cos(90(t - 14)/(ts - 14)) - 1) (39) 

If solar heating is occurring, the air temperature and humidity are adjusted to 

the fuel level as described earlier for the daily computation. 

T ~ t/!a. 

1 4 ~--.... --..... "'''. --...... , 

''e. 

'" 

" @T .. >""'Jr.:\ 

ort " " .. fI' \!I H ",uta' ........ ..,. . ...- H 

_. 

~.---- ..... 14 '=T" 

... FIN/! FUEL MOISTURE ---i!lm . ..' 

@ INPUTS 

[!] OUTPUTS 

• INTERMEDIATE 

HOURLY VALUES 

1200 

NOON 

1400 1800 PROJECTION 

TIME 

Figure 8. - Typical late afternoon weather 

and moisture relationships. 

22 
Nighttime.-For nighttime, in addition to the 1400 weather data, the user 

must supply weather conditions at sunset and at the projection time. 

The afternoon equations and the diurnal code are used to advance fuel moisture to sunset. Beyond sunset a new set of sinusoidal curves is used to describe 

temperature and humidity. No corrections for radiation cooling are made; consequently, cloud cover at night is not needed at this time. (Corrections for cooling 

due to nighttime radiation losses and dew formation should be considered for 

an update to this model if greater accuracy is needed for the morning.) Windspeed is assumed to vary linearly between sunset and projection time. 

Temperature is assumed to be represented by another quadrant of the sine 

curve from sunset to sunrise as shown in figure 9 and expressed as: 

T = Ts + (Tr - Ts) sin(90(t - ts)/(tr - ts)) (40) 

The user enters a forecast temperature at a projection time. This is used first 

to fix the end point of the sine curve at sunrise and then temperature is calculated at every hour up to projection time. 

After sunset, humidity of the air at shelter height is assumed to be the same 

as humidity in close proximity to the fuel surface. 

A sine curve shape between 0 and 90 0 is assumed to match humidity between 

sunset and sunrise as shown in figure 9 and expressed as: 

H = Hs + (Hr - Hs) sin(90(t - ts)/(tr - ts)) (41) 

Predicted relative humidities will not be allowed to go beyond 100 percent. 

Interestingly, the model may have to artificially set sunrise humidity above 100 

percent to develop the correct shape of the sinusoidal humidity curve up to 

proj ection time. 

1200 1400 

NOON 

SUNSET PROJECTION 

TIME 

Figure 9. - Typical nighttime weather and 

moisture relationships. 

23 
Purpose of 

Validation 

Morning.-Computations of fuel moisture in the morning, any time between 

sunrise and 1200 m. (noon), are a continuation of the previous afternoon and 

nighttime extrapolations. The user must specify weather at 1400 on the preceding day, at sunset of the previous day, and at sunrise on the projection day. A 

new set of sinusoidal equations is specified for temperature and humidity as 

shown in figure 10: 

Temperature, T = T12 + (Tr - T12) cos(90(t - tr)/(12 - tr)) (42) 

Humidity, H = Hr + (Hr - H12)(cos(90(t - tr)/(12 - tr)) - 1) (43) 

Cloud cover and windspeed are extrapolated linearly between sunrise and 

projection time. The haze level specified at projection time is assumed to be 

constant from sunrise to the projection time. All solar heating adjustments are 

made as per the daily code procedures. 

The Canadian hourly FFMC used to calculate fuel moisture is very similar to 

the standard daily FFMC. The equations, inputs, and procedures are given in 

appendix B. 

T ® INPUT. 

14~ H .r r;t OUTPUT. \:]............... _ ~ L::J 

........... .~.-.. 

.. ......... • INTIRIlIDIATI ~'- .'" ..... , T '" .... HOURLY VA LUI. 

'~. / ~H ~ /. 

'( m . , I> '-', (t)T 

H ,II H.. "",."M" 1 4 ". ~ ..... .L.:L .......... @ .... .-. '-="'" 

1200 1400 

NOON 

SUNSET 

T. r 

SUNRISE 

Figure to.-·Typlcal morning weather and moisture 

relationships. 

VALIDATION 

PROJECTION 

TIME 

The Canadian FFMC was developed for shaded conditions, while the FBO 

system patterned after the NFDR system was designed for worst case exposed 

conditions. This general behavior was confirmed by Simard and Main (1982). 

The purpose of the validation presented here is to determine if our new moisture model preserves the capabilities of the Canadian FFMC in shaded conditions and improves it significantly in sunny conditions. Similarly, the new 

model should be at least as good as the FBO methods in dry sunny conditions, 

and superior in the shade. 

Discussion. - The fine fuel moisture model that we have developed is a deterministic model assembled from physical and empirical relationships that expand 

the capabilities of the Canadian Fine Fuel Moisture Code. The methods of 

accounting for solar heating, diurnal predictions, and startup in mid season have 

not been tested. Two separate validation efforts for testing the complete model 

24 
Daily Version 

Validation 

(Objective No.1) 

were initiated. The first, reported here, uses data already available from several 

diverse fuel and shade conditions. The second is a study by the University of 

Montana to test the model independently. Their test will include a sensitivity 

analysis. 

We were fortunate to find a great deal of moisture data with most of the 

inputs necessary to drive the model. Most of the data were unpublished. We 

used data from Idaho, Texas, Alaska, and Arizona. The Idaho data were collected at four elevations in conifer litter in the Bitterroot Mountains of Idaho, 

just south of Missoula (Frandsen and Bradshaw 1980). The Texas data were 

taken in grass fuels (Clark 1981). The Alaska data were taken in several fuel 

types and offer a good test of the model at northern latitudes (Norum 1983). 

Arizona data were taken in open and closed ponderosa pine stands (Harrington 

1983; Sackett 1983, 1984). Sackett's data were the only set initiated after 

model development had been started so that all inputs were specified except 

haze. Data used in this analysis are shown in appendix G. Input data are in 

part A; outputs from the models are in part B. 

Specific Objectives.-

1. Determine if the daily version of the model can predict fine fuel moisture 

better than the Canadian Fine Fuel Moisture Code when the fuels are exposed 

to the sun, and better than the FBO procedures when fuels are heavily shaded. 

2. Determine if the initiation procedures that do not use a complete record of 

preceding weather work as well as those that do. 

3. Determine how well the diurnal version of the model can predict fine fuel 

moisture throughout the diurnal cycle. 

Analysis method. - When comparing predictions of models using the same 

data set, one of two models would probably be superior if it tends to have 

smaller errors than the other model. Two methods were used to compare the 

error distributions of the models: 

1. Confidence intervals 

2. Analysis of variance 

The models are unaided by a posteriori correction terms or factors. 

The confidence intervals consisted of the following (one unit is 1 percent of 

qvendry weight, the unit of fuel moisture): 

PI = percent of predictions falling within 1 unit of the actual fuel moisture 

P 3 = percent of predictions falling within 3 units of the actual value 

190 = width of a 90 percent confidence interval about the actual value 

The best model will have the largest values for PI and P 3 and the smallest 190, 

Analysis of variance provides a basis for comparing model biases. The 

procedure gives a significance level (PF), which gauges the overall repeatability 

of different subsample means and the relative importance of these means for 

explaining overall variance. It can be determined if the sample mean error (x) of 

one model is significantly different from that of another by observing the 

contrast P-Ievels produced by the analysis of variance procedure. The data 

appear to satisfy the premises of analysis of variance reasonably well. 

Specifically, the contrast P-Ievels should be meaningful for comparing the 

BEHAVE and FFMC models in this analysis. The same is true for comparing 

the BEHAVE and FBO models except for the two hardwood strata, where the 

variances are no longer equal. 

25 
Data and Stratifications.-Data were restricted to measured fuel moistures 

less than 30 percent, taken between 1200 and 1600. A separate analysis was 

done for shade conditions less than 30 percent, for 30 to 70 percent, and for 

greater than 70 percent. This presumes that the amount of shading is largely 

responsible for variations in fuel moisture. This is a good assumption when one 

weather station serves three nearby fuel collection sites with different shade, 

such as was done in Arizona, but is not necessarily true for much of the Alaska 

data. To meet objective 1, however, we will stratify by shade and presume that 

heating took place. 

One-way analysis of variance was applied to each shade class, the treatment 

variable being model choice. It is important to note that we cannot test shade 

effect per se. The low-shade-Ievel data are entirely grass and Arizona pine, 

while the high-shade data are heavily loaded with northern fuel types. Our 

approach is to merely perform a model comparison on three separate and 

interesting subsamples of our data. 

Model comparison by means of one-way analysis of variance was also carried 

out for six fuel types (conifer litter, needles, grass, conifer sticks, hardwood 

sticks, and leaf litter). Here we cannot test the fuel type effect per se. We 

merely show that the model comparison does not break down when performed 

by fuel type. 

Results.-Resulting model comparisons are shown in table 1, with highlights 

plotted in figures 11, 12, and 13. 

Whether objective 1 was achieved or not can be judged from figures 11 and 

12. In figure 11 the positive bias of the FFMC at low shade values has been 

eliminated by the additions incorporated in the BEHAVE model. At high shade 

values, the BEHAVE model and FFMC have the same mean and variance 

values, whereas the strong negative bias of the FBO model is illustrated. 

Table 1.-Statistical summary of early afternoon moisture data comparisons 

between the three moisture models 

Mean Standard Sample Contrasts 

error deviation size Confidence P·level 

Model (X) (S) (N) P1 P3 IgO 2 3 

-- Percent -- --- Percent ---

Shade <30% 

FFMC 1.96 3.92 28 18 60 ±6.2 2 1 

BEHAVE -.64 3.93 28 57 81 ±5.9 2 84 

FBO -.86 3.88 28 47 86 ±5.5 1 84 

PF = 0.01, R2 = 10% 

30 <shade ~70 % 

FFMC -1.10 5.33 25 7 45 ±10.2 58 23 

BEHAVE -1.92 5.04 -25 26 52 ±9.9 58 50 

FBO -2.93 5.39 25 14 52 ± 13.0 23 50 

PF = 0.46, R2 = 2% 

Shade >70% 

FFMC 0.40 5.24 170 22 57 ±8.1 90 0 

BEHAVE .47 5.21 170 22 58 ±8.1 90 0 

FBO -3.31 5.48 170 21 51 ± 10.3 0 0 

PF = 0, R2 = 10% 

26 
10 • FFMC 

• BEHAVE 

8 +FBO 

.... 6 0 

a. 

r£ 4 

0 

a: 

a: 2 

LLI 

LLI 0 a: 

;:) 

.... 

0 -2 

0 

:& -4 ... 

LLI 

;:) -6 La. 

-8 

-to 30-70 70-100 

PERCENT SHADE 

Figure 11.-Early afternoon mean 

and standard deviation trends for the 

three moisture models in three shade 

conditions. 

NO CONTRAST ~ 1 00 

80 .... , 

" .... 

Z 

w 60 0 

rc 

w 40 Q. 

20 

NO SIMILARITY~ 0 

I 

0 

" 

II 

30 

ff~C ~ ..as ,,~~ ~~ 

" ~ • 

.,~~ 

'~41'. ,~ .. ',"I:- ,~o 

" " 

II 

70 

PERCENT SHADE 

Figure 12.-Contrast P level between BEHAVE and 

other moisture models. 

• 

• . I 

100 

This is further confirmed in figure 12 where the contrast P level comparing 

BEHAVE and FFMC increases with shade level. At low shade there is no 

similarity between the means of the two models, while at high shade they are 

nearly identical. Contrast between BEHAVE and FBO indicates an inverse 

trend. At high shade there is no similarity, while at low shade there is very 

high similarity. Figure 12 is a strong indication that we achieved our first 

objective. 

27 
Actual accuracies are compared by the confidence intervals in table 1. The 

relative frequency for an error within 1 percent fuel moisture is illustrated with 

bar graphs in figure 13. At low shade levels, 0 to 30 percent, BEHAVE is 

within 1 percent of the actual moisture 57 percent of the time, three times 

better than the FFMC unaided by solar heating corrections. The BEHAVE 

model, capturing 47 percent of the data within 1 unit of fuel moisture (1 

percent), was also better than the FBO model, which worked well.At high shade 

values, the three models are comparable, with regard to P l' 

tO 

a. 

... a. 

60 

50 

40 

30 

20 

10 

o 

r--

II-

-

II-

-

~ 

W 

> 

c 

:c 0 r- W ID 

ID II. r-- au 

CJ > 

2 C - :c II. 

~r w 0 II. ID ID 

II. 

0-30 40-70 

PERCENT SHADE 

Figure 13.-Errors within 1 percent for 

the three moisture models in three 

shade conditions. 

~r--_ 

au 

> CJ C 0 :E :c ID II. W II. II. ID 

70-100 

At mid-shade levels, 30 to 70 percent, the results are more difficult to 

interpret. All three models show a negative sample-mean (fig. 11), and there is 

little contrast between them (fig. 12). BEHAVE does notably better in keeping 

errors to within 1 percent (fig. 13). The intermediate shade data set has the 

lowest R2, 2 percent, and a Pf value of 0.46, whereas the other two sets had Pf 

of 0.01 and 0.00. Thus, while there is strong repeatability of observed meandifferences at low and high shade, there is not for intermediate shade. 

Some of the uncertainty may be due to the source of the mid-shade-Ievel 

data. Much of it comes from Alaska where the low sun angles often cause less 

heating and drying. Sorting by shade may not be the best choice for 

illustrating model capability. 

Furthermore, amount of shade caused by canopies is not an independent 

variable collected on-site; it is calculated by the BEHAVE model and combined 

with cloud shade to give percentage shade. Thus, partial results from one model 

are used in the analysis by shade level for testing all three models. 

28 
Model comparisons by fuel type are shown in table 2. (Note that the table is 

not meant to reflect a separate fuel type effect.) Data from the Alaska 

hardwood sticks and leaf litter, as well as the conifer sticks from both Alaska 

and Arizona, indicate that the BEHAVE and FFMC models are directly 

comparable and have small mean errors ranging from -1.45 to 0.577 percent, 

whereas the FBO model has large negative mean errors ranging from -3.55 to 

-6.53 percent. Grass data from Texas and pine needle data from Arizona 

reflect more favorably toward the BEHAVE and FBO models. This is probably 

attributable to the more open sites. Although the Idaho data consist of only six 

cases, the results typify the tendency of all three models to underpredict at the 

Idaho site. In all stratifications tried, the BEHAVE model performed best. 

Table 2.-Comparison of the three moisture models, sorted by fuel types 

Mean Standard Sample Contrasts 

error deviation size Confidence P·level 

Model (X) (S) (N) P1 P3 IgO 2 3 

-- Percent -- --- Percent ---

Conifer sticks (Alaska spruce, 

Arizona pine) 

FFMC -0.80 5.61 30 27 49 ±10.6 97 5 

BEHAVE -.84 5.72 30 27 49 ±10.7 97 5 

FBO -3.55 4.82 30 29 54 ± 11.8 5 5 

PF = 0.08, R2 = 6% 

Hardwood sticks (Alaska) 

FFMC -1.45 4.70 37 22 47 ±9.3 100 0 

BEHAVE -1.45 4.70 37 22 47 ±9.3 100 0 

FBO -5.65 6.01 37 14 37 ±15.6 0 0 

PF = 0.00, R2= 13% 

Leaf Iitter"(Alaska) 

FFMC 0.57 7.32 47 9 49 ±13.3 100 0 

BEHAVE .57 7.32 47 9 49 ±13.3 100 0 

FBO -6.53 5.27 47 9 19 ±15.2 0 0 

PF = 0.00, R2 = 20% 

Grass (Texas) 

FFMC 1.94 4.55 31 18 44 ±7.0 5 1 

BEHAVE -.39 4.66 31 45 65 ±7.7 5 57 

FBO -1.03 4.24 31 42 77 ±7.0 1 57 

PF = 0.03, R2 = 8% 

Needles (Arizona pine) 

FFMC 1.63 2.73 71 29 78 ±4.3 51 1 

BEHAVE 1.33 2.72 71 37 80 ±4.3 51 6 

FBO .47 2.79 71 29 77 ±3.9 1 6 

PF = 0.03, R2 = 3% 

Litter (Idaho) 

FFMC -4.68 2.92 6 0 27 ±8.8 41 51 

BEHAVE -2.97 3.86 6 8 33 ±8.4 41 21 

FBO -6.17 4.36 6 0 17 ±14.3 51 21 

PF = 0.36, R2 = 13% 

29 
The relative accuracy of the three models is illustrated by ranking them for 

mean error, PI level, and Ps level in tables 3, 4, and 5, respectively. In table 3 

(mean error) the BEHAVE model ranked first or tied for fir~t in four of six fuel 

types; BEHAVE was second twice and never last. The ties can be attributed to 

shading and less heating in Alaskan fuels where BEHAVE reverts to the 

FFMC. For both confidence level PI and Pa (tables 4 and 5), BEHAVE is first 

or tied for first in five of six fuel types, is tied for second once, and is never 

last. Whether the changes to the FFMC which resulted in the BEHAVE model 

really produced an equal or better model can be strongly inferred from the 

results of these three tables wherein the FFMC only ranked better than 

BEHA VE in one example, the mean error in conifer sticks, and in that case the 

difference is insignificant: -0.80 compared to -0.84. 

Table 3.-Ranking the three moisture models by daily mean error X, percent 

Fuel 

Grass (Texas) 

Needles (Arizona) 

Leaf litter (Alaska) 

Conifer sticks (Alaska 

and Arizona) 

Hardwood sticks 

(Alaska) 

First 

BEHAVE -0.39 

FBD 0.47 

BEHAVE 057 

FFMC . 

FFMC -0.80 

BEHAVE -145 

FFMC . 

Second 

FBD -1.03 

BEHAVE 1.33 

BEHAVE -0.84 

Third 

FFMC 1.94 

FFMC 1.63 

FBD .,6.53 

FBD -3.55 

FBD -5.65 

Conifer litter (Idaho) BEHAVE -2.97 FFMC -4.68 FBD -6.17 

Table 4.-Ranking the three moisture models by confidence level P1 

Fuel First Second Third 

Grass (Texas) BEHAVE 45 FBD 42 FFMC 18 

Needles (Arizona) BEHAVE 37 FFMC 29 FBD 

Conifer sticks (Alaska FBD 29 BEHAVE 27 

and Arizona) FFMC 

Hardwood sticks BEHAVE 22 FBD 14 

(Alaska) FFMC 

Leaf litter (Alaska) all tie 9 

Conifer litter BEHAVE 8 FFMC 0 FBD 

Table 5.-Ranking the three moisture models by confidence level P3 

Fuel First Second Third 

Needles (Arizona) BEHAVE 80 FFMC 78 FBD 77 

Grass (Texas) BEHAVE 65 FBD 77 FFMC 44 

Conifer sticks (Alaska FBD 54 BEHAVE 49 

and Arizona) FFMC 

Leaf litter (Alaska) BEHAVE 49 FBD 19 

FFMC 

Hardwood sticks BEHAVE 47 FBD 37 

(Alaska) FFMC 

Conifer litter (Idaho) BEHAVE 33 FFMC 27 FBD 17 

30 
Initialization 

Validation 

(Objective No.2) 

The variances, 82, and confidence interval results, P l' P 2' and 190, are 

important operationally. As indicated by the low R2 values (table 6), there is a 

lot of noise unrelated to model choice. Two results that stand out are the large 

error dispersions for the FBO model in Alaska hardwood sticks and leaf litter 

and Idaho conifer litter. 

Table 6.-Summary of initialization verification for options 2, 3, and 5 of the 

BEHAVE moisture model 

Mean Sample Contrasts 

error Variance size Confidence P·level 

Option (X) (S) (N) P1 P3 190 2 3 5 

Percent -- Percent --

2 -1.78 13.5 29 28 53 ±6.4 22 

3 -1.01 15.4 29 30 56 ±5.9 22 

5 + 1.16 57.5 29 32 53 ±14.4 

Initialization estimates the previous day's 1400-hour fine fuel moisture, 

referred to as mo' I t is a reference value and is not displayed to the user. 

Because fine fuels respond relatively fast, this value need not be highly 

accurate, but it does have a large range, from 2 percent to over 100 percent, 

which requires a good estimate. The test of the initialization process should 

confirm a reasonable estimate of mo' 

There are five options for initiating the BEHAVE model in midseason. Validation requirements differ by option. 

Option 1 accepts a known fine fuel moisture; hence no validation is necessary. 

Option 2 uses the full set of weather inputs just as the FFMC was designed 

to be operated and so becomes a standard for comparison. 

Option 3 presumes it has rained within the past week and makes several 

assumptions about weather conditions within the intervening time period. It 

should be compared with option 2. 

Option 4 uses persistence forecasting. It presumes that the weather has been 

stable for several days, so that fine fuels will approach a similar early afternoon moisture each day. Today's early afternoon weather fine-tunes it to 

today's conditions. No validation is presumed to be necessary. 

Option 5 is a last resort if none of the first four options are applicable. It is 

an approximation that needs validation. 

Option 3 is tested by comparing it with option 2. Early afternoon moisture 

data that included precipitation within the preceding 2 to 7 days were 

selected. This provided 29 cases for which both options can be exercised. 

Exercising option 2 (table 6) on these cases, the values of the mean error (X2), 

variance (8~), and the relative frequencies PI and P a are: 

X2 = -1. 78, 8~= 13.5, 

PI = 0.28, Pa = 0.53. 

Exercising option 3, we obtain 

Xa = -1.01, 8~ = 15.4, 

PI = 0.30, Pa = 0.56. 

Using the F-test, it can be shown that an assumption of equal variances is 

reasonable for the two error distributions. 

31 
Validation of 

Diurnal Capability 

(Objective No.3) 

The differences between the PI-values and between the P 3-values had P 

values of 0.59 and 0.48, respectively. This test is based on the binomial process 

with 29 trials. A Student-t statistic computed from X3 - X2 had a P value of 

0.22. 

In conclusion, option 3 is about as accurate (perhaps slightly better) on three 

of the four tests, having (perhaps) a slightly higher variance than option 2. 

Initialization by use of option 5 was simulated by using the same 29 cases, 

but with the period length reduced to 1 day of propagation and the first fuel 

moisture set to 6, 16, or 76 percent. The three fuel moisture levels represent 

the three possible qualitative descriptions of the preceding week's weather. To 

simulate this, the equilibrium fuel moisture was computed for each day and 

averaged. The closest of the three moisture levels (6, 16, or 76) to this average 

was chosen as the initial value to use. 

Exercising this simulated option 5: 

X5 = 1.16, S2 = 57.5, PI = 0.32, P3 = 0.53 

The F-ratio Sg/S~ is significant at <0.005; consequently, a meaningful comparison of the mean errors of options 2 and 5 requires a different method. Assuming normally distributed mean errors and that the actual error variances are 

13.4 and 57.5, respectively, then 

(X2 - u)/(13.4/29)Y2 and (X5 - u)/(57.5/29)Y2 

are normal random variables with a mean of zero and variance of 1. The 

hypothesis that X2 and X5 have the same mean (p.) can be tested. The sample 

values of these two standardized random variables are -0.48 and +0.48, 

respectively. The probability of that is (0.32)2 or 0.10; the means are different 

at a significance level of 10 percent. Differences between the PI- and P3-values 

are significant at 0.43 and 0.63, respectively, for the 29-trial binomial tests. 

Option 5 generates errors having a mean which is quite different from that of 

option 2 and much greater variance. The scores PI and P 3 are not significantly 

different, however. 

Based on rather noisy data, it is apparent that option 3 is as good as option 

2, while only the large errors are worsened by the use of option 5 in place of 

option 2. Evidently, any difference between the true values of PI and P3 is 

sometimes masked by data noise if we assume that extra input information 

cannot harm model performance. 

Validation of diurnal capability is concentrated on the BEHAVE model using 

the Canadian code with hourly prediction capability. This is because neither the 

FBO model nor the tables developed by the Canadian Forestry Service (Van 

Wagner 1972; Alexander 1982) for the FFMC have the forecasting capabilities needed for the BEHA VE system. 

Sackett (1983, 1984) collected fine fuel moisture data over 24-hour periods 

during June and October 1983 in northern Arizona. This provided a chance to 

test the model with high and low sun angles. He also collected data beneath 

three densities of crown canopy. These data are summarized in table 7. Prediction from the BEHA VE diurnal model using these data are shown in table 8. 

32 
Table 7.-Summary of diurnal data taken in northern Arizona by Steve Sackett in 1983 

Observed weather Measured fuel moisture 

Time Ta Ha U10 Sc C = 4.4 C = 74 C = 94 

of Pct Milh --------------- Percent ---------------

Date - 6/28/83, Elevation - 7,440 ft, Aspect - 225 0, Slope == 4%, T SR - 4_8, T ss - 19_2 

1516 76 11 5-12 10 3.3 3.4 4.2 

1614 75 15 8-13 10 2.8 3.4 4.0 

1725 75 17 9-13 10 3.2 3.5 4.0 

1810 71 18 8-12 0 4.0 3.8 4.4 

1908 67 23 O· 5 0 3.75 4.1 5.8 

2117 52 37 0- 4 0 4.3 4.8 5.7 

2218 50 37 0- 3 0 7.3 5.1 5.4 

2357 50 37 0- 2 0 4.9 5.8 6.0 

0157 47 42 0- 4 0 5.0 6.1 5.7 

0403 46 41 0- 3 0 6.2 5.9 7.0 

0550 41 53 0 0 6.2 6.2 7.4 

0700 53 48 0 0 6.0 7.05 7.7 

0815 64 20 0-10 0 4.3 6.6 7.0 

0940 70 20 8-12 0 4.1 5.3 6.1 

1040 75 15 8-12 0 3.3 4.4 5.4 

1140 76 11 8-12 0 3.4 4.2 3.9 

Date - 10/20/83, Elevation - 7,440 ft, Aspect - 225°, Slope == 4%, TSR - 6.5, Tss - 17.5 

1310 61 23 0- 5 0 9.0 8.0 13.1 

1510 63 15 5-10 0 5.0 9.0 10.7 

1710 57 22 3- 6 10 6.6 8.9 11.8 

1910 40 58 0 0 12.25 10.7 13.6 

2030 37 63 0- 2 0 15.1 10.3 14.0 

2230 31 72 0 0 11.3 13.7 14.6 

0130 27 77 0- 2 0 11.6 13.0 15.0 

0330 27 77 0- 1 0 11.4 12.8 14.3 

0945 57 30 2- 5 0 8.9 11.4 15.2 

1210 63 25 5- 8 0 8.3 13.95 11.9 

Table S.-Calculations from the BEHAVE diurnal model with data from northern 

Arizona 

Crown Crown Crown 

closure = 4.4 % closure = 74% closure = 94% 

Time Ta Ha U10 Sh m Sh m Sh m 

June 28, 1983 -

1400 77 8 8 15 3.4 82 3.4 91 4.3 

1516 76 9 7 15 2.6 90 3.4 95 4.1 

1614 75 11 6 16 2.3 96 3.4 98 4.1 

1725 72 17 5 16 2.4 100 3.4 100 4.1 

1810 70 18 4 20 2.7 100 3.5 100 4.2 

1908 67 23 3 36 2.8 100 3.8 100 4.4 

2117 58 31 3 100 3.7 100 4.5 100 4.7 

2218 55 34 3 100 4.1 100 4.9 100 5.0 

2357 50 38 2 100 4.9 100 5.7 100 6.1 

0157 45 43 2 100 5.7 100 6.5 100 6.9 

0403 43 45 2 100 6.7 100 7.4 100 7.7 

0550 44 44 3 100 7.2 100 8.0 100 8.4 

0700 46.5 41.0 4.2 32 7.4 100 8.4 100 8.7 

0815 52 34 6 10 7.2 95 8.7 98 8.9 

0940 62 26 8 7 6.0 85 8.7 88 8.9 

1040 69 18 9 5 5.0 76 8.4 82 8.5 

1140 76 11 10 5 4.5 69 7.8 75 8.0 

October 20, 1983 -

1400 61 20 5 14 6.7 97 8.4 98 12.1 

1510 60 21 5 15 6.4 98 8.3 99 11.6 

1710 57 32 4 36 6.7 100 8.4 100 11.2 

1910 47 44 4 100 7.4 100 8.9 100 11.3 

2030 43 50 3 100 8.0 100 9.3 100 11.5 

2230 37 58 3 100 9.0 100 10.2 100 12.1 

0130 31 69 2 100 10.8 100 11.7 100 13.2 

0330 28 74 2 100 11.9 100 12.6 100 14.0 

0945 40 55 .5A 16 13.5 99 14.9 99 15.9 

1200 63 25 6.5 10 10.4 93 13.9 96 15.6 

33 
Predictions by the BEHAVE model of temperature, humidity, and moisture 

from 1400 one day to 1200 (noon) the next are shown in figures 14 to 18. For 

these predictions the model was given initial weather and moisture at 1400. In 

place of forecasts at sunset and sunrise, it was given measured weather and the 

final value. Hourly predictions of T, H, and m are plotted as lines for comparison with the measured data points. 

120 

100 

U- 80 0 

iii' 

a: 

:) 

... 

c( 60 • a: 

w 

A. 

:IE 

w 

... 40 

20 

0 ___ 00l0000-__ 

1200 1600 2000 2400 0400 0800 1200 

TIME,H 

Figure 14.-Diurnal temperature measurements (dots and squares) and model predictions (lines) for June and October in Arizona. 

120 

100 

80 

t-

(.) 

A. 

,: 60 !: 

c 

:IE 

:) 

:J: 40 

20 • 

o----'---~ 

iii 

." 

;~CT' 

\ 

• 

1200 1600 2000 2400 0400 0800 1200 

TIME. H 

Figure 15.-Diurnal relative humidity measurements (dots and squares) and model 

predictions (lines) for June and October in 

Arizona. 

34 
24 

20 

.. 

CJ 18 Ct. 

ui 

CIC 

~ 

... 12 fI) 

(5 

• 

~ 

1&1 • ~ 8 

LL 

4 

0 ..... --...... __ 

1200 1800 2000 2400 0400 0800 1200 

TIME, H 

Figure 16. - Diurnal fuel moisture measure· 

ments (dots and squares) and model predictions (lines) for June and October In Arizona 

beneath a 4.4 percent crown closure 

ponderosa pine stand. 

24 

20 

... 

CJ 18 Ct. 

ui 

a: 

:::» 

.. fI) 12 

0 

:I 

~ 

1&1 8 • ~ 

LL 

4 

OCT. 

• 

• 

• •• 

o --~!----~ 

1200 1800 2000 2400 0400 C 800 1200 

TIME, H 

Figure 17.-Dlurnal fuel moisture measurement. (dots and squares) and model predlc· 

tlons (lines) for June and October In Arizona 

beneath a 74 percent crown closure ponderosa pine stand. 

35 
24 

20 

tU 16 A. 

W 

II: 

= t- • (/) 12 

0 

:I 

... 

w 

= 8 &&. 

4 

0 ____ -... __ _ 

1200 1600 2000 2400 0400 0800 1200 

TIME. H 

Figure 18.-Diurnal fuel moisture measure· 

ments (dots and squares) and model predic· 

tions (lines) for June and October in Arizona 

beneath a 94 percent crown closure pon· 

derosa pine stand. 

120 

100 

&&. 80 0 

t- W U II: A. = > tC 60 

t- Il: 

0 W 

i A. 

:I 

= w :z: I- 40 

20 

0 ___ "",-__ 

1200 1600 2000 2400 0400 

TIME. H 

Figure 19.-Diurnal temperature and humid· 

ity measurements (dots and squares) and 

model predictions (lines) in Idaho in August 

beneath mixed conifer stand. 

36 

• •• • 

~ 

0800 1200 
VVe also have diurnal temperature and humidity data collected by Frandsen 

and Bradshaw at four sites in Idaho. Their moisture data were collected only in 

the morning, the most difficult period for prediction. Data from their site 3 in 

August and September illustrate the model's ability to predict temperature and 

humidity under a mixed conifer stand in a mountain location (figs. 19 and 20). 

Summaries of the performance of the BE HA VE and FBO models for afternoon, night, and morning hours are shown in table 9. Two sets of morning data 

are presented-one for Sackett's open stand and one for the Idaho data. The 

BEHAVE model performed very well, capturing 77 percent of the afternoon 

data within 1 percent of measured and 100 percent within 2 percent. During 

the night it captured 50 percent within 1 percent and 67 percent within 2 percent. In the morning it captured 29 percent within 1 percent and 86 percent 

within 2 percent. In Idaho, these latter figures fell off to 14 percent and 46 percent. The FBO performance was considerably less in all cases. 

120 

100 

II. 80 0 

t- iii (J a: a. :::I 

> t- 60 ct t- a: Q 1&1 

i a. 

:E :::» 1&1 % t- 40 

20 

o ---"-----' 

1200 1600 2000 2400 0400 0800 1200 

TIME. H 

Figure 20.-Diurnal temperature and humidity measurements (dots and squares) and 

model predictions (lines) in Idaho in 

September beneath mixed conifer stand. 

Table g.-Summary of fine fuel moisture litter data from Arizona and Idaho by period of the day 

(X = mean error, S2 = error variance) 

Place Time of day Model X S2 P1 P2 IgO n Shade 

Percent 

Arizona Afternoon (after 1400) BEHAVE -0.25 0.39 77 100 1.2 13 9·100 

Afternoon (after 1400) FBO 1.6 5.5 23 38 4.2 13 9·100 

Night BEHAVE -1.7 5.8 50 67 5 12 100 

Night FBD 3.4 9.5 0 17 6.1 12 100 

Morning (before 1200) BEHAVE 1.5 .51 29 86 2.5 7 4·40 

Morning (before 1200) FBO 2.7 4.1 29 29 4.5 7 4·40 

Idaho Morning (before 1200) BEHAVE -3.4 11.4 14 46 8.2 35 26·95 

Morning (before 1200) FBO -6.4 12.8 0 9 12.1 35 26·95 

37 
The statistical summary indicates that the BEHAVE diurnal model performs 

very well. Figures 14 through 20 reveal more about its capabilities. Predictions 

of temperature and humidity through the late afternoon and night are surprisingly accurate, in both Arizona and Idaho. An exception may be in the predictions of temperature and humidity in October in Arizona. The trend of the 

actual data is followed, but through the night actual temperatures are about 50 

cooler than predicted and humidities about 10 percent higher. As shown in the 

October fuel moisture predictions (figs. 16, 17, and 18), moisture is underpredicted during the night. 

In the morning the model responds fastest for conditions in the open stand 

(fig. 16) because the solar heating functions bring the predicted fuel moisture 

down faster than in the shaded sites (figs. 17 and 18). More diurnal data are 

needed to determine if these effects are persistent enough to warrant changes 

to the model. 

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1986. 

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38 
Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain 

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files. 

Countryman, Clive M. Radiation effects on moisture in ponderosa pine litter. 

Research Paper PSW-126. Berkeley, CA: U.S. Department of Agriculture, 

Forest Service, Pacific Southwest Forest and Range Experiment Station; 

1977. 23 p. 

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

William; Schroeder, Mark J. National Fire-Danger Rating System. Research 

Paper RM-84. Fort Collins, CO: U.S. Department of Agriculture, Forest 

Service, Rocky Mountain Forest and Range Experiment Station; 1972. 165 p. 

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Gisborne, H. T. Deadwood lying on duff drier than in air. Journal of Forestry. 

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Gisborne, H. T. The principles of measuring forest fire danger. Journal of 

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39 
Forest and Range Experiment Station, Intermountain Fire Sciences 

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40 
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41 
NOMENCLATURE 

G' 

h 

h* 

hi 

H 

Ha 

Hf 

Hr 

Hs 

H14 

I 

Ia 

J 

k 

1 

Definition 

elevation angle to the sun (-90 0 s A s 90 0 ) 

bole shadow area 

shadow area projected on a horizontal reference 

plane by the sun at solar altitude A 

net "effective" tree shadow 

vertical projection of S onto the horizontal 

vertically proj ected crown area of one tree 

horizontal unit surface area 

crown closure 

tree bole diameter 

crown diameter 

day of month 

elevation above sea level 

horizontal angular coordinate of tangential solar 

ray in conifer crown 

vertical angular coordinate of tangential solar ray 

in deciduous crown 

tree bole height 

hour angle from the local 6 a.m. 

vegetation height 

relative humidity at time t 

relative humidity of air 

relative humidity adjacent to fuel 

relative humidity at .sunrise 

relative humidity at sunset 

relative humidity at 1400 

incident radiation intensity on the forest floor 

irradiance at the forest floor perpendicular 

to the solar ray 

incident radiation attenuated by the atmosphere 

solar constant (= 1.98 cal/cm2.min); incident 

solar radiation on the upper atmosphere 

extinction coefficients for attenuation function 

log drying rate 

proj ection of radial coordinate, r I , 

perpendicular to solar ray 

optical path length of direct solar radiation 

through the atmosphere 

optical path length at the zenith at elevation E 

optical path length at sea level zenith 

crown height 

initial fuel moisture 

optical air mass 

month 

42 

Units 

degrees 

square feet 

square feet 

square feet 

square feet 

square feet 

acres 

percent 

feet 

feet 

days 

feet 

feet 

degrees 

feet 

percent 

percent 

percent 

percent 

percent 

percen~ 

callcm2.min 

cal/cm2.min 

cal/cm2·min 

cal/cm2• min 

ft-I 

feet 

feet 

feet 

feet 

feet 

percent 
NOMENCLATURE (Con.) 

Symbol Definition Units 

n number of trees on unit area 

Nn fractional area shaded by n average trees 

per unit of horizontal surface area 

NJ Julian date days 

p transparency coefficient (= 0.745) 

r earth-sun (center of mass) distance multiples 

of mean value 

r' radial coordinate of tangential solar rayon feet 

deciduous crowns 

Sc cloud cover percent 

t reference time (local standard) hours since 

midnight 

tp projection time hours since 

midnight 

tr time of sunrise hours since 

midnight 

ts time of sunset hours since 

midnight 

T temperature at time t of 

Ta air temperature of 

Tf fuel temperature of 

Tp temperature at projection time of 

Tr temperature at sunrise of 

Ts temperature at sunset of 

T14 temperature at 1400 of 

U wind velocity mi/h 

Uh , windspeed at vegetation height mi/h 

U20+h , windspeed at 20 feet above vegetation mi/h 

V crown volume cubic feet 

X intracrown path length feet 

z solar azimuth degrees 

a slope angle from horizontal at slope azimuth degrees 

{3 aspect of slope (the azimuth) degrees 

{) solar declination degrees 

€ Julian date correction for February and 

leap years 

r solar angle to the slope in the plane normal to degrees 

the slope 

e absolute atmospheric pressure at the site mb 

eo sea level pressure (= 1,000 mb) mb 

Tn net transmittance 

Tc cloud transmittance 

Tt tree transmittance 

I/; slope angle at solar azimuth z degrees 

c/> latitude degrees 

43 
LIST OF EQUATIONS 

Tf - Ta = I1(0.015Uh, + 0.026) 

Hf = Ha exp(-0.033(Tf - Ta)) 

I = (la Ir 2) sin A 

sin A = sin h * cos D cos cf> + sin D sin cf> 

tan z = sin h * cos D sin cf> - sin D cos cf> 

cos h* cos D 

cos z = cos h * cos D I cos A 

r2 = 0.999847 + 0.001406(D) 

D = 23.5 sin(0.9863(284 + NJ)) 

NJ = Julian date 

= Integer Value (31(Mo - 1) + Dy - O.4Mo - 1.3 + E) 

I = la sin r 

sin r = sin(A - ~)(cos ex)/cos ~ 

tan ~ = tan ex sin(z - (3) 

la = 1M Tn 

1M = 10 pM 

M = lM/lzo = lz (CSC A)llzo 

lz = lzo Qlc20 

Q = Qoexp( -0.0000448E) 

M = (QIQo) csc A = exp(0.0000448E) csc A 

la = 10 TnpM 

Tn = Tc • Tt 

Tc = (1 - ScIlOO) 

Ah = 7rD2/4, for conifers, if tan A ~ 2L/D, or 

= (7r - G)D2/4 + DL cot A sin G, if tan A < 2L/D 

cos G = (2(L/D) cot A)-l 

Ah = 7rDl/(2 sin A) for deciduous 

l = r' sin(G' - A) 

tan G' = -(LID) cot A 

r' = (L/2)(sin2G' + (L/D)2 cos2G,)_1/2 

X = V/(Ah sin A) 

= 7r D2L/( 12 Ah sin A) for conifers 

= 7rD2/(6 Ah sin A) for deciduous 

Ab = (213) dh cot A 

Ah = Ab + Ah (1 - exp( -JX)) 

As = Ah (cos ~ sin A)/sin(A + ~) 

Nl = As IAu 

N2 = Nl (1 - N1) + Nl 

N 3 = N 1 (1 - N 2) + N 2 

Nn = Nl (1 - Nn- 1) + Nn- 1 

Nn == 1 - exp(-nN1) 

Tt = 1 - Nn = exp(-nN1) 

A; = 7rD2/4 

N{ = A;/Au 

N~ = C = 1 - exp(-nN{) 

n = -In(1 - C)/N { 

44 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

(10) 

(11) 

(12) 

(13) 

(14) 

(15) 

(16) 

(17) 

(18) 

(19) 

(20) 

(21) 

(22) 

(23) 

(24) 

(25) 

(26) 

(27) 

(28) 

(29) 

(30) 

(31) 

(32) 

(33) 

(34) 
LIST OF EQUATIONS (Con.) 

n = -4~1 In(l - C)/1f'D2 

Uh, IU20- h , = 1I1n((20 + O.36h')/0.13h') 

k = a + b(U 20)°·5 

T = T 14 + (T 14 - Ts)(cos(90(t - 24)/(ts - 14)) - 1) 

H = H14 + (H14 - Hs)(cos(90(ts - 24)/(t - 14)) - 1) 

T = Ts + (Tr - Ts) sin(90(t - ts)/(tr - ts)) 

H = Hs + (Hr - Hs) sin(90(t - ts)/(tr - ts)) 

T = T12+ (Tr - T12) cos(90(t - t r)/(12 - tr)) 

H = Hr + (Hr - H 12)(cos(90(t .;.... t r)/(12 - tr))- 1) 

45 

(35) 

(36) 

(37) 

(38) 

(39) 

(40) 

(41) 

(42) 

(43) 
Explanation 

APPENDIX A: CANADIAN STANDARD DAILY FINE 

FUEL MOISTURE CODE (FFMC) 

(Adapted from Simard 1982.) 

1. Adjust initial fuel moisture code (fo) for rain (R) if R > 0.02 inches. 

RA = min(R,1.5) 

{

-56 - 55.6 In(RA + 0.04) if RA S 0.055 inches 

F = -1 - 18.2 In(RA - 0.04) if 0.055 < RA ~ 0.225 inches 

14 - 8.25 In(RA - 0.075) if 0.225 <RA 

fR = max(0,(F·fo/100) + 1 - 8.73 exp(-0.1117fo) 

if R ~ 0.02 inches, fR = fo. 

2. mR = 101 - fR 

3. En = (0.942Ho.679) + 11 exp[(H/10) - 10] 

4. Ew = (0.597Ho.768) + 14 exp[(H/8) - 12.5] 

5. m = Ew + (mR - Ew)/1.9953 if mR < En 

6. X = 0.424(1 - (HIl00)1.7) + 0.088 WO.

5(l - (H/100)8) 

7. m = En + (mR - En)/(lOX) if mR > En 

8. m = mR if mR = En 

{ 

mO ax( -16.,(T - 70)(0.63 - 0.0065fR) 9. 6. = 

if fo < 99% 

if fo ~ 99% 

10. f = max(0,min(99,101-m+ 6.)), fuel moisture = 101 - f. 

Variable 

fo 

T 

H 

W 

R 

fR 

En 

Ew 

mR 

m 

6. 

f 

Definition 

initial fine fuel moisture code 

temperature (OF) 

relative humidity (%) 

windspeed (between 1 and 14 mi/h at 20 feet or above) 

rain (inches) 

fo modified for rain 

equilibrium drying curve 

equilibrium wetting curve 

initial fuel moisture adjusted for rain (%) 

fine fuel moisture adjusted for humidity and wind 

adjustment for temperature (%) 

final FFMC 

Initial FFMC (fo) is first adjusted to a value (fR) based on the amount of rainfall (R) provided that R >0.02 inches. (Note: fo is a code-when subtracted from 

101, a fuel moisture percentage is obtained.) 

If the adjusted initial fuel moisture (mR) is above the drying curve (En)' m is 

computed by equation 7. If mR is below En' a wetting trend is in effect and m 

is computed from equation 5. If mR = En' moisture is initially at or near 

equilibrium. m is set to the initial value mR. Up to this point, temperature is 

ignored. . 

Finally, temperature is considered and the final FFMC (f) is computed from m 

by equations 9 and 10. f represents the new FFMC based on the initial value (fo)· 

46 
APPENDIX B: CANADIAN HOURLY FINE FUEL 

MOISTURE CODE 

Listed below are the equations and basic instructions for the dry weather 

routine to be used in the hourly computation of the FFMC from Van Wagner 

(1977). Weather values are in SI units except wind which is in kmlh. 

(1) mo = m calculated from Standard Daily FFMC 

(2a) Ed = 0.942Ho.679 + llexp[(H - 100)/10] 

+ 0.18(21.1 - T)(1 - exp(-0.115H)) 

(2b) Ew = 0.618Ho.753 + 10exp[(H - 100)/10] 

+ 0.18(21.1 - T)(1 - exp(-0.115H)) 

(3a) ka = 0.424 [1-(H/I00)1.7] + 0.0694Wo.5 [1 - (H/I00)8] 

(3b) kd = 0.0579 ka exp(0.0365T) 

(4a) kb = 0.424 [1-((100 - H)/I00)1.7] + 0.0694Wo.5 [1-((100 - H)/I00)8] 

(4b) kw = 0.0579 kb exp(0.0365T) 

(5a) m = Ed + (mo - Ed)exp( - 2.303 kd) 

(5b) m = Ew - (Ew - mo)exp(-2.303 kw) 

where 

mo = initial fine fuel moisture (%) 

m = final fuel moisture (%) 

Ed = EMC for drying (%) 

Ew = EMC for wetting (%) 

ka and kb = intermediate steps to kd and kw 

kd = log drying rate for hourly computation, log to base 10 

kw = log wetting rate for hourly computation, log to base 10 

H = relative humidity, % 

W = wind, kmlh (s 22.5) 

T = temperature, °C. 

The Standard Daily FFMC provides the first mo' Subsequently, the previous 

hour's m becomes mo' 

Compute Ed by (2a). 

If mo > Ed' compute kd by (3a) and (3b). 

Compute m by (5a). 

If mo < Ed' compute Ew by (2b). 

If mo < Ew' compute kw by (4a) and (4b). 

Compute m by (5b). 

If mo = Ed or Ew' m = mo' 

If Ed >mo >Ew' m = mo' 

Note that precipitation is not involved. 

47 
APPENDIX C: CORRECTION FOR INITIAL SHADE 

CONDITIONS IN FFMC 

The correction for solar heating must consider the possibility of solar heating 

on the fuels that were used in the initial development of the Canadian Fine 

Fuel Moisture Code. I t cannot be assumed that there was no solar heating even 

though the fuel moisture data were collected beneath a forest canopy and some 

of it possibly on cloudy days. In lieu of reconstruction of the initial conditions, 

that is, description of overs tory and cloud conditions at the time of data collection, the concept of a threshold value was examined to see if an effective shade 

condition could be found for adjusting the FFMC. 

In the daytime, above some level of shading, the correction of T, H, and W 

to fuel-level conditions should have little or no effect on the fuel moisture 

prediction. The following method was used to roughly estimate or bound such a 

threshold. The Alaska black spruce stick data (45 cases) were used with trial 

threshold values and our adapted model was allowed to completely shade the 

fuel for cases having shade above the threshold. Effectively, we used a combination of two models. By varying the threshold shade used to select the model, 

we could search for that model-combination (threshold) that reduced the error 

the most or was optimal in some other sense. As might be expected, the Alaska 

spruce stick data favored total use of the Canadian FFMC, whose average error 

was only -0.7%. Other, more open sites, however, favored our model. The 

shade percentage varied from 50 percent to 95 percent in the Alaska spruce 

stick data. For trial thresholds below 75 percent, the mean errors (-0.7% to 

-1.5%) for our new model were comparable to those at other sites. Not wishing 

to overpredict on the other sites, and not wanting to seriously underpredict for 

Alaska spruce sticks, we set the threshold at a tentative 70 percent. Subsequent validation showed that this allowed the adapted model to perform on all 

data sets without large mean errors. 

APPENDIX D: SUNRISE AND SUNSET 

DETERMINATION 

Referring to figure 3 and equation 4 in the main text, we can solve the equation for the hour-angle (h *) sine: 

(1) sinh* = (sinA - sin ¢ sin o)/(cos ¢ cos 0) 

where 

A = elevation angle of the sun (-90 0 ::; A ::; 90 0 ) 

¢ = latitude 

o = declination == 23.45 (sin(0.9863(284+ N))) (degrees) 

N = Julian date 

h* = hour angle from 6 a.m. 

We know that the earth's polar axis tilts twice annually to the extent that at 

the higher latitudes not all the sun-elevation angles (A) are possible. For 

instance, there may be perpetual day or perpetual night, and no such thing as 

sunrise (A = 0) or sunset (A = 0) for long periods. In such cases, equation (1) 

must not have a solution if it is to be a valid equation. This line of thought 

leads to the condition 

(2) -cos (0 + ¢) ::; sin A ::; cos (0 - ¢) 

on 0, ¢, and A in order for there to be an hour angle (time) for the elevation 

angle to equal a given A-value. 

48 
When condition (2) is satisfied with A = 0 the hour angles for sunrise and 

sunset are obtained from equation (1) with 

cos h* = "';1 - sin2h* at sunrise 

cos h* = - "';1 - sin2h* at sunset 

This will always be possible if I cf> I ~ 66.5°. If I cf> I ~ 66.5°, 10 I must be small 

enough. The time (LST) of the event, in either case, is 

t = (h*/I5) + 6 

if h* is in degrees. Knowing these times and the local standard time, it is easy 

to determine whether it is day or night and thus apply correct diurnal trends 

for fuel moisture calculations. 

When condition (2) is not satisfied with A = 0, we either have perpetual day 

or perpetual night, and all we need to know is cf> and 0 to determine which: 

Perpetual day will occur for 

(3) cf> > 66.5° during summer when cf> + 0 > 90° or 

(4) cf> < -66.5 ° during winter when cf> + 0 < -90°. 

Perpetual night occurs for 

(5) cf> > 66.5 ° during winter when cf> - 0 > 90 ° or 

(6) cf> < -66.5° during summer when cf> - 0 < -90°. 

This method applies only when condition (2) is violated. 

The equation (1) and the condition (2) assume flat terrain and do not account 

for orbital eccentricities or the "equation of time." A computer program 

(SUNELT) is available to implement the method described above. By entering 

the date and the latitude, the user will obtain the times of sunrise and sunset. 

This program can be obtained by sending a letter and clean tape to Glen Morris, 

Intermountain Fire Sciences Laboratory, P.O. Box 8069, Missoula, MT 59807. 

APPENDIX E: METHODS OF ESTIMATION FOR 

MISSING MODEL INPUTS 

In the initialization section and the diurnal section, it is sometimes necessary 

for the implementing software to supply missing data. This is done as a convenience to the user who may not always have all the inputs. This appendix 

explains how it is done. 

The model inputs are: 

1. mo = initial 1400-hour fuel moisture 

2. T l' T 2' ... , TN = 1400-hour temperatures for N days 

3. HI' H2, ••• , HN = 1400-hour humidities for N days 

4. WI' W2, ••• , WN = 1400-hour windspeeds for N days 

5. CI' C2, .•• , CN 

6. Ro 

7. [T] 

8. [H] 

9. [W] 

10. [C] 

= 1400-hour cloud cover for N days 

= initial rain amount 

= diurnal temperature data table 

= diurnal humidity data table 

= diurnal wind data table 

= diurnal cloud cover data table 

11. t p ' tr, ts = times of projection, sunrise, and sunset 

12. Site parameters and the date. 

49 
Internal Estimation 

of H2, H3, ••• , HN 

and Other 

Humidities 

Internal Estimation 

of T2, T3, ••• , TN- 1 

Internal Estimation 

of mo 

As implemented in the BEHAVE program, the model requires carefully 

observed values for the mandatory inputs. These are: 

1. TI, TN' HI 

2. [T], [W], [C] 

3. t p' t r , ts 

4. Site parameters and the date. 

The other values are sometimes "talked in" through the use of categorical 

descriptors or estimated internally by the model. The model is capable of 

estimating the following inputs internally 

1. mo 

2. T2, T3,···, TN- I 

3. H2, H3, ••• , HN-l' HN. 

Assuming that the air mass stays constant, we have a constant absolute 

humidity and therefore a constant dew point (T d) (Schroeder and Buck 1970). 

When the model detects that humidity input is missing, it invokes this assumption and computes 

Td = -398 - 7469/((ln Hi) - 7469/(Ti + 398)) of. 

Under our assumption we can replace TI with T2 in this equation, and solve for 

H2. The model does this with all the missing humidities (Hi): 

Hi = exp(7469(1I(Tj + 398)) - lI(Td + 398)). (E-1) 

As long as the air mass is constant and as long as the Ti value is kept current, 

the estimated humidity (Hi) should be valid. 

Equation (E-1) is explained in appendix F and a reference is given there. 

These temperatures, if input as -1°F, are taken to be missing and computed 

from T 1 and TN by linear interpolation. This procedure is most likely to work 

well when day-to-day, 1400-hour temperatures are following a steady trend and 

not subject to frontal passages (large variations). 

At the beginning of a period of days, whatever initial moisture the fuel may 

have had may be unknown. If the model is given a value of -1 for mo' it will 

take this as a signal to estimate mo using T l' HI' WI' CI' and Ro. Correcting T 1 

and HI to fuel level, the model iterates the Canadian Fine Fuel Moisture Code 

to equilibrium, to obtain the value of fuel moisture (mo) which would be at 

equilibrium with TI and HI at 1400. Now, mo is meant to represent 1400-hour 

fuel moisture on the day before day 1 of the period of interest. This procedure 

will be valid enough if 

(1) The air mass is constant in such a way that the 1400-hour temperature 

and humidity were constant, or 

(2) The estimation is made sufficiently far in advance of the projection day 

that errors made in the initial estimate of mo will have been corrected by subsequent estimates of m with better data (3 days should be adequate). 

50 
External Estimation 

of Missing Inputs 

The BEHAVE program queries the user for the inputs it needs and calls our 

fuel moisture model. As said before, some variables, if unknown, can be "talked 

in" using categorical descriptors. These are 

1. mo 

2. Cl' C2, ••• , CN and [C) 

-3. Ro' 

This procedure is likely to work all right for mo and Ro if the propagation 

period length (N) is long (3 or more days). The cloud cover estimates can be 

very critical near the end of the period when the canopy is sparse. BEHAVE 

has the ability to ask the user to select one of three categories for each of these 

inputs. 

Wind inputs are not, at this time, talked in, but supplied by the user. Under 

relatively shaded conditions, windspeed is not critical, and the user can supply 

a rough estimate-what he believes to be the average value. 

APPENDIX F: FORMULA USED FOR HUMIDITY AND 

DEW POINT CALCULATIONS 

The humidity fraction of air is closely approximated by 

H = e/es 

where 

e = vapor pressure 

es = vapor pressure at saturation. 

In order to relate humidity to dew point (T d) for a given temperature (T), the 

straightforward approach is to look up equations for e and es in terms of T and 

T d' But this leads to very cumbersome equations that cannot be easily solved 

for T d in terms of T and h. 

In Buck (1981), a very handy formula is given for 0 < T(OC) < 50. This is: 

lnH = {3-y (Td - T)/(Td + -y)/(T + -y) (F-1) 

For temperatures in of, this becomes 

In H = 7469(1/(T + 398)- lI(Td + 398)). 

Solving easily now for T d' 

Td = -398 - 7469/((ln H) - 7469/(T + 398)) of. 

51 
Measured Data 

-,:;.' 

APPENDIX G: SUMMARY OF VALIDATON DATA 

IDAHO FOREST LITTER (FRANDSEN DATA, 

---------_.-------.------.---------.---------.-.------------------ ROW DATE .. -----.------------.~ ... ,------_._! 

, MO , DAY! 

TIME , TEM- I HUMIDITY' 20-FOOT I PRECIP- , ! PERATURE' IWINDSPEEC' ITATION ! 

(HOURS" eDEG F" (PCNT) , (MPH' I (IN' , 

PERIOD I FUEL , LENGTH I MOISTURE' 

(DA'S' I (PC,." I 

,--.--~-------------- .. --.-----------.--------.-----.-----~-------.-.------.--.~.--.. ~-.-~, 1 8 13 1'+.5 6,.0 '+0.0 • 0.00 311 1".0 

2 a , 13.0 72.0 33.0 • 0.00 1. 12.0 

3 8 9 13.8 66.0 29.0 • 0.00 1. 1 ... 0 

4 8 13 13.3 51t.0 67.0 • O.QO 3. 15.0 

5 9 13 13.8 57.0 36.0 • 0.00 2. a ... o 

6 10 9 12.6 ..... 0 54.0 ! * 0.00 4. 19.0 

,.------_._-----------_._---------------_._.-------------.----.----~.-----~.----.--..... -., 

ARIZONA PINE NEEDLES (HARRINGTON CLOSED STANO DATA, 

--------.---.----------.----~--.---------~ .. ---------.-.-----.-.---.. --.-.-.---.---.. ~ .. -.. ROW DATE I TIME , TEM- I HUMIDITY' 20.FOOT I PRECIP- , PERIOD f FUEL , 

1---------, , PERATURE' IWINDSPEED, ITATION , LENGTH , MOISTUREI 

, MO I DAY! (HOURS' ! eOEGF'! (peNT) I (MPH' cIN' eOA'IS' , (PCNT' , 

!----------------------._.---_ .. _.-----.-.---.-.---._.-------------------·_---···-··_·_--·t 1 6 '7 1'+.5 65.0 ,+6.0 8.0 0.00 1. 10.8 

2 " 13 15.5 7'1.0 2,+.0 5.0 0.00 ... 5.' 

3 6 15 '''.0 78.0 26.0 5.0 0.00 1. 6.0 .. 6 17 15.0 65.0 29.0 '0.0 0.03 2. 6.! 

5 6 21 13.0 78.0 23.0 2.0 0.00 1. 5.7 

6 6 25 1!5.1t 79.0 19.0 5.0 0.00 2. •• 1 

7 6 28 13.0 82.0 2E,,0 5.0 0.00 1. 6.2 

e 7 4 1".0 71.0 31.0 10.0 0.03 3. 6." 

9 7 13 13.5 73.0 51.0 5.0 0.00 5. 7.3 

10 7 16 13.0 78.0 36.0 12.0 0.00 1. 5.0 

11 7 27 15.0 '79.0 "6.0 1.0 0.00 5. I.! 

12 8 3 14.0 7 ... 0 48.0 5.0 1'.00 ". 8.1 

13 8 6 15.5 72.0 '17.0 1.0 0.00 1. a.o 

14 8 20 13.0 65.0 50,0 5.0 0.00 1. 1.8 

,.-----------------------------_._-_.-.------._ .. -._.---.------.--.. --.---.-.-~ ..... --.... , 

ARIZONA PINE STICKS (HARRINGTON CLOSEO STAND DATA' 

.. ---------------.----------------.--.----._.-.. -._--.-------.-----~--.-.-.~-.-.-~ ..... -~. ROW ! OATE , TIME , TEM- I HUMIDITYI 20-FOOT , PRECIP- I PERIOD I FUEL , 

,---------1 , PERATUREI 'WJNCSPEED' ITATION , LENGTH I .. OISTUREI 

, no , DAYt (HOURS' I CO[G FI' (peNT' , (MPH' I UN) I tcAyst I (PtNT' , -------.--.-----------------~--------.------ .. ------.-.-.. --.-..... ----.-....•...•.•. ~.--, 1 6 13 15.5 7 ... 0 2".0 5.0 0.00 ... '.2 

2 6 21 13.0 '78.0 2!.0 2.0 0.00 1. ?o 

3 7 .. 1'+.0 71.0 31.0 10.0 0.03 3. 7.9 

4 7 27 15.0 '79.0 46.0 1.0 0.00 5. sa., 

5 8 3 1'+.0 7".0 "8.0 !S.O 0.00 ... •• 9 

6 8 (, 15.5 72.0 '+7.0 1.0 0.00 1. 9.1 

-----------.-._------.---------------.------.-----.-•• -----.--.-.--~----- •• -----~--.~ •• --! 

.NOTE -- THE IDAHO DATA HAS NO WINOSPEEO MEASUREMENTS. 10 MPH WAS 

USEO FOR THE CASES TABULATED HERE. 

52 

(eon.) 
Prediction IDAHO FOREST LITTER (FRANDSEN DATA) 

------.---------------------------.-------------.--.------._.--.---_.-.. -----.-----_._---- ROW SHADE , FUEL MOISTURE (peNT' ERROR 

!---------------------------------------!-----------------------------! ACTUAL' BEHAVE' FFMC FBO BEHAVE' FFMC FBO 

!----------------------------------------_ .. ---_.----- -------~-------------------.-------, 1 ~9.9 1~.0 8.3 8.6 9.0 -5.7 -5 ... -5.0 

2 31.6 12.0 6.9 10.6 9.0 -3.1 -1 ... ·3.0 

3 36.3 1~.0 10.5 10.3 9.0 -3.5 .. 3.7 -!S.O It 96.6 15.0 16.5 13.2 13.0 1.5 -1.8 -2.0 

S 38.6 2~.0 15.7 15.3 10.0 -8.3 -8.7 -1_.0 

6 76.5 19.0 20.3 11.9 11.0 t.!! -7.1 -0.0 

,-----------------------------------------------------··------·····--"··--······-········f 

ARIZONA PINE NEEOLES (HARRINGTON CLOSED STAND DATA, 

-.---------------------------------------------._--.--------.---------------_.------------ ROW S~AOE , FUEL MOISTURE (PCNT) ,ERROR , 

,---------------------------------------,-----------------------------, ACTUAL' BEHAVE! FFMC' FBO r BEHAVE! FFMC , FBO !---------_._----------------------------------_.-----------------------------------_._--! 1 100.0 10.8 13.1 13.1 10.0 2.3 2.3 -0.8 

l 100.0 5.6 8.2 8.2 6.0 2.6 2.6 0._ 

3 100.0 6.0 7.0 7.0 7.0 1.0 1.0 1.0 

4 100.0 6.3 7.9 7.9 8.0 1.6 1.6 1.7 

5 100.0 5.7 6.~ 6.4 6.0 0.7 0.7 0.3 

6 100.0 4.1 5.2 5.2 5.0 1.1 1.1 0.9 

7 100.0 6.2 6.0 6.0 7,0 -0.2 -0.2 0,8 

8 100.0 6.~ 10.1 10.1 &.0 3.7 3.7 1.6 

9 100.0 7.3 9.0 9.0 10.0 1.7 1.7 2.7 

10 100.0 5.0 7.5 7.5 8.0 2.5 2.5 3.0 

11 100.0 8.3 10.2 10.2 10.0 1.9 1.9 1.7 

12 100.0 8.3 11.0 11.0 11.0 2.7 2.7 2.7 

13 100.0 8.0 10.3 10~3 11.0 2.3 2.3 3.0 

1_ 100.0! 7.8 14.0 1~.0 11.0, 6.2 6.2 3.2 

,--------------------------------------------------.-------------------------------------, 

ARIZONA pINE STICKS (HARRINGTON CLOSED STAND DATA' 

ROW SHADE I FUEL MOISTURE (peNT) ,ERROR I 

,---------------------------------------,-----------------------------! ACTUAL! BEHAVE I FFMC I FBO I BEHAVE' FFMC , FBO , 

,------------------------------------------~-.----.-.- ----------------------·_-----------t 1 

2 

3 

~ 

5 

6 

100.0 

100.0 

100.0 

100.0 

100.0 

100.0 

6.2 

7.0 

7.9 

13.6 

9.9 

9.3 

8.2 

6.'+ 

10.~ 

10.1 

11.0 

11.3 

8.2 

6.'+ 

10.4 

10.1 

11.0 

11.3 

6.0 

6.0 

8.0 

10.0 

11.0 

11.0 

0.0 

-0.6 

2.5 

-3.5 

1.1 

2.0 

0.0 

-0.6 

2.5 

-3.5 

1.1 

2.0 

-2.2 

.1.0 

0.1 

-3.6 

1.1 

1.7 

!----------------------------------------------------------------------~-----------------! 

(con.) 

53 
APPENDIX G (Con.) 

Measured Data TEXAS GRASSES (CLARK DATA) 

-------------~---------------------------------.------ ---------.--------------------------- ROW , OATE I TIME TEM- , HUMIDITY! 20-FOOT ! PRECIP- I PERIOD ! FUEL , 

1---------1 I PERATURE! IWINDSPEED! IunON ! LENGTH , PlOISTURE! 

, , ,,0 ! DAY' (HOt/RS) I (QEG n I ( peNT) I (MPH' ! (IN) I (DAYS' I (peNT) t 

,------------------- ------------------------------~------------------.--.----------------! 

1 3 , 16 12.3 63.0 36.0 6.6 0.00 1. 15.1 

2 3 16 1'+.1 66.0 :51.0 12.0 0.00 1, 9.2 

3 3 If, 15.3 6,+.0 3,+.0 15.6 0.00 1. 12.5 

'+ 1+ t '+ 12.2 6,+.0 35.0 12.9 0.00 1. 5.5 

5 '+ '+ 1'+.6 70.0 22.0 21 ... 0.00 1. ".2 6 '+ '+ 15.2 70.0 21.0 21.5 0.00 1. '+.2 

7 '+ '+ 15.8 70.0 19.0 20.,+ 0.00 1. ".2 

6 2 10 14.0 53.0 1+1.0 11.8 0.00 I, 6.1 

9 2 10 1'+.4 63.0 32.0 11.8 0.00 1. 5.1 

10 2 10 15.3 62.0 33.0 10.2 0.00 1. 5.1 

11 2 10 15.8 62.0 35.0 16.8 0.00 1. 5.1 

12 '+ 2 12.0 68.0 25.0 31.4 0.00 1. 3.1 

13 '+ 15 12.5 85.0 16.0 11+.2 0.00 1. 3.2 

14 4 15 13.7 65.0 12.0 17.'+ 0.00 1. 3.2 

15 4 15 15.6 87.0 12,0 16.5 0.00 1. 3.2 

16 3 19 12.6 61.0 26.0 2.9 0.00 1. 12.8 

17 3 24 1'+.3 79.0 27.0 18.8 0.00 1. 21.5 

18 3 25 15.1 63.0 57.0 17.'+ 0.00 1. 13.5 

19 4 10 13.9 71.0 61.0 14.9 0.00 1. 20.1 

20 '+ 11 12.'+ 86.0 49.0 9.5 0.00 1.. 11.0 

21 3 13 13.2 69.0 31.0 11.4 0.00 1. 6.2 

22 3 13 14.3 61.0 34.0 12.2 0.00 1. 6.2 

23 3 13 16.0 11.0 33.n 17.9 0.00 1. 6.2 

24 3 19 12.6 75.0 21.0 14.8 0.00 1. 6.0 

25 3 19 13.0 79.0 20.0 15.8 0·00 1. 5.9 

26 3 27 12.3 ~9.0 81.0 9.9 0.00 1. 15.6 

27 3 12 12.0 85.0 18.0 23.8 0.00 1. 1.0 

28 :5 12 12.8 88.0 14,0 22.7 0.00 1. 1.0 

29 3 16 13.5 74.0 2'+.0 7.2 0.00 1. 4.0 

30 4 :5 12.1 65.0 25.0 10.2 0.00 1. 3.9 

31 4 3 12.3 69.0 25.0 10.9 0.00 1. 3.9 

t----------------------------------------------------- --~------- .. ----------------------.-, 

ARIZONA PINE NEEDLES (SACKETT OPEN STANO DATA) 

----------.---.-------.------.. ---.-_._--.---------.-----------.-------------------.------- ROW OATE I TIME , TE"'- 1 HUMIDITY, 20-FOOT , PRECIP- I PERIOD , FUEL I 

1---------1 ! PERATURE I IWINDSPEEO. ITATION , LENGTH , ~OISTURE' 

! MO , DAY! (HOURS) , (OEG n I (peNT) I (MPH) I (IN' I 'OAYS) I (PCNT, , 

,-----------------._--------------------_.------------------------------------------------, 1 5 26 14.4 74.0 21.0 3.0 0.00 1. '+.8 

2 6 1 14.0 72.0 22.0 12.0 0.00 1. 5.2 

3 6 6 11+.0 70.0 23.0 12.0 0.00 1. 4.6 

4 6 10 13.5 71.0 21+.0 3.0 0.00 1. 1.1 

5 6 13 14.8 69.0 16.0 10.0 0.00 1. 3.9 

6 6 15 14.3 74.0 11.0 7.0 0.00 1. 2.9 

7 6 17 1'+.5 79.0 16.0 12.0 0.00 1. 3.1+ 

8 6 22 13.8 16.0 18.0 !S.O 0.00 1. 3.1 

9 6 29 13.7 78.0 15.0 12.0 0.00 2. 2.7 

10 7 6 13.1 82.0 23.0 10.0 0.00 1. 2.6 

11 7 a 13.2 72.0 46.0 3.0 0.00 1. 9.9 

12 7 11 11+.0 61.0 22.0 :s.o 0.00 1. , .. 2 l' 1 B 14.1 "0.0 17.0 7.0 G.OO 1. 11.0 

14 1 20 13.0 70.0 38.0 5.0 0.00 '-. 6.5 

15 7 27 lij.O 7,..0 ,,0.0 11.0 0.00 1. 7.8 

16 7 29 13.5 17.0 :52.0 8.0 0.00 1. '+.7 

17 A 1 14.0 66.0 ft5.0 3.0 0.00 1. 9.0 

18 8 5 11+.0 82.0 :53.0 3.0 0.00 2. 4.5 

19 6 19 13.1 64.0 60.0 ~.o 0.0.0 1. 10.8 , ____________ - ____ - ____ -4 ___________________________ --------------------------------------t 

(con.) 

54 
Prediction TEXAS GRASSES CClARK DATA, 

-.----.---.-------.---.-----------_.-------.-.-----.------._.------------.---------------. ROW SHADE ! FUEL MOISTURE (peNT) ERROR 

,-----._--------------------------------,-------_._._-----------_._._-, ACTUAL I BEHAVE , FFMC I FBO BEHAVE I FFMC FBO 

1----------------------------------------------_·_---- -----~.---------------------------., 1 5".0 15.1 10.2 11.3 10.0 • ... 9 -3.8 ·S.l 

2 51.0 9.2 9.1 9.9 9.0 ·0.1 0.7 .0.2 

3 "2.0 12.5 9.9 10.7 6.0 -2.6 .t.8 -6.5 

'+ 15.0 5.5 5.7 10.9 7.0 0.2 5 ... 1.5 

5 5.0 ".2 ".7 7.7 5.0 0.5 !.5 0.8 

6 0.0 ".2 ... 5 7.5 5.0 0.3 3.3 0.8 

7 0.0 '+.2 ".6 7.0 ".0 0 ... 2.8 ·0.2 

8 0.0 6.1 8.2 13.1 7.0 2.1 7.0 0.9 

9 0.0 5.1 5.6 10.3 6.0 0.5 5.2 0.9 

10 0.0 5.1 6.3 10.6 6.0 1.2 5.S 0.9 

11 0.0 5.1 8.6 11.0 7.0 3.5 5.9 1.9 

12 37.0 3.1 7.6 8.5 6.0 ... 5 5 ... 2.9 

13 22.0 3.2 ... 2 ".9 3.0 1.0 1.7 ·0.2 

1'+ 13.0 3.2 3.6 ... 3 3.0 0." 1.t ·0.2 

15 0.0 3.2 3." ... 3 3.0 0.2 1.1 ·0.2 

16 9.0 12.8 3.9 9.1 6.0 -8.9 -3.7 ,·6.8 

17 22.0 21.5 5.6 7.2 5.0 ·15.9 -1 ... 3 -16.5 

18 0.0 13.5 9.2 15.6 9.0 • ... 3 2.1 .... 5 

19 87.0 20.1 13.3 13.3 12.0 -6.8 -6.8 ·a.l 

20 18.0 11.0 6.3 10.5 8.0 - ... 7 ·0.5 -3.0 

21 67.0 6.2 9.5 9.8 9.0 3.3 3.6 2.8 

22 "9.0 6.2 9.8 10.6 6.0 3.6 ..... .0.2 

23 11.0 6.2 1.5 8.1 7.0 1.3 2.5 0.8 

2 .. 26.0 6.0 ... 1 6.1 ... 0 -I.! 0.1 -2.0 

25 21.0 5.9 '+ ... 5.8 ... 0 ·1.5 -0.1 -1.9 

26 80.0 lS.6 2S.9 25.9 15.0 10.3 10.3 -0.6 

27 22.0 1.0 ".2 5.3 ".0 3.2 '+.3 3.0 

'-8 ".0 1.0 3.9 ... 5 3.0 2.9 3.5 2.0 

29 10.0 't.o 't.2 6.7 4.0 0.2 2.7 0.0 

30 20.0 3.9 4.3 8.6 6.0 0.4 ... 1 2.1 

31 29.0 3.9 4.9 8.'+ 6.0 1.0 ".5 2.1 

!-----------------------------------------------------------------------------------_.-.-! 

ARIZONA PINE NEEDLES (SACKETT OPEN STANO DATA) 

-------------------------._--------.-----------_.-._-----------------------------------.-. ROW SHADE FUEL MOISTURE (peNT) ERROR 

,---------------------------------------1-----------------------------, ACTUAL , BEHAVE , FFMC FBO BEHAVE I FFMC FaD 

.----.-----------.-------.---._-----------.-.-._-.. --------_ .. _--_ .... _---_._._._. __ ._.-, 1 90." ".8 6.1 6.1 6.0 1.! 1.3 1.2 

2 1 ... 0 5.2 ' .. 2 6.4 3.0 -1.0 1.2 .2.2 

3 33.1 4.6 ,+.5 7.9 3.0 -0.2 3.3 -1.6 

It 71.3 1.1 8.1 8.1 6.0 1.0 1.0 -1.1 

5 ... ct 3.9 3.6 6.2 3.0 ·0.3 2.3 -0.9 (, 14.0 2.9 2.7 ... e 2.0 -0.1 1.9 -0.9 

7 52.2 3.4 ... 3 '+.9 5.0 1.0 1.6 1.6 

a 61.8 3.1 3.8 4.2 5.0 0.7 1.0 1.9 

9 9.2 2.7 3.1 ... 2 2.0 0 ... 1.5 .0.1 

10 52.2 2.6 5.0 6.3 6.0 2.4 3.6 3." 

11 90.4 9.9 11.1 11.1 10.0 1.2 1.2 0.1 

12 "2.6 '+.2 ".4 6.1 3.0 0.3 2.0 -1.2 

13 "2.6 '+.0 ... 2 !S.1 2.0 0.2 1.2 -2.0 

14 66.5 6.5 1.0 1.6 8.0 0.5 1.1 1.5 

15 52.2 1.a 9.'+ 10.0 9.0 1.5 2.1 1.2 

16 ao., ".7 8.2 8.2 8.0 3.!5 5.5 3.5 

17 100.0 9.0 17.0 17.0 13.0 7.9 1.9 ".0 

18 ~7.9 ".5 5.9 10.2 6.0 1.3 5.6 1.5 

19 100.0 10.8 1&.2 1&.2 12.0 5." 5 ... 1.2 

!------------------------------------------------------------------------.... _._---------! 

(con.) 

55 
APPENDIX G (Con.) 

Measured Data ALASKA SPRUCE STICKS (NaRUM DATA) 

----------------------------------------------------------------------------------_._ ... -.-

ROW DATE TIME I TEM- , HUMIDITY' 20-FOOT , PRECIP- I PERIOD , FUEL I 

!---------, ! PERATUkE! !WINDSPEED! ITATION I L(NGTH t MOISTURE! 

, MO , DAYI (HOURS' I (OEG F)' (peNT) I ,PlPH) , (IN' , (DAYS' t (PCNT) , 

,. ______ -______________ -- ___________ --._---_____ .. __ --------------------------------------1 

1 6 20 13.5 60.0 49.0 0.0 0.00 1. 19.3 

2 7 23 11+.4 75.0 41.0 3.7 0.00 1. 9.1 

:3 6 2A 12.6 65.0 48.0 4.3 0.00 1. 13.3 

4 e 1 15.6 62.0 42.0 5.4 0.00 1. 9.2 

5 6 19 14.2 52.0 75.0 2.6 0.00 1. 13.6 

(, 8 1 13.9 64.0 39.0 2.7 0.00 1. 15." 

7 8 13 12.5 73.0 46.0 2.5 0.00 1. 11.9 

(, 7 24 14.2 82.0 37.0 6.8 0.00 1. 8.5 

9 e 3 12.7 67.0 31.0 5.0 0.00 1. 10.6 

10 e 13 15.0 77.0 42.0 5.3 0.00 1. t".4 

11 5 25 13.0 58.0 42.0 0.0 0.00 1. 11.1 

12 ~ 21 13.0 60.0 ..... 0 0.0 0.00 1. 21.5 

13 (, 16 14.1 S'+.O 45.0 0.0 0.00 1. 11.0 

14 7 2 13.8 £9.0 51.0 0.0 0.00 1. 10.7 

15 7 23 12.0 7£,.0 39.0 0.0 0.00 1. 25.0 

16 6 15 12.3 59.0 48.0 0.0 0.00 1. 11.3 

17 7 25 12.7 71.0 ,,3.0 0.0 0.00 1. 8.5 

lb 6 15 13.2 59.0 &+8.0 0.0 0.00 1. 18.1 

19 6 19 13.4 56.0 50.0 0.0 0.00 1. 16." 

20 (, 25 1'+.1 59.0 58.0 0.0 0.00 1. 16.6 

21 7 23 13.1; 76.0 32.0 0,0 0.00 1. 1~.6 

22- 7 22 l~.O e ... O :5!5.0 0.0 0.00 1. 19.1 

23 7 24 15.0 59.0 73.0 0.0 0.00 1. 7 ... 

24 7 30 ! 13.0 6e.o 43.0 0.0 0.00 1. 17.! 

1 ___________________________ • _______ - ____________ - __ --------------------------------------, 

Measured Data ALASKA HARDWOOD STICKS (NORUM OATA' 

------------------.---.---------------.------------.-------------------------.--_.-.. ------ ROW DATE TIME I TEM- , HUMIDITY I 20-FOOT I PAECIP- I PERIOD , FUEL I 1------_·_, ! PERATURE! IWINDSPEEof ITATION , LENGTH I PlOISTUAE, 

! MO ! OAY' (HOURS l , (OEG F)' (peNT) r (MPH' (IN) r (DAYS' , (PCNT' ! 

,----------------------------------------------------------------------_._._------_._-----, 1 6 20 12.e 56.0 5!5.0 0.0 0.00 1. 1'.5 

2 7 23 13.7 1 ... 0 40.0 2.2 0.00 1. 18.2 

3 7 25 12.1 73.0 36.0 1.6 0.00 1. 17." 

4 6 20 15.0 57.0 53.0 6.'+ 0.00 1. 15.1 

5 7 20 15.2 71.0 53.0 0.0 0.00 1. 1".1 

6 !5 30 13.8 55.0 49.0 0.0 0.00 1. 9.6 

7 6 1, 13.5 50.0 56.0 0.0 0.00 t. 10.1 

8 8 1 14.5 6e.O 3!5.0 0.0 0.00 1. 10.7 

9 e 13 12.1 73.0 46.0 0.0 0.00 1. 7.5 

10 5 29 12.3 68.0 39.0 0.0 0.00 1. 10.! 

11 6 19 15.8 61.0 45.0 0.0 0.00 1. 11.6 

12 7 24 12." 77.0 43.0 !.o 0.00 1. '.5 

13 8 3 13.3 6".0 48.0 3.3 0.00 1. 9.6 

14 8 13 15.1 78.0 43.0 5.! 0.00 1. 6.e 

15 6 8 14.7 6e.O 28.0 2.7 0.00 1. 22.2 

16 6 11 15.2 67.0 34.0 2.5 0.2~ 3. 11.9 

17 6 15 12.1 70.0 51.0 2.4 0.03 ... 15.1 

1ft 6 22 14.2 60.0 68.0 2.2 0.08 7. 12.7 

19 6 24 14.2 71.0 34.0 2.5 0.00 2. U.5 

20 7 28 14.3· , 68.0 51.0 1.3 0.00 1. 25.1 

21 8 8 12.1 68.0 51.0 0.5 0.00 5. 26.9 

22 6 11 14.2 66.0 33.0 0.6 0.17 3. 20.6 

23 6 20 14.3 67.0 48.0 1.8 0.10 5. 13.6 

24 6 2ft 15.0 73.0 36.0 1.1 0.05 4. 11.9 

25 5 31 12.8 62.0 69.0 2.3 0.00 2. 15 ... 

26 6 8 13.7 68.0 28.0 3.2 0.02 3. '.8 

27 6 15 13.2 73.0 1+0.0 1.4 0.00 2. 11.2 

28 6 20 13.2 64.0 52.0 0.3 0.02 5. 10.6 

29 6 24 13.3 70.0 34.0 1.e 0.00 2. 10.1 

30 7 .. 14.0 60.0 33.0 3.8 0.00 3. 18.2 

31 8 8 15.3 68.0 51.0 0.3 0.00 !5. 26.5 

32 6 3 14.0 48.0 51.0 4.1 0.00 1. 25.5 

33 6 5 12.6 60.0 40.0 1.2 0.02 2. 28.1 

34 6 11 12.5 68.0 33.0 3.6 0.09 , 3. 17.ft 

35 6 14 13.1 72.0 40.0 0.0 0.15 , 3. 15.1 

36 6 20 12.1 65.0 53.0 1.9 0.09 I 6. 11.9 

37 6 24 12.3 66.0 "1.0 0.8 0.0" , 2. 16.1 !-.-----------------------------------------_._---------------------------------------.... ! 

(con.) 

56 
Prediction ALASKA SPRUCE STICKS (NORUM DATA) 

----;~~------;~A~~-!-------F~E~-~~is;~RE-~PC~;;------------;---------ERROR---------------, 

,--.. --------------------_·-------------t.------------·_---_·_·-------1 , , , ACTUAL r BEHAVE I FFMC r FBO, BEHAVE I FFMC I FDO , 

,._--------------------------------------------*---.----_._--------------------._--_.-.. _, I 1 ! ~1.0 f 19.3 ! 1~.5 r 1~.5 , 10.0 r -~.e , -~.e , -9.3 , ,2 8~.0 I 9.1 10.0, 10.0 r 9.0 r 0.9, 0.9 r -0.1 

'3 97.0' 13.3 13.6 I 13.6 I 10.0, 0.3 I 0.3' -3.3 ,4 73.0 9.2 12.6, 12.6 10.0! 3.~' 3.~' ole 

,5 73.0 13.6 23.2 I 23.2 13.0, 9.6' 9.6 -0.6 

(, 52.0 15.4 11.8, 11.8 10.0, -3.6 I -3.6 -5.~ 

7 73.0 11.9 11.1 r 11.1 11.0, -0.8 r -o.e -0.9 

8 100.0 8.5 8.8, 8.8 8.0! D.! r 0.3 -0.5 

9 73.0 10.6 9.9 I 9.9 9.0 r -0.7 -0.7 -1.6 

10 73.0 14.4 10.0 t 10.0 10.0 I -~.~ -4.~ -~.4 

11 97.0 11.1 13.1! 13.1 ~.o, 2.0 2.0 -2.1 

12 73.0 21.5 13.3 I 13.3 9.0' -e.2 -8.2 -12.5 

13 73.0 11.0 14.3' 1~.3 10.0! 3.3 3.3 -1.0 

14 73.0 10.7 13.8, 13.8 10.0, 3.1 3.1 -0.7 

15 52.0 25.0 e.5 r 9.5 8.0 I -16.5 -15.5 -17.0 

16 73.0 11.3 1~.4' 14.4 10.0, 3.1 3.1 -1.3 

17 73.0 8.5 10.2! 10.2 9,0, 1.1 1,7 0.5 

18 73.0 18.1 1~.~' 14.4 10.0, -3.7 -3.7 -a.l - 19 97.0 16.4 15.2, 15.2 10.0, ·1.2 -1.2 -6.4 

20 73.0 16.6 16.1, 16.1 11.0 I 0.1 0.1-5.6 

21 43.0 15.6 7.8, e.2 8.0, -7.8 -7.4 -7.6 

22 52.0 19.8 8.4! 8.4 8.0, -11.4 -11.4 -11.8 

23 97.0 7.4 20.8, 20.8 12.0, 13.~ 13.~ 4.6 , 24 , 73.0 , 17.3 I 12.3 I 12.3 9.0, -4.9 .~., ·a.! 

,.------_ ..... _-----------------------... _--------.. -------_.---------.. --------........ -, 

Prediction ALASKA HARDWOOD STICKS (NORUM DATA) 

.. --------... -------------------._----------------._--------.--.--.---._------------------ ROW SHADE , FUEL MOISTURE (peNT) ERROR 

,.-_ .. "_ ..............••...•.••.•••••••. , .•........................... , 

ACTUAL' BEHAVE I FFMC r FBO BEHAVE' ~FMC FBO 

!--------------------_._------------------------------------------------------------_._._, 1 8e.8 19.5 16.5 16.5 11.0 -3.0 -3.0 -8.S 

2 80.0 18.2 9.9 9.9 9.0 ·-8.3 -8.3 .9.2 

3 eo.o 17.~ 9.2 9.2 a.o -8.3 -8.3 -9.~ 

~ 96.3 15.1 15.5 15.5 10,0 o.~ o.~ -5.1 

5 66.3 1~.1 12.5 12.5 10.0 -1.6 -1.6 -4.1 

6 ge.8 9.6 15.1 15.1 10.0 5.5 5.5 o.~ 

7 88.8 10.7 17.9 17.9 11.0 7.2 7.2 0.3 

8 80.0 10.7 10.7 10.7 10.0 0.0 0.0 -0,7 

9 88.8 7.5 11.0 11.0 11.0 3.5 3.5 3.5 

10 9s.8 10.3 11.5 11.5 9.0 1.3 1.3 -1.3 

11 ee.8 11.6 13.~ 13.4 10.0 1.8 1.8 -1.6 

12 e8.8 1.5 10.2 10.2 9.0 2.7 2.7 1.5 

13 a8.8 9.6 13.7 13.7 11.0 4.1 4.1 1.~ 

1~ 88.8 6.8 10.1 10.1 10.0 3.3 3.3 3.2 

15 99.3 22.2 18.5 18.5 8.0 -3.7 -3.7 -14.2 

16 91.5 17.9 13.6 13.6 8.0 -~.3 -~.3 -9.9 

17 89.3 15.1 11.1 11.1 10.0 -4.0 -4.0 -5.1 

18 91.5 12.7 13.7 13.7 12.0 1.0 1.0 -0.7 

19 88.0 11.5 10.1 10.1 8.0 -1.~ -1.4 -3.5 

20 93.3 25.1 21.8 27.8 10.0 2.6 2.6 -15.1 

21 95.8 26.9 15.2 15.2 11.0-11.6 -11.6 -15.9 

22 9_.3 20.6 15.6 15.6 8.0 -5.0 -5.0 -12.6 

23 93.9 13.6 9.8 9.8 10.0 -3.8 -~.8 -3.6 2~ '3.8 11.9 11.~ 11.4 e.O -0.5 -0.5 -3.' 

25 93.6 15.~ 20.~ 20.~ 12.0 5.0 5.0 -3.4 

26 93.5 9.8 9.8 9.8 e.o 0.1 0,1 -1.8 

27 86.9 11.2 10.1 10.1 9.0 -1.1 -1.1 ·-2.2 

28 e9.9 10.6 10.1 10.1 10.0 -0.6 .0.6 .0.6 2~ 88.0 10.1 10.7 10.7 S.O 0.6 0.6 -2.1 

30 89.& 18.2 13.8 13.8 8.0 -4.3 -~.! -10.2 

31 93.~ 26.5 14.7 14.7 11.0 -11.8 -11.8 -15.5 

32 9&.3 25.5 27~0 21.0 10.0 1.5 1.5 -15.5 

33 78.1 28.1 16.~ 16.4 9.0 -11.8 -11.8 -19.1 3~ 83.1 17.~ 13.7 13.7 8.0 -3.1 -3.7 -9.4 

35 16.1 15.1 1_.5 1_.5 9,0 -0.6 -0.6 -6.1 

36 75.8 11.9 11.0 11.0 10.0 -1.0 -1.0 -1.9 

37 72.0 16.1 12.3 12.3 9.0 -a.e -3.e -7.1 1---·-----------------------------._------------------------_--_. __ ._. __ .... ____ . ___ ... __ , 

(con.) 

57 
APPENDIX G (Con.) 

Measured Data ALASKA LEAF LITTER (NORUM DATA' 

------------------.--------------------------------------------._-----._-----.-----.---_.-. ROW DATE TIME , TEM- , HUMIDITY' 20-FOOT , PRECIP. , PERIOD , FUEL , ~---------! , PERATURE' !WtNDSPEED, ITATION ! LENGTH , MOISTURE! 

! MO I DAY' (HOURS) , (DEG F" (peNT' f (MPH) (IN' , (DAYS' ! (PCNT' ! !---------------------------------_.---------------------------------------------------_._! 1 6 20 12.8 56.0 55.0 0.0 0.00 1. 2".5 

2 7 23 13.7 71t.O "0.0 2.2 0.00 1. 12.7 

:3 7 25 12.1 73.0 36.0 1.6 0.00 1. IS.8 .. 6 20 15.0 57.0 53.0 6." 0.00 1. 17.6 

5 7 20 15.2 71.0 53.0 0.0 0.00 1. 10.7 

6 5 30 13.8 55.0 '+9.0 0.0 0.00 1. 16.6 

7 6 19 13.5 50.0 56.0 0.0 0.00 1. 15.2 

e e 1 lIt.S 68.0 35.0 0.0 0.00 1. 9.9 

I) 8 13 12.1 73.0 '+6.0 0.0 0.00 1. 9.3 

10 5 29 12.3 68.0 39.0 0.0 0.00 1. 12.7 

11 6 19 15.8 61.0 "S.O 0.0 0.00 1. 10.0 

12 7 24 12.'+ 77.0 '+3.0 3.0 0.00 1. 7.2 

13 e 3 13.3 6 ... 0 '+8.0 3.3 0.00 1. 10.6 

14 8 13 15.7 78.0 '+3.0 5.3 0.00 1. 8.6 

15 6 A 1".7 68.0 28.0 2.7 0.00 1. 1".9 

16 ,; 11 15.2 67.0 3'+.0 2.S 0.2'+ 3. 11.2 

17 6 ~5 12.1 70.0 51.0 2.'+ 0.03 ... 17.2 

18 6 22 1".2 60.0 68.0 2.2 0.05 7. 17.1 

19 6 2'+ 1'+.2 71.0 3'+.0 2.5 0.00 2. 12.9 

20 7 25 1'+.8 67.0 63.0 0.'+ 0.00 1. 23.3 

21 7 28 1'+.3 68.0 51.0 1.3 0.00 1. 28." 

22 8 18 1'+.0 S9.0 3 ... 0 0.0 0.00 1. 29.5 

23 6 3 12." '+9.0 '+3.0 0.8 0.00 1. 2".1 

24 6 11 1".2 66.0 33.0 0.6 0,00 1. 11.1 

2S 6 20 14.3 61.0 "8.0 1.8 0.10 5. 18.0 

26 6 24 15.0 73.0 36.0 1.1 0.05 ... 12.6 

27 7 .. 12." 60.0 40.0 5.0 0.00 3. 26.9 

28 7 28 15.0 68.0 55.0 0.0 0.00 1. 21.2 

29 5 31 12.8 62.0 69.0 2.3 0.00 2. 16.3 

30 6 8 13.7 68.0 28.0 3.2 0.02 3. 12.3 

31 6 15 13.2 73.0 ,,0.0 1.4 0.00 2. 13.6 

32 6 20 13.2 64.0 52.0 0.3 0.02 5. 13.6 

33 6 24 13.3 70.0 34.0 1.8 0.00 2. 11.2 

34 7 .. 1'+.0 60.0 33.0 3.8 0.00 3. 16.6 

35 e 8 lS.3 68.0 51.0 0.3 0.00 5. 20.5 

36 8 18 12.4 53.0 45.0 1.2 0.00 1. 26.9 

37 6 3 1".0 48.0 51.0 4.1 0.00 1. 17.9 

38 6 5 12.6 60.0 40.0 1.2 0.02 2. 13.4 

39 6 8 12.4 63.0 30.0 1.3 0.00 1. t2.' .. 0 6 11 12.5 68.0 33.0 3.6 0.09 3. 12.3 

41 6 14 13.1 72.0 "0.0 0.0 0.15 3. 10." 

42 6 20 12.1 65.0 S3.0 1.9 0.09 6. 12.1 .. ~ 6 2 .. 12.3 66.0 41.0 0.8 0.04 2. 12.1 

44 7 3 13.9 58.0 47.0 3.5 O.O! 2. 11.3 

45 7 25 13.3 68.0 57.0 2.5 O.OG 1. 21,1 

46 7 28 12.3 68.0 51.0 1.8 0.00 1. 19.5 

47 6 a 13.4 68.0 5'.0 1.0 0.00 S. 17.3 

!---------------------------------------------------------------------------------_.------, 

(con.) 

58 
Prediction ALASKA LEAF LITTER (NaRUM DATA) __________ . _________________________ - __________________________ .e_. ______ • ___ • _____ . ______ 

ROW SHADE I FUEL MOISTURE (PCNT) ERROR !---------------------------------------!----------------------_._.---, ACTUAL I BEHAVE I FFHC FBO BEHAVE , FFHC FBO !------------------------------------._-------------------------------_.-----------------, 1 88.8 2'+.5 16.5 16.5 11.0 -e.o -e.o -13.5 

2 eo.o 12.7 9.9 9.9 9.0 -2.8 -2.8 -3.7 

3 130.0 15.6 9.2 9.2 8.0 -6.6 -6.(, -7.8 

4 96.3 17.6 15.5 15.5 10.0 -2.1 .2.1 -7.6 

5 66.3 10.7 12.5 12.5 10.0 1.8 1.8 .0.7 

6 98.8 16.6 15.1 15.1 10.0 -1.4 -1.4 -6.6 

7 86.8 15.2 17.9 17.9 11.0 2.7 2.7 - ... 2 

8 80.0 9.9 10.7 10.7 10.0 o.e o.e 0.1 

9 813.e 9.3 11.0 11.0 11.0 1.7 1.7 1.7 

10 CJ6.8 12.7 11.5 11.5 9.0 -1.2 -1.2 -3.7 

11 6~.8 10.0 13." 13.4 10.0 3." ~ ... 0.0 

12 ee.s 7.2 10.2 10.2 9.0 3.0 3.0 1.8 

13 68.8 10.6 13.7 13.7 11.0 3.1 3.1 0.4 

14 se.s 8.6 10.1 10.1 10.0 1.5 1.5 1.4 

15 99.3 14.9 37.5 37.5 s.o 22.6 22.6 -6.9 

16 91.5 17.2 13.5 13.5 8.0 -3.7 -3.7 -9.2 

17 89.3 17.2 11.1 11.1 10.0 -6.1 -6.1 -7.2 

18 91.5 17.1 13.7 13.7 12.0 -:5.,+ -3.,+ -5.1 

19 88.0 12.9 10.1 10.7 8.(' -2.2 -2.2 -4.9 

20 93.3 23.3 ~7.2 37.2 11.0 13.9 13.9 -12.3 

21 93.3 28.4 '+5.0 4S.0 10.0 1~.~ 16.6 -18.4 

22 88.0 29.5 11.1 11.1 9.0 -18.3 -18.3 -20.5 

23 99.5 24.1 21.7 21.7 10.0 -3.0 -3.0 -n.7 

24 95.5 17.7 15.1 15.1 8.0 -2.1, -2.6 -(Je 7 

25 93.9 18.0 '.8 9.8 10.0 -8.2 -8.2 -8.0 

26 93.8 12.6 11.5 11.5 8.0 -1.1 -1.1 -4.6 

27 95.5 26.9 21.5 21.5 9.0 -5.4 -5.,+ -17.9 

28 99.5 21.2 '+3.'+ 43.4 11.0 22.2 22.2 -10.2 

29 93.6 16.3 20.1 20.1 12.0 3.9 3.9 -4.3 

30 93.5 12.3 10.1 10.1 8.0 -2.2 -2.2 -4.3 

31 86.9 13.6 11.3 11. ~ 9.0 -2.'f -2.'f -4.6 

32 89.9 13.6 10.1 10.1 10.0 -3.5 -3.5 -3.6 

33 a8.0 11.2 11.6 11.6 8.0 0.4 0.4 -3.2 

34 89.8 16.6 19.3 19.3 8.0 2.1 2.7 -8.6 

35 93.4 20.5 14.5 1'f.5 11.0 -6.0 -6.0 -9.5 

36 99.3 26.9 34.2 34.2 11.0 7.3 7.3 ·15.9 

37 96.3 11.9 20.1 20.1 10.0 2.2 2.2 -7.9 

38 7e.l 13.'f 14.7 1,+.7 9.0 1.3 1.3 -'+.4 

39 72.0 12.8 11.2 11.2 8.0 -1.7 -1.1 - ... 8 

40 83.1 12.3 13.1 13.1 8.0 o.e 0.8 -4.3 

41 76.1 10.4 14.4 1'+.1+ '.0 4.0 4.0 -1.4 

42 75.8 12.1 10.9 10.9 10.0 -1.1 -1.1 -2.1 

43 72.0 12.7 12.1 12.1 9.0 -0.6 -0.6 -3.1 

44 78.1 17.3 27.4 27.4 10.0 10.1 10.1 -7.3 

4S 84.3 21.3 15.9 15.9 11.0 -5.5 -5.5 -10.3 

'1-6 98.3 19.5 22.' 22.9 10.0 3.,+ 3.4 -'.5 

47 90.2 17.3 13.6 13.6 12.0 ';'3.7 -3.7 -5.3 

!---------------------------------_.-----------------------------------------------------! 

(con.) 

59 
APPENDIX G (Con.) 

Measured Data ARIZONA PINE NEEDLES (SACKETT DATA, CLOSURE=7~~' 

-.----.--------------------------------------------.------------------.. ------------------- ROW DATE TIME , TEM- I HUMIDITY I iO-FOOT I PRECIP- ! PERIOD , FUEL I 

!---------I , PERATURE I IWINDSPEEDI nATION ! LENGTH , MOISTURE! 

! MO , DAY! (HOURS)I (DEG Ftl (PCNT) ! (MPH' , (IN' (DAYS) ! 'PCNT) ! !-----------------------------------------------------------------------------------------! 

1 5 26 lQ.q 7~.0 21.0 3.0 0.00 1. 5." 

2 6 1 1'+.0 72.0 22.0 12.0 0.00 1. '+.4 

3 6 8 14.0 70.0 23.0 12.0 0.00 1. 3.7 

.. 6 10 13.~ 71.0 2'+.0 3.0 0.00 1. 9.2 

5 6 13 14.8 69.0 16.0 10.0 0.00 1. 3.8 

6 6 15 14.3 7Q.0 11.0 7.0 0.00 1. '+.2 

7 6 17 1Q.5 79.0 16.0 12.0 0.00 1. 3.1 

a 6 ! 22 13.8 76.0 lS.0 5.0 0.00 1. 3.8 

9 6 29 13.7 7e.O 15.0 12.0 0.00 2. 2.e 

10 7 6 13.1 82.0 23.0 10.0 0.00 1. 3.9 

11 1 8 13.2 72.0 46.0 3.0 0.00 1. 15.6 

12 7 11 1~.8 81.0 22.0 3.0 0.00 1. 6.1 

13 7 13 14.1 80.0 17.0 7.0 0.00 1. S .1 

14 7 20 13.0 70.0 38.0 5.0 0.00 2. '+.,+ 

15 7 27 14.0 7,+.0 ~O.O 11.0 0.00 1. 9.5 

11l. 7 29 13.5 77.0 32.0 8.0 0.00 1. 5.7 

17 8 1 14.0 66.0 65.0 3.0 0.00 1. 9.6 

18 e. 5 1'+.0 82.0 33.0 3.0 0.00 2. 6.5 

19 8 19 13.7 61+.0 60.0 3.0 0.00 1. 17.9 !-----------------------------------------------------------------------------------------! 

ARIZONA PINE NEEDLES (SACKETT DATA, CLOSURE=91f", 

ROw ! DATE , TIME , TEM- I HUMIDITY, 20-FOOT , PRECIP- I PERIOD I FUEL , 

!---------! , PERATURE I IWINDSPEEDI ITATION I LENGTH I MOISTUREI 

I ! MO 'DAY! (HOURS)' (DEG Fl! (PCNT) I (MPH) ! (IN) I 'DAYS' I (peNT)! 

1-----------------------------------------------------------------------------------------, 1 5 ! 26 I 1'+.'+ I 74.0 I 21.0 I 3.0 I 0.00 I 1. I 6.5! 

2 6 1 1'+.0 72.0 22.0 12.0 0.00 1. I 4.5 

3 6 e 1'+.0 70.0 23.0 12.0 0.00 1. I 4.3 

~ 6 10 13.5 71.0 24.0 3.0 0.00 1. I 10.6 

5 6 13 1~.8 69.0 16.0 10.0 0.00 1.! 5.0 

6 6 15 llf.3 1,+.0 11.0 7.0 0.00 1. I ~.8 

7 6 17 14.5 79.0 16.0 12.0 0.00 1. 4.~ 

6 6 22 13.8 76.0 18.0 5.0 0.00 1. 4.0 

9 6 29 13.7 78.0 15.0 12.0 0.00 2. 3.5 

10 7 6 13.1 82.0 23.0 10.0 0.00 1. 3.8 

11 7 8 13.2 72.0 ~6.0 3.0 0.00 1. 21f.S 

12 7 11 14.8 81.0 22.0 3.0 0.00 1. 6.2 

13 7 13 llf.l 80.0 17.0 7.0 0.00 1. 5.9 

14 7 20 13.0 70.0 38.0 5.0 0.00 2. 5.5 

15 7 21 14.0 11f.0 '+0.0 11.0 0.00 1. 10.3 

16 7 29 13.5 77.0 32.0 8.0 0.00 1. 7.'+ 

11 6 1 14.0 66.0 65.0 3.0 0.00 1. 13.3 

18 e 5 14.0 82.0 3~.0 3.0 0.00 2. 6.0 

19 8 19 13.7 6,+.0 60.0 3.0 0.00 1. 17.3 

!-----------------------------------------------------------------------------------------, 

(con.) 

. :,-.1:' 

60 
Prediction ARIZONA PINE NEEDL£S (SACKETT DATA. CLOSURE=7~.) 

-.-.--------------.--------------------------------.--------------.----.-----.--_.-------- ROw SHADE , FUEL fIIOISTURE (PCNT) ERROR , 

,---------------------------------------,-----------------------------, , ACTUAL I BEHAVE ! FFMC , FBO , BEHAVE , FF"C , FBO , !-------------------------------------------_._----_.------------------------------------, 1 97." 5 ... 6.1 6.1 6.0 0.7 0.7 0.6 

2 76.6 &t." 6.4 6.&t 6.0 1.9 1.9 1.6 

3 81.8 3.7 7.9 7.9 6.0 4.2 4.2 2.5 

" 92.2 9.2 e.l 8.1 6.0 -1.1 -1.1 .3.2 

5 7&t.O 3.8 6.2 6.2 6.0 2.'t 2." 2.2 

6 76.6 4.2 ,+.8 '+.8 5.0 0.6 0.6 0.8 

7 87.0 3.1 ,+.9 ... 9 5.0 1.8 1.8 1.9 

e 89.6 3.6 '+.5 't.5 5.0 0.7 0.1 1.2 

9 75.3 2.8 ,+.1 't.l 5.0 1.3 1.3 2.2 

10 87.0 3.9 6.3 6.~ 6.0 2.,+ 2.'+ 2.1 

11 97.4 15.6 11.1 11.1 10.0 -It.!5 -'t.5 .5.6 

12 a ... 't 6.1 6.1 6.1 6.0 0.0 0.0 ·0.1 

13 e".~ 5.1 5.1 5.1 5.0 0.0 0.0 -0.1 

1'+ 90.9 ..... 7.5 1.5 8.0 3.2 3.2 3.6 

15 87.0 9.5 12.2 12.2 9.0 2.7 2.7 -0.5 

16 94.8 5.7 8.2 8.2 8.0 2.5 2.5 2.3 

17 100.0 9.6 17.0 17.0 13.0 7.3 7.3 3.4 

18 83.1 6.5 10.7 10.7 9.0 't.2 4.2 2.5 

19 100.0 17.9 16.2 16.2 12.0 .1.7 -1.7 .S.9 

1------------------------------------------·---·----------------------.. -----------------, 

ARIZONA PINE NEEDLES (SACKETT DATAt CLOSURE=94", 

--------~.-------------------------------------------- ------------.----------------------- ROW SHADE I FUEL MOISTURE (PCNT, ERROR , !---------------------------------------!-----------------------------! ! , ACTUAL' BEHAVE 1 FFMC 1 FBO, BEHAVE I FFMC , FBO ! 

1----------------------------------------------------------------------------------------1 I 1 I 99.'" 6.5, 6.1, 6.1 I 6.0 -0..., -0... , -o.s I 2 94.6!'" 5 I 6. It, 6.4 I 6. a 1 • ., 1.9' 1.5, 

:3 95.8 f ".3' 7.9, 7.9 1 6.0 3.7 3.7 I 1.8, 

.. 98.2' 10.6, 8.1 I 8.1 I 6.0 -2.6 -2.6' -4.6 , 

5 94.0' 5.0, 6.2 I 6.2' 6.0 1.2 1.2' 1.0' 

6 94.6 3.8 f 4.8 4.8 I 5.0 1.0 1.0 I 1.2 

7 91.0 ..... 4.9 4.9 I 5.0 0.6 0.6 I 0.6 

e 97.6 ".0 4." 't." 5.0 0.4 o.'t, 1.0 

9 94.3 3.5 ... 3 4.3' 5.0 0.8 0.8' 1.5 

10 97.0 3.8 6.3 6.3! 6.0 2.5 2.5, 2.2 

11 99.4 24.5 11.1 11.1! 10.0 -13.4 -13.4, -14.5 

12 96.'+ 6.2 6.1 6.1' 6.0 -0.1 -0.1, .0.2 

13 96.4 5.9 5.1 5.1 1 5.0 -0.8 -0.8 I -0.9 

14 97.9 5.5 7.8 7.8 I a.o 2.3 2.3 I 2.5 

15 97.0 10.3 13.1 13.1 I 9.0 2.6 2.6 I -1.3 

16 98.8 7.4 8.2 8.2' 8.0 0.8 0.8 I 0.' 

17 100.0 13.3 17.0 17.0 I 13.0 3.7 3.7' -0.3 

18 96.1 6.0 11.1 11.1' 9.0 5.1 5.1' 3.0 

19 100.0 17.3 16.2 16.2' 12.0 -1.1 -1.1, -5.3 !------------_._------------------------_.--------------------------------------._-------! 

:.--. 

* u.s. GOVERNMENT PRINTING OFFICE: 1986-676-039/20037 

61 

Rothermel, Richard C.; Wilson, Ralph A.; Morris, Glen A.; Sackett, Stephen S. 

Modeling moisture content of fine dead wildland fuels: input to the BEHAVE 

fire prediction system. Research Paper INT-359. Ogden, UT: U.S. Department of 

Agriculture, Forest Service, Intermountain Research Station; 1986 61 p. 

Describes a model for predicting moisture content of fine fuels for use with 

the BEHAVE fire behavior and fuel modeling system. The model is intended to 

meet the need for more accurate predictions of fine fuel moisture, particularly 

in northern conifer stands and on days following rain. The model is based on 

the Canadian Fine Fuel Moisture Code (FFMC), modified to account for solar 

heating of fuels and to predict diurnal trends in fine fuel moisture. The model 

may be initiated without extensive data on prior weather. When compared to the 

FFMC and the fire behavior officers' procedures, the new model gave consistently better predictions over the complete range of fuel conditions. 

KEYWORDS: fuel moisture, fine fuels, model, fire behavior, diurnal, solar, shade 
INTERMOUNTAIN RESEARCH STATION 

The Intermountain Research Station provides scientific knowledge and technology to improve management, protection, and use 

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is designed to meet the needs of National Forest managers, 

Federal and State agencies, industry, academic institutions, public 

and private organizations, and individuals. Results of research are 

made available through publications, symposia, workshops, training 

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the lands in the Station area, about 231 million acres, are classified 

as forest or rangeland. They include grasslands, deserts, shrublands, alpine areas, and forests. They provide fiber for forest industries, minerals and fossil fuels for energy and industrial development, water for domestic and industrial consumption, forage for 

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