analysis of small-scale convective dynamics in a crown fire using

VOLUME 38 OCTOBER 1999J O U R N A L O F A P P L I E D M E T E O R O L O G Y

q 1999 American Meteorological Society 1401

Analysis of Small-Scale Convective Dynamics in a Crown Fire UsingInfrared Video Camera Imagery

TERRY L. CLARK, LARRY RADKE, JANICE COEN, AND DON MIDDLETON

National Center for Atmospheric Research, Boulder, Colorado

(Manuscript received 23 June 1998, in final form 10 December 1998)

ABSTRACT

A good physical understanding of the initiation, propagation, and spread of crown fires remains an elusivegoal for fire researchers. Although some data exist that describe the fire spread rate and some qualitative aspectsof wildfire behavior, none have revealed the very small timescales and spatial scales in the convective processesthat may play a key role in determining both the details and the rate of fire spread. Here such a dataset is derivedusing data from a prescribed burn during the International Crown Fire Modelling Experiment. A gradient-basedimage flow analysis scheme is presented and applied to a sequence of high-frequency (0.03 s), high-resolution(0.05–0.16 m) radiant temperature images obtained by an Inframetrics ThermaCAM instrument during an intensecrown fire to derive wind fields and sensible heat flux. It was found that the motions during the crown fire hadenergy-containing scales on the order of meters with timescales of fractions of a second. Estimates of maximumvertical heat fluxes ranged between 0.6 and 3 MW m22 over the 4.5-min burn, with early time periods showingsurprisingly large fluxes of 3 MW m22. Statistically determined velocity extremes, using five standard deviationsfrom the mean, suggest that updrafts between 10 and 30 m s21, downdrafts between 210 and 220 m s21, andhorizontal motions between 5 and 15 m s21 frequently occurred throughout the fire.

The image flow analyses indicated a number of physical mechanisms that contribute to the fire spread rate,such as the enhanced tilting of horizontal vortices leading to counterrotating convective towers with estimatedvertical vorticities of 4 to 10 s21 rotating such that air between the towers blew in the direction of fire spreadat canopy height and below. The IR imagery and flow analysis also repeatedly showed regions of thermalsaturation (infrared temperature . 7508C), rising through the convection. These regions represent turbulentbursts or hairpin vortices resulting again from vortex tilting but in the sense that the tilted vortices come togetherto form the hairpin shape. As the vortices rise and come closer together their combined motion results in thevortex tilting forward at a relatively sharp angle, giving a hairpin shape. The development of these hairpinvortices over a range of scales may represent an important mechanism through which convection contributes tothe fire spread.

A major problem with the IR data analysis is understanding fully what it is that the camera is sampling, inorder physically to interpret the data. The results indicate that because of the large amount of after-burningincandescent soot associated with the crown fire, the camera was viewing only a shallow depth into the flamefront, and variabilities in the distribution of hot soot particles provide the structures necessary to derive imageflow fields. The coherency of the derived horizontal velocities support this view because if the IR camera wereseeing deep into or through the flame front, then the effect of the ubiquitous vertical rotations almost certainlywould result in random and incoherent estimates for the horizontal flow fields. Animations of the analyzedimagery showed a remarkable level of consistency in both horizontal and vertical velocity flow structures fromframe to frame in support of this interpretation. The fact that the 2D image represents a distorted surface alsomust be taken into account when interpreting the data.

Suggestions for further field experimentation, software development, and testing are discussed in the conclu-sions. These suggestions may further understanding on this topic and increase the utility of this type of analysisto wildfire research.

1. Introduction

High-intensity crown fires account for a significantpercentage of the forest biomass burned throughout theworld. Crown fires are forest fires that consume the

Corresponding author address: Dr. Terry L. Clark, National Centerfor Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000.E-mail: [email protected]

canopies of trees and (particularly when accompaniedby other indicators of extreme fire behavior such aslofting of burning embers, intense burning, and rapidspread rates) can present a great hazard to firefighters.However, a good physical understanding of the initia-tion, propagation, and spread of crowning fires remainsan elusive goal for fire researchers. Fire managersthroughout the world continue to use empirically basedfire-spread models in their fire-behavior prediction sys-tems. Examples of such models are those derived from

1402 VOLUME 38J O U R N A L O F A P P L I E D M E T E O R O L O G Y

the work of McArthur in Australia (Nobel et al. 1980)and Rothermel (1972) in the United States. The essenceof these models is that local fire spread rate is prescribedas a function of wind speed, terrain slope, humidity, andfuel characteristics. No account is taken, except for tun-ing the coefficients, for direct interactions between thefire and the atmosphere. Intense crown fires are an areawhere strong and nonlinear fire–atmosphere interactionsoccur and, therefore, stress the credibility of the em-pirical fire-spread models (Alexander et al. 1998). Fur-ther, the resulting unexpectedly violent fire behavior isa serious threat to the lives of firefighters and to plansfor wildfire containment.

Recent increases in computer power make it possiblefor researchers to develop more physically based fire-spread models. Some notable attempts in this directionare the coupled fire–atmosphere simulations of Grishin(1992) and Clark et al. (1996a,b). Eventually this typeof fully interactive model should allow realistic predic-tions of fire spread by explicitly treating the dominantphysical processes. They also should allow researchersto understand better the range of fire–atmosphere in-teractions as well as the conditions under which theycan be expected to occur. Such models then can be usedto improve our understanding of fire behavior and tohelp to improve the operational fire-spread models usedfor actual fire spread and behavior predictions.

Fire spread involves the physics of convection, ra-diation, and mechanical advection effects such as thoseinvolved in rolling embers and spotting. The couplingof these processes combined with the physics and chem-istry of combustion compose the essence of a fully cou-pled fire model. Such models already exist for pool fires(Tieszen et al. 1996) that involve the rupture of liquid-hydrocarbon fuel tanks and subsequent ignition, wherethe combustion process is treated as diffusion limited.In forest or grass fires, the fuel is attached to the surfaceand is relatively porous, allowing air to blow throughand around the fuel. This difference is seemingly minorbut is important and can make forest and grass firesreaction-rate rather than diffusion limited, that is, lim-ited by the time it takes fuel to burn given an amplesupply of oxygen. As fire size increases, however, por-tions of the fire often are oxygen limited (Radke et al.1991).

Intense vortices of various strengths and sizes oftenare observed in fires. These vortices may be createddirectly by the fire dynamics at the fire front or mayinvolve interactions with atmospheric convection.Strong rotation was observed experimentally by Churchet al. (1980) and in model simulations (e.g., Heilman1992; Heilman and Fast 1992; Clark et al. 1996a,b).McRae and Flannigan (1990) describe fire vortices thatin one case were observed to rip out and loft standingtrees. One of us (Radke) observed a fire vortex risingmore than 3 km above ground level (AGL), with flamingmaterials that were visible at about 2 km. McGrattan etal. (1996) were successful in simulating a pool fire

where counterrotating vortices were observed in thestructure of the rising smoke. Banta et al. (1992) ob-served similar vortices in the Batersby and Left HandCanyon fires using a 10-mm lidar and a 3-mm radar;the scale of the observed vortices was on the order of100 m. On the other hand, fire vortices on the scale ofmeters continually occur at the fire front, are an essentialcomponent of the convection, and almost certainly playa fundamental role in the physics of fire spread. Thus,vortex tilting not only is suspected of being a hazard initself to nearby firefighters, who have described the for-mation of dangerous fire whirls and how they sometimestopple unpredictably to the ground, but is an importantfire spread mechanism through both local dynamics andthe ability to loft flaming objects into areas well re-moved from the former fire front.

One major difficulty in developing a realistic forestand grass fire model is field validation. Some data existthat describe rate of spread and some qualitative aspectsof fire behavior; however, no wildfire data presentlyexist to describe the very small timescale and spatialscale involved in the convective processes that help todetermine fire spread. This type of data is necessary forboth physical guidance and the eventual validation offully coupled fire–atmosphere biomass fire models.

The purpose of this paper is to attempt to derive sucha dataset, albeit with some limitations, using data fromthe International Crown Fire Modelling Experiment(ICFME) (Alexander et al. 1998). A gradient-based im-age flow analysis scheme is presented and applied to asequence of high-frequency, high-resolution radianttemperature images (3–5 mm) obtained by an Infra-metrics ThermaCAM instrument during an intensecrown fire to derive wind fields and sensible heat flux.The present IR data were obtained using pixel scalesthat at the distances of 239–82 m correspond to reso-lutions of 0.16–0.05 m, respectively, with a time res-olution of 0.03 s per frame. This temporal resolution ismuch finer than currently is attained using either scan-ning radar or lidar and is necessary to resolve the veryfine scales of motion that determine fire behavior. Thisdata and analysis technique was used here to examinethese very fine scales of motion to find energy-contain-ing scales on the order of meters, with timescales offractions of a second.

It is important to consider what the IR imagery rep-resents in order to interpret physically the thermal andderived-velocity fields. First, it is clear that the IR imagerepresents a sheet of data in the x–z plane with the ycoordinate (depth) varying considerably over the image.As a result, apparent motions in the image may containmotions into or out of the image whereas we estimateonly those that project onto the two-dimensional dis-torted sheet. For example, thermals that are estimatedto be rising rapidly also may tilt and propagate towardthe instrument as the air rises, that is, they may formturbulent bursts or hairpin vortices. The current datasetand analysis software are inadequate to allow quanti-

OCTOBER 1999 1403C L A R K E T A L .

tative estimation of these forward motions. Second, thedepth of the distorted sheet of data is important. If theIR camera temperature represents an average over a sig-nificant depth into the flame front, then the IR temper-atures and derived-velocity components are represen-tative for similar depths. Both the coherency of the hor-izontal motions and the large regions of relatively coolIR temperatures (,7508C) suggest that the high con-centrations of soot expected in a crown fire such as thishave limited the averaging depth to a shallow layer. Itis the variability in distributions of hot soot and theirmotion that allows estimation of the fire winds. Thereis no way of estimating the maximum IR temperaturesthat might have existed in the saturated (i.e., radianttemperatures above 7508C, the maximum that theThermaCAM was recording) regions but they certainlywere well above 7508C. Maximum temperatures ex-pected in such diffusion-type combustion are about12008C. Further experimentation that combines obser-vations of both the IR temperature and CH or C2 rad-icals, which occur only in the combustion zone, mayhelp to resolve these issues.

2. Background and motivation

a. Relationship between convection and radiation inwildfires

A central question in forestry is the relative roles ofradiative and convective heating in causing fire spread.Baines (1990) defined a dimensionless parameter P asthe ratio of radiative heating to convective cooling toassess whether radiation from the flame can cause firepropagation. Using idealized wind and flame structures,he argued that radiation from the flame cannot propagatethe fire and that convection dominates when P is lessthan 1 but that radiation from the flame probably canpropagate the fire when P is greater than 1, althoughthis condition was not precise because he had omittedfuel-bed radiation. His particular model predicted thatP would increase with increasing fire size, with con-vection dominating small laboratory fires (P , 1) andradiation dominating large fires (P . 1).

We question this type of analysis for a number ofreasons. First, our observations show that the radianttemperatures are similar in both grass and crowningforest fires, that is, they are mostly below about 7508Cwith intermittent regions of saturation above these tem-peratures. Thus, we have seen no indication that biggernatural biomass fires are significantly hotter. Second,and probably more important, one should expect astrong Reynolds number dependence associated with thecharacter of convection. The Reynolds number is de-fined as Re 5 Ul/n, where U is a characteristic velocity,l is a characteristic length scale, and n is the kinematicviscosity; small Re indicates laminar flow; if Re is large,the flow generally will be turbulent. Small fires, suchas laboratory fire tunnels, have small to moderate Re

whereas the much larger biomass fires have a muchlarger Re, which likely can become asymptotically largeand indicate fully developed turbulence. Whether thefire winds are laminar or turbulent, there is always astrong interdependence between convection and radia-tion because convection is the vehicle that controls theflame surfaces from which the fire radiates onto the dryfuel. In low-Re fires, one observes well-structured flow,whereas for large Re the local vorticity dynamics leadto the type of structures seen in highly turbulent flow.Instead of simply encountering hot air rising in well-organized thermals, one encounters vortex tilting thatleads to intense motions in almost every conceivabledirection at the fire front. Our current observations andprevious three-dimensional coupled fire modeling(Clark et al. 1996a,b) corroborate this point.

Since the manifestations of vorticity production andits resulting levels of turbulence scale with Re and ther-mal forcing, it is not clear at this time how one mightattempt to scale the relative importance of radiation ver-sus convection or whether this question is even wellposed. Thus, it is clear that a good understanding of firebehavior demands a clear picture of the nature of thethree-dimensional local fire wind, particularly at highRe when it is strongly turbulent. The relationship be-tween radiation and convection logically will follow.

b. Application of infrared cameras to fire research

Sequences of visual camera images often have beenused to calculate atmospheric motions in isolated smokeplumes (e.g., Templeman et al. 1990; Hidalgo 1993).With developments in IR technology, sequences of IRimages could be analyzed to discern plumes from theirenvironments more distinctly (Rickel et al. 1990), al-though the overwhelming amount of data provided byIR video cameras motivated users to limit their analysesto selected images every few minutes.

Infrared cameras have been used successfully to de-tect and map wildfires. Although human eyes are verysensitive receivers to radiation with wavelengths in thevisible range between 0.4 and 0.7 mm, we are effectivelyblind to thermal emissions in the 3–15-mm IR wave-lengths. Because these thermal emissions are propor-tional to the fourth power of the surface temperature,they are largely independent of solar illumination, andso IR cameras are effective both at night and during theday.

Increasingly sensitive image converters are beingmade available now and we can think of them as tele-vision cameras, sensitive in the IR. This synthetic visiongives a familiar view of surroundings but offers someuseful advantages to fire researchers. For example, veryhot objects such as smoldering coals do not stand outin our vision but appear very bright in the IR.

Furthermore, IR vision provides a large comparativeadvantage over normal vision when the field of interestis obscured by smoke and the electromagnetic radiation


FIG. 1. Outline of burn plots for ICFME in Jun–Jul 1997. Theforested areas are shaded. Areas between are the cleared fire breaks.The thin perimeter line marks the boundary of the experimental area,outside of which are trees and muskeg. The dates indicate when, ifat all, the plot was burned during the 1997 experiment. The crossesmark locations of IR cameras and the two lines extending from thecross nearest plot 6 represent NCAR’s IR camera’s FOV (see text forfurther details). North is toward the top of the page.

is being scattered and absorbed by interactions withsmoke aerosols. Smoke very effectively (on a mass ba-sis) obscures vision because of very efficient electro-magnetic interactions that result from the size of smokeparticles. Biomass fires produce smoke particles that aremostly in the 0.1–1.0-mm sizes (Radke et al. 1991) thatspan the wavelengths of normal vision (0.4–0.7 mm).Since attenuation peaks when the wavelengths and aero-sol particles are the same ‘‘size’’ (Ditchburn 1963), theability to observe through smoke is improved greatlyby increasing the wavelength of the viewing imager.Our 3–5-mm imager can observe the hot flaming firestructures clearly when they are shrouded so completelyby thick smoke that not a hint of flame can be discernedvisually.

3. Description of experiment and instrumentation

In this work, the high-frequency, high-resolution pas-sive measurements of infrared radiation in the 3–5-mmrange are analyzed to derive atmospheric wind velocitiesduring the crown fire that occurred during the burningof plot 6 in ICFME.

a. International Crown Fire Modelling Experiment

The ICFME took place between 19 June and 12 July1997, about 40 km northeast of Fort Providence in theNorthwest Territories (NWT) of Canada. This area con-tains boreal forest composed primarily of an overstoryof 12-m-tall 65-yr-old jack pine with a dense understoryof black spruce. Isolated rectangular forest plots of 150m per side were created and then instrumented for burnsin weather conditions that favor the development ofcrowning fires. Instrumentation included an array ofground temperature sensors, towers of radiometers, au-tomatic weather stations, and IR and visual cameras.Three plots were burned during the initial year of theexperiments; the burn of plot 6 on 9 July 1997 wasparticularly successful. Analyses of IR data taken forthis burn with an Inframetrics ThermaCAM SC1000will be presented.

Figure 1 shows a schematic of the prepared forestplots. The cleared perimeters were 50 m wide. Numbersthat identify the plots are shown along with the dateson which they were burned during the 1997 experiment.A cross in the clearing to the southeast of plot 6 marksthe position of the U.S. Forest Service (USFS) 50-fttower. The National Center for Atmospheric Research’s(NCAR) IR camera plus two USFS visual cameras werepositioned at the top of this tower. One visual camerawas a regular Super Video Home System/National Tele-vision System Committee (SVHS/NTSC) camcorder;images from this burn were part of a USFS video (NWTCrown Fire Experiment, July 1997). The second visualcamera was a USFS high-speed camera that took 15seconds of film at 250 frames per second. A secondcross approximately 150 m to the east of the southeast

corner of plot 6 marks the location of the CanadianForest Service’s (CFS) IR line scanner that also operatedduring this experiment. We have yet to analyze any oftheir data from this burn but we were able to view thedata and will comment on it later. Their view from theside proved particularly revealing in regard to certainaspects of the dynamics.

b. Meteorological conditions on 9 July 1997 and theplot-6 burn

The three experimental crown fires conducted atICFME in 1997 were, to our knowledge, the most wellmonitored of such experimental fires to date. Here, anal-yses of the burn of plot 6 are presented.

On 9 July 1997 the wind was between 16 and 17 kmh21 from the north to north-northeast during the burn.The temperature and relative humidity were 248C and45%, respectively. The estimated total fuel load was 4.3kg m22, while 1.9 kg m22 of this load was estimated tocontribute to the advancing flame front. The plot wasignited at the north face using a Terra Torch (a truck-mounted pressurized flame thrower) held by a joggeron the ground behind a vehicle holding the liquid na-palm. The ignition started at the northeast corner andproceeded to the northwest corner, taking approximately50 s. The fire crowned almost immediately and burnedthrough to the southern end in approximately 4.5 min,which converts to an average spread rate of about 0.6m s21. Photographs from an overhead helicopter showthat the fire took on a parabolic shape. The visual fireline width was estimated to be approximately 30 m dur-ing the burn (D. Latham 1998, personal communica-tion). Evidence suggests that the fire was still acceler-ating at the conclusion of the burn, indicating that the


FIG. 2. Calibration curve used to convert luminance measured bythe Inframetrics ThermaCAM SC1000 camera to infrared tempera-ture. Solid, dashed, and dotted lines represent factory calibration,quadratic fit, and linear fit, respectively.

maximum spread rate was considerably greater than the0.6 m s21.

The accelerating nature of the burn was evident inthe outline of spotting in the break to the east of plot6. Strong updrafts in the burning fuel result in countlessfire brands filling the atmosphere near the fire. The firebrands are lofted in all directions and ignite nearly allexposed roots in the cleared regions between the plotsthat are within the envelope of the fire-brand trajectories.When the plot-6 burn ended, a well-defined outline ofburning roots remained, extending from the northeastcorner of plot 6 and linearly expanding to the east ofplot 6 for the entire length of the burn. We estimate theangle at which the spotting expanded with distance wasapproximately 68. Our interpretation of the spotting en-velope’s linear increase with distance is that the con-vective motions in the fire were continually increasing,causing spotting to extend farther with time.

c. Inframetrics ThermaCAM

The Inframetrics ThermaCAM SC1000 (TCAM) is apalm-sized hand-held infrared focal plane array radi-ometer designed for scientific, research, and laboratorytemperature measurements. The sensing array is cooledto cryogenic temperatures with a miniature Stirling ther-modynamic cycle refrigerator, eliminating the need tocool with liquid nitrogen. Unlike scanning instruments,each element in a mosaic of 256 3 256 platinum silicidedetectors stares continuously, providing a high thermalsensitivity. The TCAM, weighing 3.7 lb (1.7 kg), pro-vides temperature measurement accuracy of better than628C at temperatures up to 20008C and can resolvetemperature differences of less than 0.18C. The tem-perature range is selected by choosing the temperatureat the bottom of the range; in this work, the range wasset to be 4008–7508C.

The camera has interchangeable lenses and filters,various remote control options, extensive postprocess-ing software, and battery operation. Each lens incor-porates a system of thermal sensors and lens identifi-cation magnets for automatic recognition and calibrationby the system. The use of an ambient temperature com-pensation program and LOWTRAN-7 atmospheric at-tenuation correction model built into the camera enablesaccurate, drift-free measurements. This system has ben-efits over other bulky infrared measuring devices, in thatit does not require a large external cooling device orcryogenic liquids and can be held and directed like avisual video camera.

The two lines drawn between the USFS tower andplot 6 in Fig. 1 represent the field of view (FOV) ofNCAR’s IR camera during the burning of plot 6. Theaverage distances to the southern and northern edges ofthe plot’s fuel were 63 and 239 m, respectively. Thecamera images were recorded continuously during theburn using a standard SVHS/NTSC video recorder at30 frames per second.

The analog information recorded on SVHS media wassampled into a motion-JPEG (Joint Photographic Ex-perts Group standard for video) digital format using aquality factor of 0.75, giving a separate disk file forevery frame. Motion-JPEG is a lossy (some amount ofunneeded data is lost during compression) intraframe(nontemporal) compression scheme that employs a dis-crete cosine transformation on 8 3 8 pixel regions. Atransfer from analog into an uncompressed digital for-mat would have been ideal but was not possible due tobandwidth limitations in the digitizing system. The mo-tion-JPEG data subsequently were converted into astream of 8100 uncompressed, byte-scaled grayscale im-ages covering the 4.5-min burn.

After image conversion using motion-JPEG, 432 3478 pixels of digital data per frame were retained. Forthe 178 3 168 Inframetrics lens, this resolution translatesto pixels that span approximately 0.165 m 3 0.122 mat the beginning of the burn (looking at the distantflames) to 0.044 m 3 0.036 m (looking at the nearestflame front).

The process of converting digital camera data to an-alog and then back to digital using motion-JPEG intro-duces appreciable noise into the data. Furthermore, tapequality degrades severely with copying, and a copy wasused to create the digital files. This noise is exacerbatedfurther because the 60-Hz rate of NTSC combines twoscans to form a single frame. Thus, each frame is com-posed of two interlacing frames, the first recorded usingonly odd-numbered lines and the second with even-numbered lines. As a result, some of the noise is sys-tematic.

Figure 2 shows the calibration curve used to convertluminance to IR temperature. The calibration curve is


weakly nonlinear and is approximated easily using apolynomial fit. The factory-supplied calibration isshown by the solid line. We use a quadratic fit that isshown by the dashed line, and the straight dotted linedemonstrates the degree of nonlinearity in the calibra-tion. Our quadratic approximation for the IR tempera-ture f is

f 5 400 1 1.728436g 2 0.00139562g2, (1)

where g is the resulting 1-byte digitized datum repre-senting the luminance. Values of g of 0 and 255 rep-resent luminance values of 1055 and 2636 lm, respec-tively. This conversion uses a calibrated emissivity. Ourcalibration assumed that the emitter is a blackbody,since the emitters in these cases are mainly glowingsoot particles, which have an emissivity close to 1.0.

The digitized data from the 4.5-min burn amount to2.5 Gbytes. This amount was too large to process atonce so the analysis was limited to 17 windows of dataequally spaced 0.25 min apart. Sixteen consecutiveframes of data were retained for each window exceptfor a later one in which 100 consecutive frames wereretained. Large segments of the 4.5 min were processedand rendered into video clips that are described at theend of section 5.

4. Description of image flow analysis

a. Image flow algorithm

We considered gradient-based methods of image pro-cessing to be the most applicable for extracting windestimates from the IR imagery. Horn and Schunck(1981) initially proposed using a single equation thatdescribes the conservation of irradiance. Their methodto formulate a unique solution was to cast the problemin a variational form by adding a smoothness constraint.This approach and subsequent developments for eval-uating image motion are reviewed by Schunck (1986).Schunck also describes alternate methods such as dif-ference picture, matching, and correlation. Tuttle andFoote (1990) use a correlation technique to deriveboundary layer winds from single Doppler radar data.Verri et al. (1990) present more general methods to es-timate two-dimensional motion in the image’s plane.This approach involves describing the motion as a com-bination of the five elementary motions from Helm-holtz’s theorem for deformable objects. These motionsare composed of two components of translation, a ro-tation, a uniform expansion, and two orthogonal com-ponents of shear. As an example, Bab-Hadiashar andSuter (1995) and Bab-Hadiashar et al. (1996) minimizea functional composed of four of the six elementarymotions, namely, the two components of translation,rotation, and pure expansion.

Their method was considered to be too advanced forour first attempt to derive fire winds from IR imagery.Instead, we chose to solve just the two components of

translation and used these results to assess whether toconsider more complete image flow analysis in the fu-ture. In the following equations the subscripts generallyindicate first- or second-order partial differentiationw.r.t. the subscript variable. The governing equation forimage flow is

df 5 f 1 uf 1 wf 5 0, (2)t x zdt

where f represents, in this case, the IR temperature TIR.The variables u and w are the horizontal (x direction)and vertical (z direction) components of the wind, re-spectively. Time is indicated by t. The basic assumptionis that f is approximately conserved over the short timerequired for analysis. Here, this would be 0.03–0.07 s.If it is assumed that u and w are locally translational,then one can take the gradient of (2) to form the matrixequation

f f u 2 fxx xz tx5 , (3)1 21 2 1 2f f w 2 fxz zz tz

which describes pure translation. The determinant detof (3) is

det 5 f xx f zz 2 .2f xz (4)

Providing there is sufficient curvature to the flow, thatis, |det| is relatively large, then well-conditioned solu-tions for u and w can be obtained. The possibility that(3) could be ill defined is termed the ‘‘aperture problem’’(e.g., Verri et al. 1990).

Solutions of (3) for the fire imagery result in a finemosaic formed by the contours of zero eigenvalues. Onecan obtain reasonable solutions for u and w in pixelslocated within most tiles of this mosaic that are wellremoved from any corner. Nagel (1983) gives a topo-logical description of the grayscale field, from visualimagery, discusses the so-called corner problem, andpresents solutions. Again, this approach is somethingthat we may want to consider in the future. Instead wechose to solve (3) using a variation of the robust sta-tistical and least mean squares approach used by Bab-Hadiashar and Suter (1995, 1997). This approach is ap-plied easily to our problem and is computationally ef-ficient.

The image flow method consists of two steps. First(3) is solved to identify outliers. Whenever solutions to(3) give wind speeds greater than, say, 40 m s21, thatparticular pixel is flagged as an outlier. Once outliersare identified, the solution of (3) is formulated in theleast squares approach using an affine model, that is,one in which transformations such as translation, rota-tion, or uniform stretching map into polynomial fits.Variables u and w are locally approximated as u, w,where

u 5 a0 1 a1x 1 a2z, (5)

and


w 5 b0 1 b1x 1 b2z. (6)

The functional L is formulated as2L 5 n [( u f 1 wf 1 f )O O i, j xx xz xt

i j

21 ( u f 1 wf 1 f ) ] (7)xz zz zt

and minimized to form the symmetric sixth-order matrixequation [using a 2d-order fit in (5) and (6) results in12th-order matrices]:

A C a g15 . (8)1 21 2 1 2C B b g2

Here ni,j is normally taken as unity except for outlierpoints where ni,j 5 0. The summation in (7) is usuallytaken over a 7 3 7 local patch of pixels.

Using the definitions2 2am 5 f 1 f , (9)xx xz

2 2bm 5 f 1 f , (10)zz xz

cm 5 f ( f 1 f ), (11)xz xx zz

g1 5 2 f f 2 f f , (12)xt xx zt xz

and

g2 5 2 f f 2 f f , (13)xt xz zt zz

we can write (where summations here and subsequentlyare over a local path of data and dot products are used)A as

am x · am z · amO O O

2A 5 x · am x · am xz · am (14) O O O

2z · am xz · am z · am O O Oand similarly for B and C by replacing am with bm andcm, respectively. Here aT 5 [a0, a1, a2] and bT 5 [b0,b1, b2], respectively, and the transposes of the right-hand side components of (8) are

Tg 5 g1, x · g1, z · g1 (15)O O O1 [ ]and

Tg 5 g2, x · g2, z · g2 . (16)O O O2 [ ]Here (8) reduces to the simplest equation set when

the first-order polynomial is reduced to zeroth order,that is, for a fixed u and w (a1 5 a2 5 b1 5 b2 5 0).In this case, the normal matrix equation is obtained:

am cm g1O O Ou

5 . (17) 1 2wcm bm g2 O O OOne might consider using (17) because it is far more

efficient than (8). As will be shown, (17) worked rea-sonably well in kinematic tests; however, this method did

not work well for the actual fire winds because of theextreme gradients and highly transient nature of the flow.

Whether (8) or (17) are used to estimate local winds,rejection criteria that will adequately identify unac-ceptable solution points are required. The method adopt-ed is to test the innermost matrix inverse(s). In solving(8), the inverse matrix is calculated as

21 21 21 21 21F A 2F A CB, (18)

21 21 21 21 211 22G B CA G B

where

F 5 I 2 A21CB21C (19)

and

G 5 I 2 B21CA21C. (20)

In this case, data are rejected if either21 2 2|F F 2 I| . r (21)O f

or21 2 2|G G 2 I| . r , (22)O g

where some finite value for variance and , say,2 2r rf g

ø0.1, is chosen. The purpose of (21) and (22) is au-tomatically to identify rejected points dominated by out-liers. In such cases, the determinants of A and B alreadywill have been given nonzero default values to avoiddivision by zero. The threshold velocity used in theinitial outlier identification can be reasonably large tooptimize the inclusion of most of the available data. Theequivalent criteria to (21) are used in the solution of(17). A final outlier calculation is performed in whichsolutions of u and w are rejected if either component islarger than, say, 40 m s21. No outliers were encounteredafter solving (8); however, outliers were found aftersolving (17) for the fire winds.

b. Numerical approximations and filters

Estimating velocities using gradient-based methodsrequires that spatial and temporal derivatives be eval-uated. Since gigabytes of data existed, computationallyefficient methods were sought. In addition, the data maycontain considerable noise.

To process the data, first a 1–2–1 temporal filter isapplied a selected number of times as

5 ( 1 1 )/4,t11 t t tf f 2 f ft t2Dt t t1Dt (23)

where t denotes an iteration index. The number of timelevels required to filter the data temporally is 3 1 2t ;that is, one application (t 5 1) requires five time levels.Successive passes through the 1–2–1 temporal filter,always using equally filtered data, were applied untiltwo or three time levels of data remained. These re-maining data were used to calculate the time derivativeand mid–time-level (t 1 Dt/2) fields. The first time


derivative f t is determined using either the centeredapproximation,

f (t 1 Dt) 2 f (t 2 Dt)f 5 , (24)t 2Dt

or the forward-in-time approximation,

f (t 1 Dt) 2 f (t)f 5 . (25)t Dt

In the case of (24), f (t) is used in the remainingcalculations of spatial derivatives whereas for (25) f isused, where f 5 [ f (t 1 Dt) 1 f (t)]/2. While (25) pro-vides better time resolution to the data it also tends toproduce somewhat noisier solutions than (24). We arestill assessing advantages of (24) over (25) for the IRfire data.

After the data have been filtered temporally and thefirst time derivative has been calculated, one is left withfields of f and f t at each pixel. The next step is toreduce spatial noise in these fields by applying a Gauss-ian filter. A symmetrical Gaussian of the form

2 2(x 1 z )G(x, z) 5 c* exp 2 (26)

2[ ]s

is convolved over the data. The leading coefficient in(26), c* [ø1/(2ps)], is calculated to ensure that thenumerically approximated weights add to unity. The val-ue of s was determined through tuning experiments.The typical value chosen gave a weighting ratio of 1.4between neighboring pixels on either the x or z axis.The area over which the Gaussian is convolved over thefields ranges from 5 3 5 to 9 3 9 pixels, that is, anarea of order 5–9. The number of points used (order ofarea) and the neighbor-weighting ratios are noted in theanalyzed figures.

The method adopted for estimating spatial derivativesis to use a local least squares polynomial fit. The variablef is defined as

f 5 c0 1 c1x 1 c2z 1 c3xz 1 c4x2 1 c5z2 (27)

and the functional L is formed as2L 5 ( f 2 f ) , (28)O O

which is minimized to derive the coefficients of (27)that are used to calculate the first- and second-orderspatial derivatives of f. Again, an area of 7 3 7 pixelswas used in the application of (28). This method ofestimating spatial derivatives employs some degree offiltering, which reduces the need for large areal coveragein the application of the Gaussian spatial filter.

c. Validation tests

Two error estimates were used to assess the accuracyof the wind calculations: a consistency test and a testusing tracer beads in a kinematic flow field. The con-sistency test employed the assumption that the IR field

moves with the flow, which is the basic assumption inthe image flow analysis. For the assumption to be valid,it should be necessary to be able simply to translate fat t 5 t 2 Dt to positions at t 5 t 1 Dt using theestimated wind components. The translated IR field thenshould be close to the observed IR field at t 5 t 1 Dt.The consistency error estimate for the winds ec is

t2Dt 2( f * 2 f ) dx dzEe 5 , (29)c

t1Dt t2Dt 2( f 2 f ) dx dzEwhere

f *(x, z) 5 f t1Dt(x0 1 2dt u, z0 1 2dt w), (30)

and x0 and z0 are the grid positions at t 5 t 2 Dt. Onlygrid points where data actually were processed wereconsidered in the application of (29) and (30). This ap-proach can bias the error estimate to small values whenthe number of points analyzed is small due to highthreshold standards, so the percentage of the area ana-lyzed also must be kept in mind. The choice of thedenominator in (29) was somewhat arbitrary, as wouldbe instead using the number of data points, but the goalwas to look for relative accuracy; if there are no gra-dients present, then (29) does not produce a false errorestimate that indicates high accuracy. This error estimatewas used extensively in tuning the spatial and temporalfilters.

Obtaining low values of ec is only a necessary con-dition for the algorithm to have acceptable accuracy.The velocity component normal to the gradient of fcontributes by far the most to the achievement of a lowerror using this test. For example, in ‘‘gradient motion,’’such as the flow that might be predicted using Horn andSchunck (1981), little consideration is given to cross-gradient flow. In visual imagery this lack is understand-able but in fluid dynamics one expects to find significantcross-gradient flow, particularly in regions of vorticityproduction. In such cases, gradient motion may givelow ec estimates even when the solution physically isunreasonable. Thus, this test can only be viewed as anecessary self-consistency condition.

The second test consisted of using an illustrative fieldof widely separated beads in kinematic flow fields. Thistest highlighted temporal aliasing effects as well as theperformance of the image flow algorithm for small fi-nite-sized structures in the flow. For a given temporalresolution, this type of test tends to overestimate dif-ficulties in analysis because of the poorly defined gra-dients as compared to realistic thermodynamic fields.

Figure 3 shows a composite of beads in four differentkinematic flow fields. The lower right and lower left arepure divergence and rotation, respectively, while theupper two flows are pure translation. The beads appearas local bright spots. Every third wind vector is plotted,showing the nature of the derived winds. In the case of


FIG. 3. Image flow for beads in prescribed kinematic flow fields.The flows are pure divergence, pure rotation, and two cases of puretranslation. Both the analytical (light arrows) and image flow (darkthick arrows) vectors are plotted. Every third vector is shown for thecase where the pixel motion was limited to one pixel per time frame.The derived vectors were averaged locally to give a single represen-tation per bead.

TABLE 1. Error statistics for widely spaced beads in a kinematicfield. Here Dr refers to maximum pixel motion per time step, Ng isthe order of the Gaussian filter, ec(T) is the variance error for thegrayscale intensity, and ec(q2) is the equivalent error for the squaredvelocity. All cases shown used the threshold velocity of 40 m s21.‘‘Avg’’ refers to whether a single estimate was derived through localaveraging.

Dr Ng ec(T) ec(q2) Avg

111111234

579579999

0.3060.1550.0890.1550.0990.0300.2070.5370.814

0.0870.0450.0270.1060.0750.0270.1060.2560.451

YesYesYesNoNoNoNoNoNo

Fig. 3 the estimated winds represent average values tak-en over the region of a bead, giving a single solutionper bead. Comparison with results based on no localaveraging showed that averaging tended to reduce ac-curacy slightly since the temporal resolution was rela-tively high; that is, the beads were allowed to move atmost 1 pixel per time frame. The effect of allowing thebeads to move a maximum of 4 pixels per time framealso was tested. In this case the wind vector solutionsfan out, reducing accuracy significantly. Table 1 showsboth the ec error estimates and the equivalent error forthe velocity for a range of cases. The table shows errorsranging from 0.030 and 0.027 to 0.81 and 0.45 for theirradiance variance and velocity variance errors, re-spectively. The averaging of the vectors decreases theaccuracy of the error variances to 0.089 and 0.027 forthe Dr 5 1 and Ng 5 9 case, as defined in Table 1.

The results shown in Fig. 3 used 9 3 9 points in theGaussian filter. Tests were also performed using 5 3 5(Ng 5 5) and 7 3 7 points. Here ec decreased signifi-cantly with increasing areal extent of the Gaussian filter.The errors at Ng 5 5 were 0.25 compared with 0.03 atNg 5 9. The velocity variance errors (which can becalculated for this case) decreased in concert with theirradiance errors, indicating that the increase in accuracywas not simply a false reflection of increases caused bysmoother fields.

5. Fire wind analyses

The small errors obtained in the validation tests usingbeads could be considered only a necessary conditionfor the acceptance of the image flow algorithm. How-ever, the fire wind estimates using (17) were unaccept-ably noisy, perhaps because of both the strong thermalgradients and the poor temporal resolution. The maxi-mum translation is as much as 10 pixels per time framein the IR imagery, which is well beyond any time res-olution that we were able to handle accurately using(17) for the field of beads. However, the systematicstructures in the IR fields offer an advantage comparedto the beads, for which smoothly varying gradients hadto be generated through filtering. Using (8) for the firewinds reduced the noise in the derived velocity V es-timates to an acceptable level, allowing physical inter-pretation of the results. Note that the derived velocitycomponents were highly consistent from frame to frameas seen in animations. (See the end of section 5 for adescription of Web access to our animations.)

The IR images represent thermal data at the front ofa fire line oriented at a mostly unknown and variableangle. The x direction is along this front and z is thevertical direction. Precise geometric positioning remainsa problem to be resolved. At the end of the burn, theorientation was well known and was basically the south-ern boundary of the plot; many of the data shown inthis paper are for this situation. In spite of the abovelimitations, the data irrefutably capture timescales andspace scales. The consistency of the derived fields fromframe to frame indicates that the spatial and temporalresolutions were adequate to observe the turbulent mo-tions. As discussed earlier, the derived structure of thehorizontal velocities indicates that the concentration ofglowing soot was adequate to limit the depth to a shal-low layer over which the IR camera took an averageover the foremost flame surface. This phenomenon helpsto explain the temperature range observed by the cam-era. Videos from the analyses show the frequent de-velopment of regions of saturation, suggesting forward


FIG. 4. Fire winds at t 5 4 min 27 s into the plot-6 burn. The first-order affine model for pure translation was solvedusing Eq. (8) and 7 3 7 pixels. The areal coverage of successful data analysis was 94.4% of the image. Three passeswith the 1–2–1 time filter and a Gaussian filter of order 9 were applied to the raw data. (right) The estimated sensibleheat flux Fs in MW m22. No postfiltering was performed for this presentation.

bursts of thermals that bring the hotter combustion gasesand flames into view.

a. Derived estimates of horizontal and verticalrotation

At t 5 4 min 27 s, the plot-6 burn was at its mostintense, with processable data filling almost the entireimage frame. We felt that this particular time was suf-

ficiently demanding to provide a good evaluation of theanalysis technique. Also, as mentioned earlier, the ge-ometry of the image is easy to interpret at this time.

Figure 4 uses a reduced region of the full IR imageand shows the estimated fire wind vectors overlying thebackground IR temperature field. The IR temperaturescover the full 4008–7508C temperature range of the cam-era setting. For about the first 2 m above the groundthe thermal field was saturated because the IR temper-


TABLE 2. The ec statistics from the fire wind analyses. Here ec and ec(cond) refer to average values without and with the condition thatDT , 28C was predicted. ‘‘Area’’ refers to percentage points of ec; percentage points in the conditional sample are listed separately. Here NZ refersto the number of pixels in the vertical; there were 432 pixels in the horizontal. Wind components are in m s21.

Levels Area NZ ec ec(cond)/% |u|max /|w|max t(s)

333333

91.593.094.294.196.095.5

80122142162246306

0.2810.5110.3640.4510.6810.732

0.0115/600.0335/600.0200/620.0241/500.0806/590.0544/46

19.919.715.223.915.921.9

24.627.819.639.117.122.3

550/30∗3050/304050/305050/306550/307050/30

33333

92.292.894.395.695.6

414416418420420

0.8820.9460.6530.9460.824

0.0599/410.1093/410.0531/570.1030/580.0928/57

30.739.022.717.315.6

29.138.222.121.125.0

8010/308020/308030/308050/308060/30

22222

91.392.894.294.895.0

414416418420420

1.3911.1911.9571.6692.055

0.1540/640.2660/760.2860/740.2689/730.3268/75

34.323.122.217.726.2

32.329.124.624.427.7

8010/308020/308030/308050/308060/30

*(518.3 s)

ature exceeded 7508C. These regions mostly are maskedin the figure because of the effects of the filtering pro-cess. However, small regions remain visible near x 52 m and z 5 7 m. The maximum wind speeds shownare only 22 m s21, which is well below the preoutlierand postoutlier threshold value of 40 m s21. The anal-yses shown in Fig. 4 used the three-time-level approx-imation to derive the winds; that is, (8) and (24) wereapplied. When the two-time-level approximation wasused by applying (25) instead of (24), a much noisierfield was obtained, with maximum speeds of 29 m s21.The basic structures of V were similar but had largeramplitudes. Using (25) also resulted in some windspeeds that exceeded the 40 m s21 threshold value. Evenso, their occurrence did not strongly affect the analyses.

Amplitudes of ec were much larger for the fire windsthan for the field of beads, as shown in Table 2. Thepoor time resolution of the data gave ec ø 1 overall.However, when the trajectories were categorized by ac-cepting points where DTIR was less than 28C, about halfthe data points had ec between 0.03 and 0.1. The effectof using (25) was to increase ec significantly to ap-proximately 2. The conditional values (DTIR , 2) in-creased to between 0.15 and 0.30. The difference inaccuracy resulting from using (24) versus (25) is mostlikely a result of data interlacing. In the future, we willattempt to correct for interlacing in our analysis. Forthis paper, only results using the three-time-level al-gorithm are shown.

Two rising towers of hot, rotating air are shown inFig. 4. Wind vectors near the top of the tower on theright point upward and to the right, whereas the vectorsnear the top of the left tower point upward and generallytoward the left. The systematic horizontal motion mustresult from rotation since the towers remain vertical withtime. The systematic horizontal motion also suggeststhat the camera was viewing a shallow layer of soot in

the forefront rather than seeing an average through alarge portion of the tower where horizontal motions ofopposite sign would occur. The apparent rotation is con-sistent with vorticity at the fire front undergoing en-hanced vortex tilting. In this particular case the vortexon the left would result from tilting of a vortex on theleft that was broken apart effectively by the enhancedbuoyant acceleration, allowing the lower portion of thetilted vortex to maintain its rotational integrity. Simi-larly, the vortex on the right may result from similarenhanced vortex tilting on the right. If one estimates theamplitude of the vertical vorticity as the radial velocitydivided by the radius of the rising tower, one obtains zø 64–10 s21, using radial velocities of 12–20 m s21

and tower radii of 2–3 m. These values are plausiblefor vertical vorticity and are approximately twice themagnitude reported in the simulations of Clark et al.(1996b). Events similar to this one occurred throughoutthe data analysis, pointing to the strong three-dimen-sional character of the fire winds.

Another aspect of the winds shown in Fig. 4 is thatvortex tilting occurred in such a way that the two con-vective towers rotated in a sense that should have causedwinds in the 6-m gap between towers to blow towardthe camera, which is the general direction of fire prop-agation. This particular type of vortex tilting could befundamental to the physics of fire propagation. How-ever, these forward-bursting and relatively cool windsshould not be confused with the hairpin vortices thatcan cause strong forward bursts of hot gases. Using theCFS IR line scanner, T. Blake (1997, personal com-munication) observed fingers of hot gases bursting for-ward near canopy height. These fingers probably areassociated with the rising and forward-bursting motion(turbulent burst) associated with vortex tilting that even-tually leads to the tilted vortex developing the hairpinshape. These shapes, we believe, are seen in our data


as the rising saturated regions that the CFS was able tocapture by viewing the fire from the side. The IR sat-uration prevents analysis of these regions. Clear evi-dence of these forward bursts also is seen in the USFSvisual video taken from the same tower position. Un-fortunately, smoke frequently obscures convective de-tails, allowing only intermittent cases of forward burst-ing hairpin vortices to be observed.

The panel on the right of Fig. 4 shows the estimatedsensible heat flux derived from the analyzed field of wand the perturbation TIR. The heat flux Fs was calcu-lated as

F 5 rc [w(T 2 T )], (31)s p IR IR

where T IR is the background IR temperature, r is density,and cp is specific heat capacity. The use of (31) assumesthat e1/4 ø 1, where e is the emissivity, allowing one toequate the air and IR temperatures. This assumption isa reasonable estimate for the intense crown fire but prob-ably less appropriate for ground or grass fires. In anycase, the approximations employed should result in anunderestimate of Fs. A vertical 1–2–1 filter was appliedto Fs to provide a smooth vertical profile. The verticalstructure of Fs shows a gradual increase with height toabout 12 m AGL, which is the approximate canopyheight. The linear increase of Fs with height is primarilya result of the vertical profile of available fuel. However,other aspects may contribute to this type of structure tosome degree.

The uniform region of hot gas near the surface didnot define TIR sufficiently enough to allow the imageflow analysis accurately to estimate w near the surface,thus preventing estimates of Fs in this region. This re-gion also was where TIR saturation most frequently oc-curred. The horizontal vortices near the surface at thefire front would rotate in the sense of rising motion overthe fire with downdrafts in front and behind resultingfrom the return flow. Such flow structures could con-tribute directly to fire spread by drying and heating oreven igniting by transport the fuel at the leading edgeof the fire. Whereas the vortex tilting mechanism isinherently three-dimensional, this latter one is not andcould be replicated in two-dimensional models such asthose of Heilman and Fast (1992) and Linn (1997).Since the fire is driven by the 17 km h21 mean flowwind, one might expect more compensating downdraftsto occur in front than behind. As shown in Fig. 5 bythe contours of |w| 5 2 m s21, there is an almost equaldistribution of downdraft and updraft air below z ø 8m, suggesting a strong influence due to saturation.

b. Wind component analysis

Figure 5 shows four closely spaced time levels of wcontoured over the background IR temperature field.These plots are spaced only 0.1 s apart and show therapidity with which significant changes occur in the fire.Figure 5a represents the same time as Fig. 4 but shows

the full width of the image. The structure and locationof the updrafts are consistent with the apparent risingmotion of the towers that one might visually estimate.However, the areal coverage of updrafts is somewhatfragmented. This fragmentation could be a result of ei-ther deficiencies in the image flow algorithm or couldbe caused by severe levels of turbulence. Regions ofnegative w are evident throughout, although those re-gions closest to the surface are affected strongly by theIR image saturation.

Figure 6 shows the same four times as Fig. 5 butdepicts u. The two rising towers on the left of the imageshow well-defined structures of u consistent with therotation described earlier. Both towers appear to risealmost vertically yet have well-defined regions where|u| ø 6 m s21. Note that both w and u shown in Figs.5 and 6 were postfiltered for presentation. In the coolerregion just above the fire (z . 15 m) a number of ver-tically elongated structures of alternating sign in u areseen. Again these structures appear to be associated withrotating convective updrafts. It is interesting that struc-tures of u are at least as well defined in the image anal-ysis as are structures in w. This finding most likely iscaused by the ubiquity of rotation in the fire combinedwith a shallow thermal sampling by the IR camera.

Figure 7 shows a sequence of TIR and wind vectorsin the image plane V for four times separated by 66 s.This figure shows a much longer period of the fire thanwas examined previously. The approaching fire can beseen by the lowering of both the top and bottom po-sitions of the images. The horizontal (vertical) pixelsizes decrease substantially between Figs. 7a and 7dfrom 0.15 (0.12) to 0.059 (0.049) m. Since the x axisis changing with time, in both Figs. 7c and 7d it isapproximate and is taken from Fig. 7d. The figure showsthat the regions of intense convective activity variedsubstantially with time. The amplitude of the updraftsappeared to be relatively uniform from one frame to thenext when viewed as animations. The animationsshowed strong levels of variability over fractions of asecond but structures were tracked easily from frame toframe. The flow is highly turbulent and, as such, eachpanel of Fig. 7 is only a snapshot of a quickly changingstructure. One really has to view animations to appre-ciate better the data and the quality of the derived windfields.

Animations of the data were developed using FOR-TRAN software; the figures in this paper were generatedusing IDL software. [An audio/video interleave (AVI)format animation could be viewed at the time of pub-lication at http://www.mmm.ucar.edu/science/fire/ir/ir1.html.] The animations of the plot-6 data show con-tours of the IR temperature overlaid with the derivedwind vectors. The contours make it easier to discern theregions of saturation that periodically develop and canbe followed easily as they propagate (probably forward)vertically out of the image domain. The Web page ref-erenced above contains a visual from the USFS video


FIG. 5. Time sequence of w overlying the IR temperature field for the full image. (a) The time shown is 267.167 s; times for (b)–(d) are0.1, 0.2, and 0.3 s later, respectively. Solid dark contours show w values of 2, 6, and 10 m s21. Solid white contours show w values of 22,26, and 210 m s21. Here w was postfiltered for presentation.


FIG. 6. Same as Fig. 5 but showing u. Solid dark contours show 2, 6, and 10 m s21; solid white 22, 26, and 210 m s21. Here u waspostfiltered for presentation.


FIG. 7. A sequence showing TIR and the derived wind vectors for four times spaced 66 s apart during the plot-6 burn.


FIG. 8. Time sequence of vertical profiles of Fs derived throughimage processing. Times are closely spaced from near the end of theplot-6 burn.

FIG. 9. Same as Fig. 8 but times are spaced equally throughout the4.5-min duration of the plot-6 burn.

camera located on the same tower as the IR camera. Itnicely captures a forward-bursting hairpin vortex.

6. Fire wind statistics

Images were analyzed at fixed intervals throughoutthe 4.5-min duration of the plot-6 burn to calculate basicfire statistics and to assess the integrity or persistenceof the analysis technique. Sixteen consecutive framesof TIR were retained every 16.667 s, allowing derivationof only eight consecutive image flow frames. At the lasttime level we retained 100 consecutive images, of whichFig. 4 was the first.

a. Sensible heat flux

Figure 8 shows eight vertical profiles of Fs derivedfrom the image analysis using (31). The profiles arespaced 0.2 s apart and are representative of all framesanalyzed near this time. A linear increase of Fs withheight to z ø 13–15 m persists throughout. Maximumvalues range between 1.0 and 1.2 MW m22 with meanscloser to 0.6. Here Fs ø 0.5 MW m22 physically isreasonable and could be obtained by burning, say, 2 kgm22 or fine fuel (i.e., dead fuel less than 0.64 cm indiameter) in approximately 70 s.

Figure 9 shows a sequence of 16 profiles of Fs derivedthroughout the 4.5-min duration of the burn. The con-tinual decrease in height of the flux profiles with timeresults from the reduced FOV as the fire approaches thecamera, and the abrupt end at the top of the profilesrepresents the end of the image data. Only when the firebreaks through the trees bordering the southern clearing(the last frame) can we see the full vertical extent ofthe heat flux from just above the ground to the con-vection above canopy height. The amplitude of Fs showsa general trend of decreasing substantially with time.This trend is particularly true for early profiles whereFs has amplitudes exceeding 3 MW m22. Miscalcula-tions of Dz for these early times would have to be in

error by a factor of almost 3 to account for this trend.Since the amplitude of w from image analysis scalesproportionally to Dz/Dt (for a fixed Dx/Dz ratio), anoverestimation of Dz overestimates w and therefore Fs.This type of error seems unlikely and would appearconsistently throughout other statistics such as all com-ponents of the velocity extremes shown in Fig. 10. Thelarge early maxima in Fs, on the other hand, could bea direct result of the time it takes convection to adjustto the presence of the fire, that is, temporary heat build-up just above the canopy, or to contributions from thenapalm. Clark et al. (1996a,b) showed in their time his-tory of buoyancy and velocity extremes that it tookabout 1–2 min for the local convection to adjust to thelocal thermal forcing before a more efficient convectionof heat away from the fire could organize. Further as-sessment of this issue will have to wait for evaluationthrough modeling studies.

b. Wind extremes

Figures 10a and 10b show time histories of u and wextremes throughout the plot-6 burn. Here V was cal-culated at eight consecutive times spaced 0.033 s apartat intervals of 16.67 s from t 5 16.67 s to t 5 285.00s, giving only 128 samples in time. To assess the sta-tistical nature of the data, extremes were plotted usingevaluations of means and standard deviations. With


FIG. 10. Time series of derived wind component extremes. (a) The thin lines show umax/umin and the thick lines show û1& 1 and5su1

û2& 2 5 , where ^ & indicates a mean quantity and the 6 subscripts refer to positive or negative velocity components; (b) similar to (a)su2

but for wmax/wmin and ^w1& 1 5 and ^w2& 2 5 ; (c) time history of the number of standard deviations by which the u velocity extremas sw w1 2

deviate from their means—thick is for negative and thin for positive u; (d) similar to (c) but for w. Each of the 15 data points shown wasderived by postaveraging the estimates of the point extremes and standard deviations over the eight available consecutive frames.

Gaussian- or normally distributed data, extremes wouldoccur at approximately five standard deviations (s) fromthe mean. Large deviations of extremes beyond their5-s estimates could suggest that either the data are non-Gaussian or that the extremes might be influenced byartifacts of the image flow algorithm. The heavy linesin Figs. 10a and 10b show the statistical estimates of uand w extremes, plotted as umax/min 5 û6& 6 5s6, where^ & indicates the mean. Updrafts were categorized sep-arately from downdrafts; the 6 subscript means thatonly positive or negative field values were analyzed.There is a well-defined trend in the 5-s statistical es-timates of maximum w. It decreases from almost 30 ms21 at about 0.5 min to below 10 m s21 at 3.5 min. Thistrend corresponds to the same variation we saw in theestimates of Fs. The comparison for negative w is quitedifferent, where the point values maintain about 220m s21 throughout and the 5-s estimate shows an almostconstant 25 m s21. There is also a trend toward de-creasing amplitudes with time for u but it is quite minor

in comparison with that seen for positive w. If the pointestimates of the extremes (thin lines) result mainly fromartifacts such as thresholding in the image processing,then one might expect a reasonably erratic or large sep-aration between them and their 5-s estimates.

Figures 10c and 10d show the time history of thenumber of standard deviations by which the velocityextremes deviate from their means. The figures showthat wmax is initially near 6 standard deviations and sys-tematically increases to 13 standard deviations from itsmean. On the other hand, wmin is consistently about 20standard deviations from its mean for the entire burn.The statistics for u show that both positive and negativevalue extremes range between 10 and 15 standard de-viations from their means. These results suggest that thederived velocity extremes most likely are resulting fromartifacts of the analysis scheme, or the distribution isnon-Gaussian. The values of wmax for the first 2–3 minof the burn may represent an exception. The problems,if such is the explanation, appear to be most severe for


FIG. 11. Same as Fig. 10 but for the kinetic energy statistics. Eachof the 15 data points shown was derived by postaveraging the esti-mates of kemax, ^ke&, and ske over the eight available consecutiveframes.

downdrafts. Considering these results, we feel that theu and w extreme estimates derived using statistical mo-ments and, say, 5-s deviations, are probably more mean-ingful than are point estimates.

In further developments of the image flow algorithmthis type of statistical comparison of u and w extremeestimates will be evaluated to see if the point and sta-tistical moment estimates can be made to compare morefavorably. A convergence of the point and, say, 5- to7-s estimates, along with improved ec errors, wouldgreatly increase confidence in the details of the imageflow analysis.

c. Kinetic energy

Figure 11 shows a time history of kinetic energy sta-tistics, including the point maximum, statistical momentestimate of the maximum assuming a 5-s deviation, andthe spatial average. Each of the 15 points on the plot iscomposed of averages over the eight consecutive framesanalyzed for each window of data. Each point representsan average over 0.267 s. These results basically wereinsensitive to this local averaging in time. There is anoscillation with a period of approximately 2 min that isapparent in all representations of kinetic energy in thefigure. We see two maxima at t 5 0.75 and 2.75 minand two minima at t 5 1.75 and 3.75 min, suggestingthat the fire intensity may be increasing and decayingover this period. There is surprisingly little detectable

variation, other than this oscillation, in a mean trendwith time. The plot shows averages per unit area ob-served and, as such, is probably the best that can bedone to evaluate mean overall characteristics of the firefrom the small sampling area. This is another charac-teristic that one might attempt to assess through mod-eling.

7. Conclusions

A gradient-based image flow analysis scheme wasapplied to the IR temperature observations of a pre-scribed crown fire in the Northwest Territories to derivefire winds and sensible heat flux. The results show thatthe technique is capable of deriving motions on a rangeof the small spatial and temporal scales associated withcrown fire convection. We believe these scales of motionplay an essential role in determining spread rates andsome other aspects of fire behavior.

It is well known that strong rotation is present in fires.This fact was certainly true here where rotation wasvisually evident throughout the fire at the time of theburn. The derived motions show that vortex tilting oc-curs through a major portion of the observations andplays an integral role in the convective portion of firebehavior and heat transport. Vertical vorticity, or rota-tion about the vertical axis, was identified by the pres-ence of strong horizontal motion in vertically rising tow-ers. Rough estimates of vertical vorticity of between 4and 10 s21 were made using the amplitudes of the hor-izontal velocities and tower diameters. These vorticeswere embedded in updrafts of between 20 and 30 ms21. In one example, the sense of the rotation was con-sistent with the tilting of horizontal vortices producedby the fire’s horizontal thermal gradients.

The analyses pointed to a number of physical mech-anisms that play active roles in determining the rate offire spread. The image flow analysis was able to identifythe tilting of vortices, leading to counterrotating con-vective towers. The sense of rotation in one exampleanalyzed was shown to be in the sense that air betweenthe towers would blow in the direction of fire spread atcanopy height and below. Probably the most importantvortex tilting evident in the data was that leading towhat we believe are forward-bursting hairpin vortices.However, these vortices were unfortunately the leastable to be analyzed using image flow techniques becausethe forward motion led to saturation of the IR image,that is, TIR greater than 7508C. The frequent occurrenceof the rising and presumably forward-bursting regionsof saturation were evident in the animation (see end ofsection 5 for details). Supporting evidence was dis-cussed in the text. There was also some evidence thatreturn flow downdrafts at the leading edge of the fireexist in the data. However, these regions usually weresaturated. Further experiments using IR imagery shouldattempt to observe a broader range of IR temperatureto capture both the cooler convection and the high-tem-


perature regions in the forward-bursting vortices and inthe near-surface fire.

Profiles of sensible heat flux were calculated by as-suming that air temperature could be approximated us-ing the IR temperatures. Maximum values of Fs rangedbetween approximately 0.7 and 3 MW m22 over theduration of the burn with the early time periods showingsurprisingly large estimates of almost 3 MW m22. Nearthe end of the burn, when the full vertical structure ofthe fire was visible to the IR camera, the profiles linearlyincreased to a magnitude compatible with fuel loads ofabout 2 kg m22 and fine fuel burnout times of 70 s.

Time histories of velocity extremes were comparedwith estimates by using statistical moments. With theexception of updrafts, the extremes were shown to de-part significantly from estimates based on five standarddeviations from their spatial mean. The departures forthe downdrafts, in particular, and the u extremes werebeyond what one might expect even for non-Gaussiandistributed data. For example, the downdraft extremeswere approximately 20 standard deviations from theirmean and the u extremes were between 10 and 15 stan-dard deviations away. This analysis suggests that thepoint estimates of the extremes in the motion field stillare being influenced by artifacts of the image-processingscheme. The statistically determined extremes, usingfive standard deviations from the mean, are more likelyto be representative at this time. They suggest that up-drafts of between 10 and 30 m s21, downdrafts of be-tween 210 and 220 m s21, and horizontal motions ofbetween 5 and 15 m s21 frequently occurred throughoutthe fire.

Time histories of the mean and extreme values ofarea-weighted kinetic energy showed a strong oscilla-tion in its strength. The data suggested there was a pe-riod of about 2 min. Unfortunately, since the entire da-taset is only 4.5 min long, this is too short for a reliableestimate. Larger crown fires of this intensity are notlikely to be prescribed, but again, this type of dynamicscould be evaluated further through modeling studiesand, perhaps, in airborne remote sensing observationsof wildfires.

In addition to statistics of the derived fire winds, twoother measures were used to evaluate the accuracy ofthe image flow algorithm. Calculations from an ideal-ized field of widely spaced beads in kinematic flowfields were used, where it was shown that image flowgave accurate results for good time resolution, that is,when the beads did not move more than 1 or 2 pixelsper time frame. These tests were obtained using an al-gorithm that assumed that wind components were purelytranslational. A second measure used was a consistencyerror defined as the sum of squared differences betweenthe advected field and its known future value. With goodtime resolution, normalized values between 0.02 and0.05 were obtained for the field of beads. By comparingthe predicted winds with their known values, we were

able to show that ec also was representative of the ac-curacy of the wind predictions.

The ec errors were much larger for the fire windswhere mean values of between 0.6 and 2.0 were ob-tained. When thresholding was used to reject pointswhere the predicted temperature difference exceeded28C, much lower ec values between 0.03 and 0.1 werefound over more than half of the processed data. Thisfinding indicates that the large ec errors are not neces-sarily a good representation of the overall accuracy be-cause exaggerated contributions occurred in regions ofstrong gradients where small errors in velocity predic-tions could disproportionately amplify the error esti-mates. Thus, alternate error estimates must be estab-lished to assess the image flow accuracy. The ec valueswere surprisingly sensitive to the numerical details ofthe image flow algorithm. For example, the seeminglyparadoxical result was obtained that it was more ac-curate to use a lower temporal resolution scheme, thatis, using three time levels spaced 0.067 s apart versustwo spaced 0.033 s apart. The ec errors using three timelevels were less than half those of the two-time-levelscheme. The large ec errors for the fire winds probablyresult from the combination of extreme thermal gradi-ents and rapid motion in the flow, which reduces thetemporal resolution. The effect of variable temporal res-olution also was demonstrated by the ec errors system-atically increasing as the fire approached the near–plotboundary and the image pixel size decreased. Initiallyec was about 0.3, and it increased to about 1.0 near theend of the burn.

The current results also provide guidance in the de-sign of future fire observations using IR imagery. Forexample, knowledge of the expected flow speeds canbe used to match pixel size to frame rate in an attemptto optimize temporal resolution of the data when suchpossibilities exist. For example, the present observationsprobably were taken too close to the fire, resulting inoverly small pixel sizes. Refined image analysis soft-ware may also allow derivation of divergence and vor-ticity fields that can be used to assess further details ofthe flow. Current estimates of divergence and vorticity(in the image plane) showed too much fine structure toallow much physical interpretation. Current plans forour future research in this area include using high-res-olution model simulations to help to interpret the presentdata as well as to assess model physics. We also planto enhance our IR observational database in the nearfuture by including some prescribed fires in tropicalgrasses and intense forest fires of opportunity over thenorthwestern United States. It also was gratifying to findstrong rotational motions throughout these tests. Notonly do these observations confirm our fire model re-sults, but, as expected, they point toward a powerfuldynamic mechanism for violent fire behavior and rapidfire spread.

Perhaps the most important experimental task is toestablish what it is that the IR camera is viewing. As


discussed in the text, the coherency and consistency ofthe derived velocity components (particularly in the hor-izontal) suggest that the high emissivity of glowing sootis limiting the depth of view to a shallow layer at theflame front. A test of this hypothesis might be to performexperiments using both IR and visual cameras usingeither CH or C2 filters. The CH and C2 radicals occuronly in the combustion zone and comparison betweensuch IR and visuals should be informative.

These results are considered preliminary but overallthey are both encouraging and exciting. They point toa number of areas where further research is required,such as image flow testing and development. Further-more, some results remain interpretative and require fur-ther evaluation and validation through modeling studies.The derived fields and their subsequent analyses rep-resent a starting point as a dynamic and thermodynamicdataset for model validation and understanding of forestfires.

Acknowledgments. We thank Laurie Gibson, DavidSuter, and Alireza Bab-Hadiashar for their helpful dis-cussions on image analysis. We gratefully thank the staffat the Northwest Territories burns for their assistancecollecting these data, particularly Bob Schuette, PaulSopko, and Jack Cohen, who scaled the USFS tower tomount the camera. The assistance and advice of Dr.Brian Stocks of Forestry Canada were invaluable. Wealso thank the Mathematics Department at Monash Uni-versity for the use of their local computing system,which was used to perform this analysis. One of theauthors, J. Coen, is supported under USDA Forest Ser-vice Research Joint Venture Agreement INT-97034-RJVA. Special thanks also to Inframetrics for their tech-nical support and to Dr. Robert Serafin (NCAR director)whose support helped foster this line of research.

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