Simple algorithm to determine the near-edge smoke boundaries with scanning lidar

Simple algorithm to determine the near-edgesmoke boundaries with scanning lidar

Vladimir A. Kovalev, Jenny Newton, Cyle Wold, and Wei Min Hao

We propose a modified algorithm for the gradient method to determine the near-edge smoke plumeboundaries using backscatter signals of a scanning lidar. The running derivative of the ratio of the signalstandard deviation (STD) to the accumulated sum of the STD is calculated, and the location of the globalmaximum of this function is found. No empirical criteria are required to determine smoke boundaries;thus the algorithm can be used without a priori selection of threshold values. The modified gradientmethod is not sensitive to the signal random noise at the far end of the lidar measurement range.Experimental data obtained with the Fire Sciences Laboratory lidar during routine prescribed fires inMontana were used to test the algorithm. Analysis results are presented that demonstrate the robustnessof this algorithm. © 2005 Optical Society of America

OCIS codes: 280.3640, 280.0280, 280.1100, 280.1120.

1. Introduction

Wildland fires are a major contributor of particulatematter and other pollutants to the atmosphere.1–3

High concentrations of particulate matter emitted bywildland fires often violate air quality standards.Meanwhile, under the provisions of the Clean Air Actof the U.S. Environmental Protection Agency, allstates by 2005 must institute special programs toreduce the emissions of particles smaller than 2.5 �m�PM2.5� in nonattainment areas. These regulationsmay challenge the planned increase in the ForestService’s and other federal agencies’ use of prescribedfire to reduce hazardous fuels.

Operative monitoring of smoke particulate dynam-ics and concentrations in forest fire areas would allowcritical, time-sensitive information on smoke distri-bution and concentrations to be obtained and docu-mented. This in turn would be helpful for promptestimation of the scale and intensity of fires and forassessment of the visibility, air quality, and publichealth effects from the wildfires and prescribed fires.Lidar is an instrument that is potentially capable of

measuring smoke particulate characteristics re-motely, over an extended area, and in real time. Toachieve these objectives, the Fire Sciences Labora-tory initiated the development of a ground-based two-wavelength mobile lidar instrument. In April 2004,lidar measurements were performed during a pre-scribed fire in the vicinity of Dillon, Montana, inwhich two-dimensional distributions of smoke partic-ulates were measured.

Similar to clouds, smoke plumes are generallymarked by sharp temporal and spatial changes of theparticulate concentration at the smoke plume bound-aries. To process lidar data, regions with high levelsof smoke backscattering must be separated from re-gions of clear atmosphere, and the distance from thelidar to the nearest boundary of the smoke plumeshould be established.4,5 In principle, lidar can easilydetect the boundaries between different atmosphericlayers so that there is no problem visualizing thelocation and boundaries of heterogeneous areas, forexample, the location of the atmospheric turbid layeror clouds from lidar scans. However, use of an auto-matic method to select these boundaries is always anissue. The exact position of any heterogeneous layeris not well specified, and a large amount of interpre-tation is often involved in the selection of a value forthe boundary layer or the cloud height. Differentmethodologies to process such data have been pro-posed that make it possible to discriminate the lay-ering with increased particulate loading from clear-air areas.6–13

In most cases, the location of the boundaries of the

The authors are with the Fire Sciences Laboratory, Forest Ser-vice, U.S. Department of Agriculture, P.O. Box 8089, Missoula,Montana 59807. The e-mail address for V. A. Kovalev [email protected].

Received 8 July 2004; revised manuscript received 14 October2004; accepted 27 October 2004.

0003-6935/05/091761-08$15.00/0© 2005 Optical Society of America

20 March 2005 � Vol. 44, No. 9 � APPLIED OPTICS 1761

enhanced scattering is found by use of empirical cri-teria. For example, in the threshold method, theheight of the atmospheric boundary layer is deter-mined as a point where the backscatter intensity ex-ceeds that of the free atmosphere or the Rayleighsignal by an established percent difference.6,7,13 Thisvalue needs to be empirically established. Differentmethods that analyze the gradient change at thetransition zone from clear air to the turbid layer weredeveloped that analyze the first- or second-order de-rivative of the range-corrected lidar signal with re-spect to the altitude.8–12

In some recent studies of tropospheric structures,including investigations of the boundary-layer char-acteristics, the wavelet technique is used.14–18 Thistechnique has many attractive specifics. Particularly,it can retrieve structures at a variety of spatial scalesand determine multiple boundaries from lidar pro-files, segregating these according to their strengthand sign. However, the technique requires the selec-tion of a particular wavelet, and this may impede itsuse in an automated mode. Additional issues areidentifying atmospheric structures with little back-scatter gradients in the transition zone and the signalnoise.16,18

In all the methods listed above, the shape of thelidar signal is analyzed, and a sharp increase or de-crease in the backscatter signal intensity is consid-ered to be a boundary of the aerosol plumes or theboundary layer. The principal problem in determin-ing turbid layer boundaries is that, due to the largevariability of atmospheric situations, the shape andintensity of the backscattered signals may be signif-icantly different. With these methods, it is quite dif-ficult to establish reliable criteria to discriminate aboundary between clear air and a turbid zone in anautomated mode.

There is an alternative method in which the vari-ance in the lidar signal intensity is used that allowslocalization of the boundary layer without use of em-pirical thresholds.19,20 To obtain convectiveboundary-layer depths and associated characteris-tics, the backscatter signals from each altitude rangeare mapped on horizontal planes, and the variance ofthe signal on each horizontal plane is calculated. Thelowest-altitude local maximum peak of the varianceprofile is considered to be the convective boundary-layer mean depth. To prevent selection of a randomlocal maximum, the behavior of the horizontal vari-ance at five consecutive altitudes was specified. Ob-viously, the results obtained with this algorithmdepend on both the behavior of the investigated aero-sol inhomogeneity and the selected altitude resolu-tion. A change of height resolution for the analyzeddata points may produce different measurement re-sults.

As follows from the above discussion, two functionsare generally used in these methods to determine theboundaries of the aerosol structures with lidar: eitherthe range-corrected signal or the signal variance (orthe standard deviation) versus range. The problemthat we met when analyzing our experimental smoke

plume data was the strong diffusion of the smokeplume at distant ranges; this dramatically reducedthe intensity and gradients of the backscatter signalfrom the smoke, impeding the reliable determinationof the near-edge smoke boundary. Moreover, analysisshowed that false spikes, originated by the noise atthe far end of the range-corrected signal, can maskthe slight increase of the backscattering at the nearedge, making it impossible to discriminate the near-edge smoke boundary. This forced us into looking foralternative functions that would have an increasedgradient at the near edge of the smoke plume.

In this study a special ratio function is imple-mented to facilitate the automatic determination ofthe near-edge boundaries of smoke plumes with agradient method. As compared with the above lidarsignal or variance profile versus range method, theratio function has increased positive gradients at thenear edge of the smoke and strongly suppressed falsenoise spikes over the far end of the measurementrange. Two variants of the algorithm used to deter-mine smoke plume boundaries with a scanning lidarare discussed. These algorithms are based on thedetermination of the location of the ratio derivativemaximum and do not require use of numerical crite-ria or threshold values to determine the location ofthe near-edge boundaries of the smoke plume underinvestigation. Both variants of this algorithm wereexamined, and results of this examination are dis-cussed.

2. Algorithm and Examples of Its Application for LidarExperimental Data

A. Variant 1

The idea behind the proposed algorithm is as follows.Consider a range-corrected backscatter lidar signalP�r�r2 from a synthetic clear atmosphere, which in-corporates a distant turbid area over some range rfrom the lidar, for example, from 2000 to 2600 m (Fig.1, curve 1). Because of the sharp increase of aerosolbackscattering in this area, the lidar signal has asharp increase at the boundary of the turbid zonerb � 2000 m. The integral of the signal (curve 2) alsoincreases in the zone of the turbid air; however, thelatter increase is delayed as compared with the sharpincrease in the signal at rb. Accordingly, the ratio ofthe range-corrected signal P�r�r2 to its integral fromsome range rmin to r has a sharp spike at the boundaryrange rb, which in turn can be additionally increasedby differentiation of the ratio. Thus the function todetermine the location of the boundary between theclear air and turbid (smoke) area can be written as

Dsign(r) �ddr �

P(r)r2

�rmin

r

P(r)r2dr�, (1)

where rmin is the minimal range of the integration;this range can initially be selected to exclude the

1762 APPLIED OPTICS � Vol. 44, No. 9 � 20 March 2005

nearest incomplete overlap zone over which the sig-nal P�r�r2 sharply increases with range. The shape ofthe function Dsign�r� for the above example is shown inFig. 1 (curve 3). One can see that the location of themaximum of this function coincides well with thenear boundary at rb � 2000 m; thus, by determiningthe location of the maximum, one determines theunknown boundary rb. Note also that the integral inthe denominator has increased values at the far endof the measurement range as compared with thatclose to rb. Therefore the signal noise component inreal range-corrected signals does not create stronglocal maxima in Dsign�r� over the distant ranges thatwould be comparable with the spikes at the near-edgerb. This specific of the ratio function is illustrated inFig. 2, in which the same range-corrected signalP�r�r2 as that in Fig. 1 but now corrupted with arti-ficial random noise (curve 1) is given. The functionDsign�r� for this signal is shown as curve 2. One can see

that, in spite of extremely large signal noise over thefar end of the measurement range, the local maximaof the function Dsign�r� over the distant ranges remainless than the global maximum at rb and do not pre-vent the determination of the boundary rb in an au-tomatic mode.

To examine the value of this method, real lidarexperimental data obtained during two prescribedfires performed by the Forest Service were used. Theresults shown in this paper were obtained from lidarsignals measured during a prescribed fire near Dil-lon, Montana, on 23 April 2004. The lidar, developedat the University of Iowa,21 was operated at the wave-lengths of 355 and 1064 nm in both the horizontaland the vertical scanning mode. For an illustration ofhow the algorithm works, an azimuthal scan at1064 nm was selected from a set of the lidar scans.The scan was made along the fixed elevation angle 8deg and over a wide azimuthal range �, from �� 80 deg to � � 170 deg with 1-deg steps; the signalfor every line of sight was an average of 30 shots. A12-bit digitizer was used to sample the signals with a2.4�m range resolution. For the analysis, a simplifiedform of Eq. (1) was used, where the scaling factor,that is, the range resolution �r of the digitized signalin the denominator, was omitted:

Dsign(r) �ddr� P(r)r2

�rmin

r

[P(r)r2]. (2)

In Fig. 3 the top panel shows the range-correctedsignal for the azimuth � � 90 deg from the smokeplume, in which the near-end edge is located at therange 1400 m. Because only the increase in therange-corrected signal P�r�r2 is the subject of interestwhen we are determining the near-edge boundary ofthe turbid structure, the negative values of Dsign�r�

Fig. 1. Conceptual drawing for determination of the near-edgeboundary between the clear air and a distant turbid layer. Theshape of the synthetic range-corrected lidar signal from a clearatmosphere, which incorporates a distant turbid layer over therange from 2000 to 2600 m, is shown as curve 1 and the signalintegral is shown as curve 2 (both in an arbitrary scale). Thefunction Dsign�r� for the above signal is shown as curve 3.

Fig. 2. Same range-corrected signal as that in Fig. 1 but nowcorrupted with artificial random noise (curve 1) and the corre-sponding function Dsign�r� (curve 2).

Fig. 3. (a) Range-corrected signal at the azimuth � � 90º as afunction of the range r. The signal intensity, in arbitrary units, isshown on the left side of the panel. (b) Function Dsign�r� withnegative values removed; the scale of the function is shown on theright side of the panel. The derivative for each range r is deter-mined for five adjacent points over the range from �r � 4.8 m� to�r � 4.8 m�.


are omitted. The scale of the signal magnitude inarbitrary units is shown on the left side of the panel.The signal has three bulges, that is, there are threerange-separated smoke plumes along this azimuthaldirection. The positive values of the function Dsign�r�,which are the subject of interest, are shown in thebottom panel. Here and in Figs. 4–12, the runningderivative is determined for five adjacent points, thatis, over the range interval of 9.6 m. One can see threeseparated bulges of the function Dsign�r� where max-ima, located at the ranges 1460, 1550, and 1680 m,coincide with the near-edge boundaries of threesmoke plumes. Note that the location of the globalmaximum of the function Dsign�r� �1460 m� coincideswith the range where the initial increase of therange-corrected signal takes place, so that it can betaken as the nearest boundary of the smoke rb. Themagnitudes of the function Dsign�r� over the range1200–1400 m are small as compared with that at thenearest boundary of the smoke at rb � 1460 m and donot prevent the determination of the actual rb in theautomatic mode. Note that actually a large number ofpositive spikes of the function Dsign�r� over distantranges �1700–2000 m� exist; however, their magni-tudes are so small that they cannot be visualizedunless a log scale is used.

The analysis of this variant revealed that the func-tion Dsign�r� nicely discriminates the individual layersin multilayer atmospheres. It also works well whenwe are determining the boundary rb between clear airand a dense smoke area with intense backscatteringand a well-defined boundary between them. How-ever, when working in highly inhomogeneous smokeplumes with high variations of backscattering, anumber of intense local maxima may appear withinthe smoke-polluted area, such as shown in Fig. 3. Insome cases this can impede use of the automaticmode to determine rb. The intensity of the maximadepends on the level of spatial variations in therange-corrected signal, and the most intense spikewill be obtained from the aerosol structures with thelargest positive gradient of its magnitude. The globalmaximum of Dsign�r� may not be located at the nearestboundary of interest; it can be located somewherewithin the smoke plume zone. This situation is oftenmet when the intensity of smoke backscattering atthe near edge is relatively low and comparable to thebackscattering from adjacent zones of clear air. Thus,to use this variant to determine rb in an automatedmode, some additional numerical criteria have to beselected and applied to separate cases when theglobal maximum is located within the smoke-pollutedareas, that is, at the ranges r � rb.

B. Variant 2

Another variant of this algorithm is based on theevaluation of the signal variance at the same ranges,similar to that in the studies of Refs. 19 and 20.However, instead of using the variance profile, weapply a ratio function similar to that in Eq. (2). Inparticular, the function in the form

DSTD(r) �ddr � STD(r)

�rmin

r

STD(r) (3)

is used, where STD�r� is the standard deviation of thethree to five range-corrected signals at the samerange r for adjacent azimuths. After an analysis ofthe obtained results, we concluded that the functionDSTD�r� is more appropriate for the determination ofthe near-edge boundary of the smoke area than thefunction Dsign�r�. Figure 4(a) shows the same range-corrected signal for the azimuth � � 90º as that inFig. 3(a). In Fig. 4(b) the standard deviation of thesignal as a function of the range, STD�r�, is shown.Here a stepped standard deviation is calculated forevery five adjacent lines of sight and is assigned tothe central line. In Fig. 4(c) the positive values of thefunction DSTD�r�, which are subjects of interest, areshown. A local running derivative is determined forthe five adjacent points, similar to that in variant 1.The location of the maximal positive value of thederivative �1430 m� where the initial increase of theSTD�r� takes place is insignificantly shifted relativeto that determined with variant 1 �1460 m�. One canalso see small positive, nonzero values of DSTD�r�around the ranges 1600 and 1750 m, where the de-rivative of the standard deviation in Fig. 4(b) changesits sign from negative to positive. However, here themagnitudes of the function DSTD�r� at the rangesr � rb are much smaller than that at the nearestboundary of the smoke at rb � 1430 m. In some cases,additional spikes (local maxima) of DSTD�r� with mag-nitudes comparable with that at rb may appear atr � rb, close to rb (Figs. 5–7). Fortunately, unlike thatof Dsign�r� obtained with Eq. (2), their magnitudes inmost cases are less than that at the range rb even forsparse smoke with decreased backscattering. The lo-cal maxima that appear at r rb are discussed below.

The most important specific of the algorithm in Eq.(3) is that it is relatively insensitive to significantchanges in the intensity of the lidar signals at thesmoke boundaries. In other words, the algorithm in

Fig. 4. (a) Same as in Fig. 3(a). (b) Running standard deviation ofthe signal, STD�r�, calculated with five adjacent lines of sight. (c)Function DSTD�r� with negative values removed. The running de-rivative is determined similar to that in Fig. 3(b).


Eq. (3) functions properly even if the lidar returnfrom smoke areas varies significantly during thescanning. In Figs. 4 and 5, the range-corrected signalintensity from the smoke plume areas ranges from600 to 1150 arbitrarily selected units. In Fig. 6 themaximal signal intensity is approximately 100 arbi-trary units; in Figs. 7 and 8 the intensity is 35 and20–25 arbitrary units, respectively. These units arecalculated with the same scale factor for all signals,so that the relative changes in the signals given in

Figs. 3–9 represent real changes in atmosphericbackscattering. Thus the signal intensities differ hereby as much as 30–50 times; however, no noticeableworsening for the determination of the boundary rb

by the DSTD�r� global maximum occurs.The data analysis showed that use of the function

DSTD�r� instead of Dsign�r� to determine rb significantlyreduces the likelihood of our obtaining false maximawithin the area of smoke plumes at r � rb. However,in some cases of extremely inhomogeneous smokeplumes, especially when combined with a signifi-cantly reduced signal intensity at the nearest bound-aries of the smoke plume, the global maximum of thefunction DSTD�r� may be located inside the plume,rather than at the boundary rb. Such a case is shownin Fig. 9. Here, because of the sharp increase in thestandard deviation within the smoke plume area, theglobal maximum of the function takes place at therange 1474 m, whereas the actual location as deter-mined with the first large spike would be 1320 m. Inthis particular case, the automated method wouldoverestimate the boundary rb by as much as 154 m.Fortunately, when we use the function DSTD�r�, thisgenerally occurs only in individual cases, and is muchrarer than when we use Dsign�r�. To correct or removethese outliers, a conventional technique of removingoutliers can be applied to the retrieved function rb��(see below).

Fig. 5. (a) Same as in Fig. 3(a) but for the azimuth at 98 deg. (b)Function DSTD�r� for the azimuth at 98 deg (only the positive valuesare shown).

Fig. 6. Same as in Fig. 5 but for � � 102 deg.





Another issue of this method is related to thepresence of the noise in the function DSTD�r� over theclear-air zone at r rb (Figs. 5–9). This is because inthe areas of the lidar measurement range, close tothe selected rmin, the accumulated sum �STD�r� inthe denominator of Eq. (3) is small, and accordinglythe function DSTD�r� is extremely sensitive even tominor local fluctuations of the standard deviationSTD�r�. In some cases, local maxima in DSTD�r� ap-pear close to rmin, whose magnitudes are larger thanthat at the smoke boundary rb. To avoid obtainingfalse global maxima in the nearest zone, an addi-tional dead zone of �r � 100–500 m, adjacent to rmin,should be established when one is determining thelocation of the global maximum in DSTD�r�. In otherwords, the summation in the denominator of Eq. (3)should start at rmin, but the global maximum of thefunction DSTD�r� should be determined over the rangestarting from r1 � rmin � �r (rather than from rmin). Toclarify the principles of the selection of the deadzone �r, let us consider the real two-dimensionalimage of the smoke plume obtained with our lidar(Fig. 10).

The relative amount of backscattering not cor-rected for the two-way atmospheric transmission,that is, the intensity of the range-corrected signal inthe arbitrary units, is defined here in gray scalegiven on the right side Fig. 10. The dark structuresare the signal intensity from smoke plume areaswith enhanced backscattering. The initial datapoints of rb retrieved with the selected rmin � 50 mand �r � 360 m are shown as white squares. Onecan see that, on the right side of the plot, most of theadjacent data points rb are close to each other andtheir location changes monotonically with thechange of the azimuth. On the left side of the plot,within the azimuthal range � � 127–167 deg, somedata points are highly scattered over a wide range

from 350 to 800 m. Our analysis revealed that onlysome of these data points originated from clearlyvisualized local smoke tatters. Most of these pointsoriginated from slight signal fluctuations, whichwere difficult to interpret. To solve the problem ofthe bad points, some principle of separation of theweak smoke-originated variations from noise fluc-tuations should be established. In particular, thefollowing procedure can be used. Unlike the goodpoints, the adjacent noise spike data points arepoorly correlated to each other; therefore the run-ning standard deviation of rb versus azimuthalrange � will have an increased value in areas ofscattered data points. This allows one to separateand remove these dubious quantities. Becausethese points are located at near distances, it is moreeffective to use the running fractional standard de-viation to distinguish such outliers. In Fig. 11 sucha dependence for the three-point running fractionalstandard deviation for the function rb�� is shown asthe bold curve at the bottom of the panel. Note thesignificant increase of this value over the rangewhere the function rb�� (dotted curve) has largedeviations. Following the conventional principles ofremoving outliers, data points were removed wherethe local fractional standard deviation was three ormore times larger than the mean standard devia-tion of rb�� over the range of intense smoke back-scattering (excluding only the boundary pointsbetween these areas). In Fig. 11, the data points ofrb that remain after the outliers are removed areshown as black squares. Now one can find moreaccurate locations of rb after removal of these badpoints. This can be achieved by determining globalmaxima of DSTD�r� by use of an increased range �r.In particular, the newly selected �r should be ex-tended enough to put all established outliers in anenlarged dead zone. In our case this can be achievedby selecting �r � 800–900 m. The boundaries rb forthe same smoke plume as in Fig. 10 but now deter-mined with �r � 850 m are shown in Fig. 12.

Fig. 10. Plot of the two-dimensional scan of the smoke plumeunder consideration. The relative amount of backscattering (notcorrected for the atmospheric transmission) is defined in gray scalegiven on the right side. The dark structures are smoke plume areaswith increased backscattering. The data points of rb retrieved withvariant 2 with rmin � 50 m and �r � 360 m are shown as whitesquares.

Fig. 11. Plot of the values of rb as a function of the azimuth � overthe azimuthal range from � � 83 deg to � � 167 deg before andafter outliers were removed (the dotted curve and black squares,respectively). The three-point running fractional standard devia-tion of rb�� is shown as the bold curve.


3. Summary

In this study we propose a modified algorithm for thegradient method, in which we use a special ratio func-tion, to determine near-edge smoke plume bound-aries using backscatter signals of a scanning lidar.Two variants of the algorithm are examined to deter-mine the location of such boundaries. In the firstvariant we determined the derivative of the ratio ofthe range-corrected signal to the integral of the signaland the location of the global maximum of this deriv-ative. In the second variant we determined the de-rivative of the ratio of the standard deviation of thesignal to the integral of the standard deviation andthe location of the global maximum of this derivative.We tested both variants with experimental data ob-tained during prescribed fires to establish whetherthe algorithms can be used to automatically deter-mine the smoke boundary without applying a prioriselected criteria.

The analysis of the behavior of the function Dsign�r�[variant 1, Eq. (2)] revealed that the algorithm nicelydiscriminates separate zones in highly heteroge-neous, multilayering smoke plumes, yielding intensewell-defined local maxima within the smoke area.However, the global maximum may be located some-where within the smoke plume zone, rather than atthe smoke near-edge boundary rb, so that use of thisvariant to determine rb in an automated mode mightbe an issue, especially for relatively weak intensitybackscattering. The alternative function DSTD�r� [Eq.(3)] used in variant 2, in which such a situation israrely met, is more appropriate for automatic deter-mination of the near boundary of the smoke thanDsign�r�.

Analyzing variant 2, we determined the runningderivative, varying the least-squares (regression)range from 4.8 to 14.4 m, and calculated standarddeviations, varying the number of lines of view fromthree to seven. In most cases, these variations eitherdo not influence the established locations of the globalmaximum of DSTD�r� or resulted in insignificantchanges in these locations; however, use of five linesof view instead three when we determined STD�r�

resulted in some reduction in the number of falsemaxima cases, particularly when we determined rb

for relatively thin smoke plumes.The method is relatively insensitive to the lidar

signal random noise at the far end of the measure-ment range, enhanced by the range-squared correc-tion, and works reliably enough even when the signalgradients in the transition zone between clear-airand smoke plume areas are reduced; however, specialprecautions should be taken to avoid false globalmaxima in the areas close to the lower limit of theintegration of the function STD�r�.

This method can be useful to determine theboundary-layer top with airborne or spacecraft lidars.

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Simple algorithm to determine the near-edge smoke boundaries with scanning lidar