# Lidar monitoring of regions of intense backscatter with poorly defined boundaries

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Lidar monitoring of regions of intense backscatterwith poorly defined boundaries

Vladimir A. Kovalev,* Alexander Petkov, Cyle Wold, and Wei Min HaoUnited States Forest Service, RMRS, Fire Sciences Laboratory, 5775 Highway 10 West, Missoula, Montana, 59808, USA

*Corresponding author: vkovalev@fs.fed.us

Received 31 August 2010; accepted 7 November 2010;posted 19 November 2010 (Doc. ID 134285); published 27 December 2010

The upper height of a region of intense backscatter with a poorly defined boundary between this regionand a region of clear air above it is found as the maximal height where aerosol heterogeneity is detect-able, that is, where it can be discriminated from noise. The theoretical basis behind the retrieval tech-nique and the corresponding lidar-data-processing procedures are discussed. We also show how such atechnique can be applied to one-directional measurements. Examples of typical results obtained with ascanning lidar in smoke-polluted atmospheres and experimental data obtained in an urban atmospherewith a vertically pointing lidar are presented. 2010 Optical Society of AmericaOCIS codes: 280.3640, 290.1350, 290.2200.

1. Introduction

There is no commonly accepted technique for remotemonitoring of the locations and temporal and spatialchanges of regions of increased backscatter withpoorly defined boundaries, such as those that arefound in dispersed smoke plumes originating in wild-fires, dust clouds, or aerosol clouds created by volca-no eruptions.To monitor the behavior of intense backscatter

regions in the atmosphere, lidar is the most appro-priate tool. In principle, lidar can easily detect theboundary between different atmospheric layersand discriminate the regions with high levels of back-scatter from the regions of clear atmosphere. Well-defined heterogeneous areas, such as the atmo-spheric boundary layer or clouds, can be identifiedthrough the visual inspection of the lidar scan andis a trivial matter [1]. However, the identificationof the exact location of the boundary of a heteroge-neous structure becomes a significant challengewhen the boundary is not well defined. Such a situa-tion is typical, for example, for smoke layers andplumes where the dispersion processes create a

continuous transition zone between the intensebackscatter region and clear air. The smoke plumedensity, its concentrations, the levels of the heteroge-neity, and the smoke dispersion are extremely vari-able and depend heavily on the distance from thesmoke plume source.The absence of unique criteria for determining the

boundary between the increased-backscatter andclear-air areas when it is not well defined is the prin-cipal issue when using any range-resolved remotesensing technique. This challenge is a general pro-blem rather than a problem of remote-sensing meth-odology. No standard definition of such a boundaryexists. When determining the boundaries of the aero-sol formation, generally, some relative rather thanabsolute characteristics are used. For example, whenusing a gradient method, one can select the boundarylocation as the range where the examined parameterof interest (e.g., the derivative of the square-range-corrected lidar signal) is a maximum or decreasesfrom the maximum value down to a fixed, user-defined level [2]. However, there is no way to estab-lish a standard value for this level, which would beacceptable for all cases of atmospheric searching. Si-milarly, the use of the wavelet technique requires theselection of concrete parameters, and this is a signif-icant challenge when a region of intense backscatter

0003-6935/11/010103-07$15.00/0 2011 Optical Society of America

1 January 2011 / Vol. 50, No. 1 / APPLIED OPTICS 103

with a poorly defined boundary is examined [3]. Inthis study, an alternative approach to this issue isconsidered.

2. Methodology

The lidar signal, Pr, recorded at the range r, is thesum of the range-dependent backscatter signal,Pr and the range-independent offset, B, the back-ground component of the lidar signal and the electro-nic offset:

Pr Pr B: 1This signal is transformed in the auxiliary functionYx, defined as [4]

Yx Pxx Px Bx; 2where x r2 is the new independent variable. In thecurrent study, we apply the simplest form of thetransformation, which does not require the use ofthe molecular profile of the searched atmosphere.The sliding derivative of this function, dY=dx, is cal-culated, and the intercept point of each local slope fitof the function with the vertical axis is found and nor-malized. The intercept function versus x is found as

Y0x Yx dYdx

x: 3

By using the intercept function instead of dY=dx, thedetermination of the systematic offset, B, in the lidarsignal [Eq. (1)] can be avoided. The retrieval tech-nique that is used here for processing the signalsof both scanning and one-directional lidar is basedon determining the normalized intercept function[4]. The normalized intercept function is defined as

Y0;normx Y0x

x xmax; 4

where xmax is the maximum value of the variable xover the selected range and is a positive nonzeroconstant, whose value can range from 0.020.05.The selection of the numerical value for is not cri-tical. The component xmax in the denominator of theequation is included only to suppress the excessiveincrease of Y0;normx in the region of small x, which,for our task, is not the region of interest. Note alsothat the numerical differentiation in Eq. (3) is madewith a constant step, r ri1 ri const:, ratherthan a constant x. Under such a condition, the stepx is variable, that is,

x r2i1 r2i r21 2rir

: 5

In this paper, we restrict our analysis to the determi-nation of the maximum heights of the regions of theincreased backscatter; the determination of the mini-mum heights, especially in a multilayering atmo-

sphere, is a much more complicated task andrequires separate consideration.

A. Determination of the Maximal Height of the Region ofIncreased Backscatter Using Scanning Lidar

Consider the case where lidar scanning is performedin a fixed azimuthal direction, , using N slope di-rections selected within the angular sector from minto max and with the stepped angular resolution of; that is, 1 min, 2 min ;, i min i 1;, and N max. The recordedsignals, measured within the range from rmin tormax, are transformed into the corresponding set ofthe normalized functions, Y0;normh, versus height,h; these functions are calculated within the altituderange from hmin to hmax with the selected height re-solution, h; that is, h1 hmin, h2 hmin h;,hj hmin j 1h;, and hM hmax; M is thenumber of heights within the selected intervalhmin;hmax.To locate the maximum height of the region of in-

creased backscatter, the absolute values of the nor-malized intercept function versus height for eachslope direction i and each hj within the altituderange from hmin to hmax, are calculated:

f i;j jY0;normi;hjj: 6

Thus, for our calculations we define the matrix F,with matrix elements f i;j N;M; that is, F f i;jNHM. The maximum matrix element, fmax maxf i;jNM , is determined and the matrix isnormalized:

R 1

fmaxF: 7

The elements of the matrix, ri;j Rj;hj, which areused for determining the areas of the smoke plume,can vary within the range 0 ri;j 1, with areas ap-proaching ri;j 1 having the greatest heterogeneity.In our original study [4], the local heterogeneity

event defined in two-dimensional space i; jwas im-plemented. The event was considered as being trueat the locations where the elements ri;j of the matrixF reach some established, user-defined level, < 1.In other words, we supposed that the atmosphericheterogeneity in the cell i; j, exists if the element,ri;j ; in the study [4], the user-defined constant was selected within the range from 0.15 to 0.3. Somemodification in selecting was considered in [5].To clarify the modified methodology for the deter-

mination of the maximal height of the smoke-polluted area and the principle for the selection of in this study, let us consider typical experimentaldata. The data were obtained by a scanning lidarin the vicinity of the Kootenai Creek Fire near Mis-soula, Montana, USA in 2009. The wildfire occurredin a wild mountainous area from which the smokeplume spread in an easterly direction across thevalley where the lidar was located. The height of

104 APPLIED OPTICS / Vol. 50, No. 1 / 1 January 2011

the lidar site was approximately 900 m below theheight of the wildfire area. The schematic of the scan-ning lidar setup is shown in Fig. 1. Lidar verticalscans were made along 23 azimuthal directions, from 45 to 155, with an angular increment 5. Thus, each scan was used to obtain a verti-cal cross-section of attenuated backscatter in the cor-responding azimuthal direction.In Figs. 25, we clarify the details of our data-

processing methodology using the results obtainedon 27 August 2009. The vertical scan analyzed belowwas made at the azimuthal direction, 55, withinthe vertical angular sector from min 10 to max 60; the total number of slope directions is N 28.In Fig. 2, the corresponding 28 functions, Ri;hj,are shown as the gray curves, with the thick blackcurve representing the resulting heterogeneity func-tion, R;maxh, defined for each altitude as

R;maxh maxR1;h;R2;h;; Ri;h;;RN ;h: 8

To determine the maximum height of the smoke-polluted region, the parameter, , can be selectedand compared to R;maxh. The maximum smokeplume height, hsm;max, can be found as the maximumheight where R;maxh . The main issue of suchan approach is the rational selection of . In the caseof a poorly defined boundary, the retrieved height ofthe smoke plume strongly depends on the selected .This observation is illustrated in Fig. 3, where theR;maxh shown in Fig. 2 is analyzed. One can seethat selecting different yields different heights ofinterest, hsm;max. For example, changing from 0.1to 0.15 decreases the retrieved height hsm;max from4581 to 3078 m.Analyzing possible retrieval techniques, we con-

cluded that the optimal solution could be achievedby taking advantage of the principles used for deter-mining the cloud base height when the ceiling has nowell-defined lower boundary. In such a case, thecloud base height is considered as the lowest level

of the atmosphere where cloud properties are detect-able [6]. In our study, the analogous definition isused for determining the maximum smoke plumeheight. Particularly, the upper smoke plume bound-ary height, hsm;max, can be defined as the maximumheight where smoke plume aerosols are detectable inthe presence of the noise component in the examinedfunction. This approach requires reliably distin-guishing the ri;j increases caused by the presenceof the actual smoke plume heterogeneity from thatof random noise fluctuations.To apply the above definition in the smoke plume

measurements, the following methodology was cho-sen. Using the retrieved functions, R;maxh (Fig. 2),the atmospheric heterogeneity height indicator(AHHI) for this azimuth is determined. The AHHI

Fig. 1. Schematic of data collection with a vertically scanning li-dar during the Kootenai Creek Fire inMontana in July andAugust2009. (The azimuthal sector 45 65, which overlaps the wildfiresite, is not shown in this figure.)

Fig. 2. Example of data obtained by a scanning lidar at the wa-velength of 1064 nm in the smoke-polluted atmosphere inthe vicinity of Missoula, Montana. The gray curves representthe set of 28 functions, Ri;hj. The resulting heterogeneity func-tion, R;maxh, is shown as the thick black curve.

Fig. 3. Black curve is the same heterogeneity function, R;maxh,as in Fig. 2, and the gray blocks illustrate thedependence of the retrieved smoke plume height, hsm;max, on theselected .

1 January 2011 / Vol. 50, No. 1 / APPLIED OPTICS 105

is a histogram that shows the total number of hetero-geneity events, nh, defined by scanning lidar at theconsecutive height intervals for the selected [4].The concept of the AHHI histogram is explained inFig. 4. The thick black curve on the left side of thefigure is the function R;maxh, the same as inFigs. 2 and 3. The AHHI derived with the level 0:15, is shown as blackgray squares. The max-imal height, where the minimal number of theheterogeneity events exceeds zero nh 1, ishsm;max 3078 m. Note also that a maximumnumber of heterogeneity events was fixed over thealtitude range 1000 m1150 m (n 28) and23502550 m (n 22), so that two separate layersat different heights can be discriminated withthe AHHI.Using such AHHI histograms, one can determine

the maximal heights of the area with the increasedheterogeneity for different . In our calculations, weutilize the consecutive values of with the fixed step; that is, 0 0, 1 , 2 2;, andk k;. For each discrete , we build the AHHIand determine the corresponding maximum height,hsm;max, that is, the maximum height where thenumber of heterogeneity events, nh, is a nonzerointeger value.The height of interest, hsm;max, is determined using

the minimal value of that allows reliable discrimi-nating of the smoke plume heterogeneity from thenoise component. Figure 5 illustrates the basic prin-ciple for the determination of optimal level, opt,which provides the most likely smoke plume height,hsm;maxopt. The methodology of determining optand the corresponding hsm;maxopt is as follows. In-itially, the level 0 0 is selected. Because of the pre-sence of nonzero instrumental noise, the height,hsm;max0, determined from AHHI as the maximalheight where nh > 0, will be equal to the selectedhmax. In our case, hsm;max0 hmax 5000 m

(Fig. 3). Then the next level, 1 0:05, isanalyzed. One can see in Fig. 5 that this level doesnot change the initial height, hsm;max 5000 m, thatis, the level 1 0:05 is still below the interferingnoise. Selecting then the larger levels, equal to 2 0:1 and 3 0:15, we plot the set of correspondingAHHI and for each determine the maximal heightswhere nh > 0, that is, the heights hsm;max2 andhsm;max3 (Fig. 5). The goal of this operation is toestablish when the erroneous heterogeneity eventscreated by noise become below the level of discrimi-nation, , so that the actual hsm;max can be found.The determination of the optimal level, opt, and

the corresponding height of interest, hsm;maxopt, isbased on the calculation of the differences betweenthe adjacent heights hsm;maxk and hsm;maxk1.The established value of opt should meet two con-ditions. First, the difference hsm;maxopt hsm;maxopt should be maximal. Second, the nextconsecutive increase of , that is, selection of equalto opt , then opt 2 should result in a slowdecrease in the corresponding hsm;max.In our case, the decrease from 0:1 to 0.15 re-

sults in the largest decrease of hsm;max from4581 to 3078 m (Figs. 3 and 5). The next consecutiveincrease of from 0.15 to 0.2, then from 0.2 to 0.25. donot reduce the extracted hsm;max significantly; thedifference between any pair of the consecutive max-imum heights, hsm;maxk and hsm;maxk1, is lessthan 100 m, that is, 3% relative to the fixed...

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