# 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

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