# Atmospheric Boundary Layer Height Monitoring Using a Kalman Filter and Backscatter Lidar Returns

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<ul><li><p>IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 8, AUGUST 2014 4717</p><p>Atmospheric Boundary Layer Height MonitoringUsing a Kalman Filter and Backscatter</p><p>Lidar ReturnsDiego Lange, Jordi Tiana-Alsina, Umar Saeed, Sergio Toms, and Francesc Rocadenbosch, Member, IEEE</p><p>AbstractA solution based on a Kalman filter to trace theevolution of the atmospheric boundary layer (ABL) sensed by aground-based elastic-backscatter tropospheric lidar is presented.An erf-like profile is used to model the mixing-layer top and theentrainment-zone thickness. The extended Kalman filter (EKF)enables to retrieve and track the ABL parameters based on sim-plified statistics of the ABL dynamics and of the observation noisepresent in the lidar signal. This adaptive feature permits to analyzeatmospheric scenes with low signal-to-noise ratios (SNRs) withoutthe need to resort to long-time averages or range-smoothing tech-niques, as well as to pave the way for future automated detectionsolutions. First, EKF results based on oversimplified syntheticand experimental lidar profiles are presented and compared withclassic ABL estimation quantifiers for a case study with differentSNR scenarios.</p><p>Index TermsAdaptive kalman filtering, laser radar, remotesensing, signal processing.</p><p>I. INTRODUCTION</p><p>THERE are several methods to retrieve the atmosphericboundary layer (ABL) height based on remote sensingtechniques. These techniques are always based on the detec-tion of a vertical feature from atmospheric variables, whichcontinuously vary with range and time, and having a well-defined transition identifiable as an edge or boundary.Height retrieval methods and their accuracy are conditionedto the characteristics of the sensing instrumentation: lidar,sodar, radar wind profilers, and radio acoustic sounding system,among others (see [1] for an extensive review), either solely orcombined [2].</p><p>A significant advantage of backscatter lidar remote sensinginstruments is that they are able to gather a range-resolvedprofile of the ABL simultaneously for the whole observationrange, which greatly improves the temporal resolution of in situsensors and radiosoundings.</p><p>Manuscript received June 19, 2013; revised August 7, 2013; acceptedSeptember 13, 2013. Date of publication October 24, 2013; date of currentversion February 27, 2014.</p><p>D. Lange and F. Rocadenbosch are with the Department of Signal Theoryand Communications (TSC), Remote Sensing Laboratory (RSLab), UniversitatPolitcnica de Catalunya (UPC)/Institut dEstudis Espacials de Catalunya(IEEE/CRAE), 08034 Barcelona, Spain (e-mail: roca@tsc.upc.edu).</p><p>J. Tiana-Alsina and U. Saeed are with the Department of Signal Theoryand Communications (TSC), Remote Sensing Laboratory (RSLab), UniversitatPolitcnica de Catalunya (UPC), 08034 Barcelona, Spain.</p><p>S. Toms is with the Institut de Cincies de lEspai-Consejo Superior de In-vestigaciones Cientficas/Institut dEstudis Espacials de Catalunya (ICE-CSIC/IEEC), 08193 Barcelona, Spain.</p><p>Digital Object Identifier 10.1109/TGRS.2013.2284110</p><p>Fig. 1. Oversimplified description of the ABL. (a) In the ABL model, U(R)is the range-corrected lidar signal (noiseless). ML stands for the MixingLayer, EZ for the Entrainment Zone, and FT for the Free Troposphere.(b) Idealized ABL erf-curve transition model, h(R), for the total backscattercoefficient with characteristic parameters, Rbl, a, A, and c. R1 and R2 are thestart- and end-range limits defining the length of the observation vector passedto the filter. R1 and R</p><p>2 are the start- and end-range limits of the erf-like ABL</p><p>transition.</p><p>Elastic-backscatter lidars use the backscattered optical powerfrom the atmospheric aerosols to profile the atmospheric struc-ture and benefit from being highly sensitive to the concentrationof aerosols. In the low troposphere, the ABL is marked by atransition interface known as the entrainment zone (EZ), wheretwo different air masses, the mixing layer (ML) and the freetroposphere (FT), merge and interact. Fig. 1 shows the locationof the aforementioned atmospheric layers. Measurements inthis transition region provide useful parameters such as theABL height or the EZ thickness. These parameters are highlyvaluable inputs to environmental models since they describethe extension and evolution of the transport of atmosphericconstituents [3].</p><p>The lidar signal shows this relative distribution of aerosolsand moisture along the troposphere in terms of the background-subtracted range-corrected power U(R) = R2P (R), withP (R) being the single scattering return power, as [4]</p><p>U(R) =K [mol(R) + aer(R)]T2(R)</p><p>T 2(R) = e2</p><p> R0</p><p>[aer(u)+mol(u)]du (1)</p><p>where R [km] is the range along the lidar line of sight (LOS) (Ris related to height z as z = R sin(), where is the LOS eleva-tion angle), K [W km3] is the system constant, and mol(R)and aer(R) [km1 sr1] are the range-dependent molecularand aerosol optical backscatter coefficients, respectively. aeris defined as aer(R) = Naer(R)((daer())/(d)), i.e., the</p><p>0196-2892 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.</p></li><li><p>4718 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 52, NO. 8, AUGUST 2014</p><p>product of the aerosol number concentration, N(R)aer [km3],and the average differential backscatter cross section of theaerosol mixture, ((daer())/(d) [km</p><p>2 sr1], which in-cludes the effects of aerosol type and moisture. The molecularcomponent, mol(R), can be computed from the U.S. standardatmosphere model [5] or radiosoundings.</p><p>Finally, T 2(R) represents the two-way path atmospherictransmittance affecting the optical pulse, with mol and aerbeing the atmospheric extinction coefficients due to aerosolsand molecules, respectively.</p><p>The transmittance factor can be included into the totalbackscatter by defining the attenuated total backscatter as</p><p>atten(R) = (R)T2(R) (2)</p><p>where (R) = mol(R) + aer(R). Inside the ML and, par-ticularly, toward the NIR or in relatively optically denseatmospheres, the aerosol backscatter component dominates, soaer(R) mol(R) and (R) aer(R). This simplificationmakes the range-corrected lidar signal, U(R), almost propor-tional to the aerosol number concentration profile, Naer(R). Incontrast, in the FT, the aerosol content is virtually nil (withthe exception of, e.g., unstable dust layers or dust intrusions[6]), and hence, (R) mol(R). As a result, in the FT, thelidar signal, U(R), becomes proportional to the profile of themolecular number concentration, Nmol(R) (see Fig. 1).</p><p>The lidar profile typically presents a sharp decrease at someheight inside the EZ, henceforth called the ABL local transition.The buoyancy-driven updrafts tend to narrow this local transi-tion, while in the case of downdrafts, the transition widens [7].This simple assumption of aerosol concentration/lidar signalpreviously mentioned is often distorted by several factors suchas instrumental noise, multilayer scenarios (transported layers,stratified layers, lateral entrainments, or the residual layer),and nonlinear effects of moisture distribution in the aerosolbackscatter. The influence of all these effects is different, de-pending on which method of ABL height detection is chosen.Thus, active research in terms of intercomparison is still underway [8], [9].</p><p>Lidar sensing of the ABL has been carried out not only byground-based systems such as backscatter lidars [10], water-vapor differential absorption lidar [11], or, more recently,ceilometers [12] but also by airborne lidars [13] and scanninglidars in a range height indicator scan [14], [15]. Ground-fixedsystems monitor the ABL structure as a function of time whileairborne and scanning lidars spatially assess the ABL. Twodifferent approaches to estimate the ABL height from lidarsignals can be outlined:</p><p>1) The geometrical approach uses the fact that the EZ regionusually appears in the individual lidar signal profiles as asharp decrease between the two air masses (this is due tothe lack of aerosols and moisture in the FT, all of whichcause a strong signature in the range-corrected backscat-ter lidar return). Geometrical-based ABL-detectionmethods rely on the detection of a meaningful transition,usually by some sort of edge-detection analysis, by meansof a threshold criterion [13], [16], [17] or gradient detec-tion [10], [18] applied to time-averaged profiles. When</p><p>high signal-to-noise ratio (SNR) and temporal resolutionare available from the lidar sensor, geometrical methodsare able to retrieve the instantaneous ABL height (hABL),which is identified as the instantaneous ABL top.</p><p>2) The statistical approach uses the high variability in thereturn signal caused by the mixing processes betweencells in the EZ and cells in the FT above or in the MLbelow. This approach requires the analysis of a set ofprofiles to produce a statistically significant estimate ofthe ML depth, taken as the mean ABL height (hABL).</p><p>In this paper, we present a tradeoff between both aforemen-tioned approaches by using an adaptive filter solution basedon the extended Kalman filter (EKF) [19] which estimatesthe time-dependent ABL height, hABL, the approximate EZthickness, and auxiliary atmospheric backscatter-coefficient pa-rameters. A preliminary study on the problem has been outlinedin [20], from the Remote Sensing Laboratory (RSLab). Becausethe filter adaptively fits a model shape function to the lidar-measured data and minimizes the mean-squared error over timein a statistical sense, it provides convenient estimates. Thefilter thus makes the most from the high temporal resolution ofcurve-fitting geometrical models and the physically significantestimate output by statistical methods.</p><p>In the concept-design implementation of the filter presentedhere, multilayer scenes are not considered. In contrast, this pa-per focuses on the impact that noise has on the filter estimates,particularly for different SNR scenarios.</p><p>This paper is organized as follows: Section II formulatesthe nonlinear adaptive estimator based on the Kalman filtertheory with which ABL parameters can sensibly be estimated.Section III shows the simulation results on the temporal evo-lution of the ABL parameters and cross-examines them withthe estimated ones from EKF and traditional nonlinear leastsquares (NLSQ) approaches. Section IV presents the results ofapplying the EKF approach to experimental lidar backscatterdata under two different SNR scenarios (high and low SNRs).Results are also compared with well-known classical ABL-detection methods in the literature. Finally, concluding resultsare presented in Section V.</p><p>II. ABL ADAPTIVE DETECTION METHOD</p><p>An EKF is applied to adaptively fit an erf-like functionmodeling the EZ lidar-signal transition curve to the range-corrected lidar measurements. The erf curve-fitting method [21]is chosen because it is a robust approach which involves thebulk of the lidar profile. Later studies have been given in [7]and [22], mostly on the convective boundary layer (CBL).</p><p>The application of the EKF to the field of lidar-signal pro-cessing to estimate the atmospheric optical parameters departsfrom previous works in [23] and [24]. On the other hand,Mukherjee et al. [25] have applied a scalar Kalman filter toestimate the ABL height from sodar signals.</p><p>A. EKF Approach</p><p>The discrete Kalman filter is an adaptive linear estimatorinherited from control system theory that operates recursively</p></li><li><p>LANGE et al.: ABL HEIGHT MONITORING USING KALMAN FILTER AND BACKSCATTER LIDAR RETURNS 4719</p><p>using a state-space model formulation. The filter is based ontwo models: 1) the measurement model (see Section II-C1),which relates the atmospheric state-vector unknowns (to beestimated) to the observation measurements (i.e., the range-corrected lidar backscatter signals), and 2) the state-vectormodel (see Section II-C2), which approximately describes thetemporal projection of the unknowns and its associated statis-tics [see (5)]. However poor this a priori information aboutthe atmospheric state vector and its statistics may be, thisinformation is of advantage to the filter in order to improve itsestimates by combining the actual estimation with the statisticalbehavior from past estimates. In what follows, a priori anda posteriori stand for before and after assimilating theinformation from the present measurement at discrete time tk,respectively.</p><p>When, as is the case of (1), the measurement model is non-linear, a linearization is made around the state-vector trajectory,which is updated at each successive iteration of the filter oncea new measurement zk is assimilated in what is called theEKF. Likewise, at each filter iteration, the state vector, xk, theestimated a priori and a posteriori error-covariance matrices,Pk and Pk, respectively, and the Kalman gain, Kk, are recur-sively updated (see, e.g., [19, pp. 215219] and [24]). By therecursive procedure, the filter corrects its projection trajectoryof the ABL atmospheric variables and improves its estimationof the ABL parameters via a new atmospheric state vector xkbeing estimated. By means of this convenient adaptive behavior,tracking the state-vector components appears as a natural anddesirable feature of the filter.</p><p>For an M -component state vector (M = 4 in the case ofthe ABL estimation model described in Section II-C1), thenumber of observation samples in the ABL transition (N) mustobviously be N M for data sufficiency. In practice, a muchlarger number of samplesas it is always the caseconveysthe extra benefit of enhanced robustness to noise (this is equiva-lent to an overdetermined system of equations in classic algebratheory).</p><p>B. ABL Problem Formulation</p><p>For moderate to clear-air atmospheres and lidar soundingranges roughly below 3 km (R 3 km), the optical thickness, =</p><p> R0 [aer(u) + mol(u)]du, can be considered low enough</p><p>( < 1) to disregard the effects of the atmospheric transmissiv-ity term T (R) in (1). Under these conditions usually found inpractice, the range-corrected lidar signal, U(R), is proportionalto the total backscatter coefficient in (1)</p><p>U(R) K(R) (3)</p><p>with (R) = aer(R) + mol(R). As a result, U(R) can beconsidered a surrogate for the total backscatter coefficient(R), which is representative of the average aerosol and molec-ular concentration of the atmospheric mixture aloft.</p><p>The range-corrected lidar signal exhibits a transition curvefrom high concentrations inside the ABL to lower concentra-tions (molecular-background level) as the height increases. TheABL transition model proposed here follows a similar formu-lation to that in [21] but for the total backscatter coefficient.</p><p>The erf-like total backscatter-coefficient model is formulated interms of four characteristic parameters, Rbl, a, A, and c, as</p><p>h(R;Rbl, a, A, c) =A</p><p>2</p><p>{1 erf</p><p>[a2(RRbl)</p><p>]}+ c (4)</p><p>where Rbl is the range position that marks the instantaneousABL height, defined as the inflection point where the function hchanges from convex to concave (equivalently,...</p></li></ul>

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