FMCW Radar Performance for Atmospheric Measurements

Transcription

1 RADIOENGINEERING, VOL. 19, NO. 1, APRIL FMCW Radar Performance for Atmospherc Measurements Turker INCE Faculty of Computer Scence, Izmr Unversty of Economcs, Izmr, Turkey Abstract. Frequency-modulated contnuous-wave radars (FMCW) have been used n the nvestgaton of the atmosphere snce the late 1960 s. FMCW radars provde tremendous senstvty and spatal resoluton compared to ther pulsed counterparts and are therefore attractve for clear-ar remote-sensng applcatons. However, these systems have some dsadvantages and performance lmtatons that have prevented ther wdespread use by the atmospherc scence communty. In ths study, system performance of atmospherc FMCW radar s analyzed and some measurement lmtatons for atmospherc targets are dscussed. The effects of Doppler veloctes and spectral wdths on radar performance, radar s near-feld operaton, and parallax errors for two-antenna radar systems are consdered. Expermental data collected by the hghresoluton atmospherc FMCW radar s used to llustrate typcal performance qualtatvely based on morphologcal backscattered power nformaton. A post-processng based on sngle-lag covarance dfferences between the Bragg and Raylegh echo s appled to estmate clear-ar component from refractve ndex turbulence and perform quanttatve analyss of FMCW radar reflectvty from atmospherc targets. Keywords Electromagnetc measurements, remote sensng, nstruments and technques. 1. Introducton At low mcrowave frequences, radars respond to spatal varatons n the ndex of refracton of the ar often characterzed by the atmospherc refractve-ndex structure functon parameter, C n. Whle remote measurement of the atmospherc boundary layer (ABL) s complcated by the low radar reflectvty of clear-ar turbulence structures, FMCW radars, havng tremendous senstvty and spatal resoluton compared to ther pulsed counterparts, have proven to be a soluton to ths problem. Whle Doppler capablty can be added to FMCW radars [1], the unque strength of ths technology les n ts ablty to montor the atmospherc refractve-ndex structure functon parameter, C n, wth unparalleled resoluton n heght and tme. Snce the frst hgh-resoluton atmospherc FMCW radar, developed n 1969 by Rchter [], a number of FMCW radars have been developed for hgh-resoluton atmospherc probng [3]-[5], whch have provded valuable nformaton about the fne structure and dynamcs of clearar turbulence. The advent of S-band, FMCW radars has opened a new research feld, whch was revewed by Gossard [6]. Despte FMCW radars beng excellent tools for turbulence studes n the convectve ABL and n the cappng nverson regon [4], relatvely few atmospherc studes reported n the lterature have used FMCW radar data extensvely for both quanttatve and qualtatve analyss of clear-ar features observed. Whle S-band FMCW radars have been desgned wth the capablty to obtan heght and tme resolutons of 1 m and 1 s, respectvely, the degree to whch these resoluton lmts are obtaned n practce depends upon the propertes of the atmospherc echo tself. Range measurement errors due to non-zero Doppler veloctes and fnte coherence of the clear-ar echo have mplcatons on both spatal resoluton and Doppler estmaton of FMCW radars. Although the theoretcal background for FMCW radars s well establshed, ther measurement lmtatons for atmospherc targets and performance mpact for atmospherc applcatons has receved lttle attenton n the lterature. A detaled revew of the theory of operaton of S- band FMCW radar and ts applcaton to atmospherc boundary layer proflng can be found n [7]. In earler work [8], performance lmtatons of an atmospherc FMCW radar are llustrated wth ntal results. In ths paper, frst theoretcal performance analyss of an atmospherc FMCW radar ncludng the effects of range- Doppler ambguty, parallax typcal for two-antenna radar systems, and near-feld operaton are dscussed. A typcal system performance s then llustrated wth data collected durng feld experments by the hgh-resoluton S-band FMCW radar descrbed n [7]. FMCW radar sgnatures of atmospherc targets detectable at S-band frequences have been analyzed by usng both qualtatve morphologcal nformaton and quanttatve backscattered power nformaton from clear-ar refractve ndex turbulence.

2 130 T. INCE, FMCW RADAR PERFORMANCE FOR ATMOSPHERIC MEASUREMENTS. Prncples Frequency-modulated, contnuous-wave (FMCW) radars may be thought of as a lmtng case of pulsecompresson radar where the duty cycle of the transmtted waveform approaches 100%. They operate by transmttng a long, coded waveform of duraton T and bandwdth B. The mprovement factor they gan over pulsed radars of equvalent range resoluton s gven by the tme-bandwdth product of the waveform BT, whch s often referred to as the compresson gan. In FMCW systems, ths gan can be very large, exceedng 60 db. Whle several types of frequency codng may be used to yeld the bandwdth B, lnear frequency modulaton s the smplest and most commonly used method n atmospherc FMCW radars. Consder an FMCW radar that transmts constant ampltude lnear FM sgnal of the form s( t) exp( jwt j( a / ) t ), Tt T (1) where w s the radan frequency and a s the chrp rate n rad/s. The echo from an atmospherc target s essentally a delayed, attenuated, and possbly Doppler-shfted replca of the transmtted sgnal. The echo s demodulated by mxng t wth a porton of the transmtted sgnal and lowpass flterng the result. The resultng beat frequency for a pont target at range R 0, movng at radal velocty u r, s gven by ur R0 4ur fr() t f ft c c () where s the electromagnetc wavelength and f a / B / T s the chrp rate n Hz/s. Here, the frst term represents the Doppler frequency shft, f D, due to radal moton, and the second term represents the shft due to the nomnal range of the target, whch s exploted prmarly by the FMCW radar. The fnal term represents defocusng due to the dlaton of the reflected sgnal s bandwdth due to the dependence of Doppler frequency to carrer frequency. For lower atmospherc veloctes, the effect of the last term on the bandwdth of the echo may be safely gnored. Thus, for the case of statonary radar and targets, the beat frequency s lnearly proportonal to range. Sgnal processng of the echo usually nvolves matched flterng, whch s most commonly mplemented for all ranges smultaneously through spectral analyss va an FFT algorthm. In ths case, the output of the matched flter, whch gves the response of the lnear FMCW radar to a movng pont target, can be expressed as D 0 0 / sn f DT RR / R yr ( ) f T RR R where f D s the Doppler frequency, and R = c /(B) s the expected range resoluton for a transmtted bandwdth (3) B ft. It s worth notng that ths result s equvalent to an mpulse response of lnear FMCW radar. For FMCW Doppler radar, Doppler nformaton can be retreved on a sweep-to-sweep bass by analyzng the sequence of echoes from a partcular range, as dscussed by Strauch et al. [1]. In ths case, the samplng frequency s the recprocal of the sweep perod T, the Nyqust Doppler frequency s 1/T, and resultng n an unambguous Doppler velocty nterval of u r / 4T assumng that range measurement errors due to Doppler can be gnored. Conventonally, two-dmensonal FFT s performed on receved sgnals to obtan range and Doppler frequency (velocty) spectrum. For a bstatc FMCW radar, the receved mean power from a dstrbuted atmospherc target of unform reflectvty for crcularly symmetrc Gaussan shape antenna patterns, s gven by [9] P R PGG t t r 1 R (4) 51ln R where P t s the transmtted power, G t and G r are transmt and receve antenna gans, Θ 1 s the one-way 3 db beamwdth, R s range resoluton, and s radar wavelength. To better estmate from the measured echo power at the output of recever, the radar system must be calbrated. Snce the fluctuatng refractve ndex n depends lnearly on fluctuatons of temperature and water vapor mxng rato, Wyngaard et al. [10] have shown that refractve ndex structure functon parameter C n can be expressed n terms of the temperature (C T ), water vapor (C Q ), and jont CTQ structure functon parameters as C n a CT abctq b C (5) Q where the coeffcents a and b depend on the wavelength and the nature of the radaton. Based on Tatarsk s theory of electromagnetc wave propagaton n a turbulent atmosphere [11] and Ottersten s work n hs 1969 landmark paper [1], clear-ar radars can estmate C n from radar backscattered power wthn scatterng volume. For Bragg scatterng from refractve ndex fluctuatons due to homogeneous, sotropc turbulence, s commonly related to C n by Ottersten well-known equaton: (6) 1/ C n. Ths equaton assumes that the Bragg wavenumber, k B = 4 / les wthn the nertal subrange. Note that structure functon parameters are defned as ensemble average, hence they vary smoothly n tme and space. In practce, such averagng s performed over space or tme assumng ergodcty. As the condtons for ergodc hypothess are generally not met n atmospherc condtons, the radar estmated values of C n often have statstcal scatter both temporally and spatally. In general,

3 RADIOENGINEERING, VOL. 19, NO. 1, APRIL mcrowave radar observatons of the clear-ar atmosphere consst of Bragg scatterng from refractve ndex turbulence and Raylegh scatterng from partculates such as nsects, dust, etc. Therefore, for S-band radars, Bragg scatter from clear ar depends much less on the wavelength of the radar than that of Raylegh scatter ( -4 dependence) by such arborne partcles. 3. Performance Analyss 3.1 Range and Doppler FMCW radar performance characterstcs, such as range-doppler couplng, can be seen from analyss of (3), whch s also ambguty functon for lnear FMCW sgnal. The presence of both range and Doppler terms n the argument of the snc functon llustrates the effect of target moton on the radar s ablty to locate. Fg. 1 shows a typcal two-dmensonal tme delay (range) Doppler (velocty) ambguty surface for a lnear FMCW sgnal wth tme-bandwdth product of As seen from Fg. 1, maxmum unambguous Doppler can be ncreased (by decreasng sweep perod) at the expense of range ambguty, or alternatvely ncreasng maxmum range results n Doppler ambguty. By rearrangng the terms n the argument n (3), the apparent range of the target can be expressed as R app = R 0 f D TR, where t s easy to see that range mslocaton by one resoluton cell occurs when f D T = 1, or u r = ± / T, whch also corresponds to the Nyqust velocty nterval for FMCW Doppler radar. Therefore, targets wth unambguously measured veloctes are msregstered by no more than one half a resoluton cell, or msregstraton occurs when target veloctes are alased. For example, for an FMCW radar system operatng at 3 GHz wth a sweep tme of 50 ms, targets wth radal veloctes wthn ±0.5 m/s are regstered properly. Addtonally, the coherence of the atmospherc target durng the sweep nterval wll lmt range resoluton of lnear FMCW radar. For complex movng targets and for volume scatterng, the coherence tme (or the recprocal of the Doppler spectral wdth) of the echo wll lmt resoluton. A dstrbuton of Doppler veloctes observed over an ntegraton tme, T, wll yeld a dstrbuton of apparent ranges. The resultng rms spread n range s determned by the transformaton of the Doppler spectrum to the range doman usng the relatonshp R app = R 0 f D TR, R f T R (7) where f s the Doppler spectral wdth of the echo. From ths relaton, t s apparent that range resoluton and senstvty are optmzed by matchng the sweep tme to the recprocal of the Doppler bandwdth of the echo. In ths case, the range spreadng s equal to the range resoluton, and the entre Doppler spectrum s confned to one range bn. No mprovement n senstvty or n resoluton s acheved by ncreasng sweep tme beyond ths value, as the resultng echo smply spreads to adjacent range bns. To maxmze resoluton and senstvty, t s desrable to make both bandwdth and sweep tme as large as possble. The effectve value of sweep tme s however constraned by the coherence tme of the atmospherc echo. For example, a samplng volume wth rms radal velocty of 1 m/s has a spectral wdth of 0 Hz at 3 GHz mplyng a coherence tme of approxmately 50 ms. Fg. 1. The ambguty surface for a lnear FMCW sgnal wth a tme-bandwdth product of Parallax and Near-Feld Operaton From the weather radar equaton (4), the receved mean power can be correctly estmated only f radar targets are n the far feld of antenna, that s R > D /, where D s the dameter of the antenna. Addtonally, for bstatc FMCW radar employng two spatally separated antennas, a correcton of the receved power s necessary at near ranges to account for the reduced beam overlap. For Gaussan shaped beams algned wth ther axes n parallel, the antenna parallax functon, or fractonal beam overlap s gven by [7], C p R d exp ln 1 R where d s the separaton dstance between transmt and receve antennas, and Θ 1 s the one-way half-power beamwdth. Note that parallax results n an apparent reflectvty reducton and parallax error of backscattered power becomes sgnfcant wthn the radatng near-feld of the antennas such that assumpton of a far-feld Gaussan beam pattern s not vald. It s also worth notng that the far-feld crteron, R f = D / s based on a conservatve specfcaton of maxmum phase error, sgnfcant effects on the shape of the man lobe are not evdent untl R R f / 4 [13]. Based on the unversal near-feld reflectvty correcton [14], 1 db reducton n reflectvty at R f / 4 s ndcated, and at closer ranges (R < R f / 4) near-feld gan (8)

4 13 T. INCE, FMCW RADAR PERFORMANCE FOR ATMOSPHERIC MEASUREMENTS Fg.. S-band FMCW radar profler mage showng 3.5-hour record of the ABL durng CASES-99 experment on 6 October begnnng at 14:7 CDT. reducton becomes much more sgnfcant. Snce at closer ranges the beam shape s no longer approxmately Gaussan and s strongly dependent upon the partcular antenna desgn, t s necessary to apply approprate reflectvty correcton for parallax and near-feld gan reducton dependng upon the parameters of radar system. Note that most atmospherc FMCW radars employ two spatally separated antennas because of the need for hgh solaton (~100 db) between the transmtter and recever. For the parameters of typcal S-band systems, t can be shown that wthn the near-feld range of the antennas, parallax has the domnant effect on reflectvty. 4. Expermental Results Data collected by the Unversty of Massachusetts hgh-resoluton FMCW radar durng recent feld experments s used to llustrate system performance and analyze radar sgnatures of atmospherc targets detectable at S-band frequences. Detaled descrpton of ths system and data processng can be found n [7]. The S-band FMCW radar system mplements an nternal calbraton loop to perform calbraton of the atmospherc echo and estmate volume reflectvty. Fg. shows one day contnuous radar record of durnal cycle of the ABL begnnng at 14:7 local tme (CDT, 19:7 UTC). The radar echo s expressed n terms of the logarthm of mcrowave C n obtaned usng (6), however, ths representaton s only meanngful for the clear-ar component of the backscatter descrbed by the Bragg scatterng mechansm. In addton to dstrbuted Bragg scatter from clear ar, Fg. shows strong pont echoes, whch are n ths paper assumed to be entrely due to Raylegh scatterers. It s worth notng that the dstrbuton of Raylegh scatter n reflectvty tme-heght mage appears to reveal qualtatvely addtonal boundary layer structure not otherwse detectable n S-band. However, the effect of much stronger Raylegh echo (due to much stronger wavelength dependence, 4 as opposed to 1/3 for Bragg scatterng) on quanttatve backscattered power nformaton s adverse. Wth hgh spato-temporal resoluton capablty of FMCW radar, by reducng tme averagng to below 1 s n Fg., t becomes possble to see undulatons of O(10 m) n the radar echo as a consequence of Doppler-nduced range measurement error due to the flappng of brd s wngs. It s estmated that vertcal veloctes of atmospherc echoes n general wll contrbute msregstraton of about one range bn at most. From Fg., four-hour tme perod of convectve ABL (between 14:30 to 18:30 local tme) s extracted to perform quanttatve analyss of radar reflectvty. In ths case, the collocated radosonde (operated by NCAR/ATD) measurements of temperature and humdty show typcal characterstc of convectve ABL bounded above by dry ar. In the three panels of Fg. 3 respectvely reflectvty, Doppler (vertcal) velocty, and the correlaton coeffcent of successve echoes for one-hour of convectve ABL are shown. The latter two products are the result of the pulsepar processng [9] averaged over 0 pulses (~1 s averagng). The reflectvty mage shows that ntally sgnfcant Raylegh backscatter s observed both above and below the cappng nverson whch peaks near 1000 m alttude at about 17:00 local tme. After ths tme, both the Raylegh scatter and the dstrbuted Bragg scatter below the nverson decrease sgnfcantly, and the strong echo at the top of the boundary layer dsappears. The velocty mage whch s derved from the phase of the sngle-lag covarance shows structure for some, but not all of the clear-ar echo (due to velocty alasng). The sngle-lag covarance panel shows very hgh (near unty) correlatons for the Raylegh scatterng whle the correlaton coeffcent for the Bragg scatterng s relatvely lower on average (due to larger spectral wdth of clear-ar echo). The fne space-tme resoluton capablty of the FMCW radar enables solaton of Raylegh scatterers from dstrbuted Bragg scatterng. To dscrmnate the dstrbuted Bragg backscatter from partculate scatter, a postprocessng method based on the correlaton coeffcent between successve sweeps (averaged over the 1 s nterval) s appled to tme-seres of backscattered power. As shown from analyss of sngle-lag correlaton coeffcent (n Fg. 3), the correlatons for solated partculate backscatter are sgnfcantly hgher than those for dstrbuted clear-ar

5 RADIOENGINEERING, VOL. 19, NO. 1, APRIL Fg. 3. Frst hour of convectve ABL echo from Fg. showng reflectvty, Doppler velocty, and sngle-lag correlaton coeffcent. backscatter. Accordng to ths method, magntude of the sweep-to-sweep correlaton coeffcent s compared to an emprcally determned threshold and hgh-correlaton ponts (due to Raylegh scatter) are removed. After some expermentaton on the reflectvty data, a fxed threshold of 0.8 s found to be the approprate choce snce a much hgher or lower threshold results n an ncrease n the probablty of false alarm. The removed solated pont target echoes are then flled wth the best estmates usng the least-squares estmaton whch uses neghborng Bragg backscatter ponts wthout sgnfcantly affectng the statstcs of the atmospherc clear-ar echo [15]. Ths processng allows estmaton of atmospherc component of the clear ar backscatter. In Fg. 4, the computed vertcal profles of mean C n (estmated from postprocessed reflectvty) for four consecutve 60-mn segments are plotted aganst heght. The small dotted profles show the correspondng mean reflectvty over the same ntervals ncludng both Bragg and Raylegh echo. Gven the mean horzontal wnds, the vertcal profles are roughly equvalent to a streamwse spatal average over approxmately 10 km. The vertcal axs of each profle s scaled by the boundary layer depth, z whch can smply be obtaned from the postprocessed reflectvty peak. In ths case, FMCW radar estmates of C n can be used to quanttatvely test theoretcal predctons on the ABL. In the free-convecton boundary layer, C n s expected to follow a z 4/3 power law, where z s the heght above ground level [16]. From Fg. 4, radar estmated C n ncreases wth heght nsde convectve mxed layer (between 0. z and 0.9 z the mean reflectvty follows a z /3 profle, a dscrepancy of z ) wth an expected sharp turbulence nduced peak at the top of the mxed layer (~z ). Note n ths case strong ground clutter affects C n measurements below 0.1 z. Ths observed dscrepancy n C n from ts mxed-layer predcton may be due to entranment effects, whch can be predcted by a model developed by Farall [17] based on a top-down and bottomup dffuson approach n the entranng, convectve boundary layer. Accordng to Farall s model, the structure functon parameter profles for the convectve boundary layer n the regon 0.1 < z / z < 0.9 can be expressed as where /3 Cc z hb( z/ z) Rchtb( z/ z) Rcht( z/ z) (9) h ( z / z ) A ( z / z ) b c, 4 / 3

6 134 T. INCE, FMCW RADAR PERFORMANCE FOR ATMOSPHERIC MEASUREMENTS Fg. 4. Vertcal profles of estmated mean C n (large data ponts) obtaned from post-processng over four consecutve 60-mn perods. The small dotted profles show the mean reflectvty ncludng both Bragg and Raylegh echo. The dashed lnes are normalzed profles of C n based on the Farall s model wth specfc R c and A c values. 1 1/ 1 z / z 0.57( z / z ), htb( z / z ).15 h ( z/ z ) 7.15( z/ z )(1 z/ z ), t and c s temperature (T) or water vapor (Q). In Fg. 4, by choosng approprate values for R c and A c parameters (respectvely top-down and bottom-up components) of the model, the predcted normalzed C n profles s ftted to the vertcal profles of mean reflectvty from expermental data. Addtonally, theoretcal models on the shape of the reflectvty profle n the nverson regon have been developed by Wyngaard and LeMone [16]. The exstence of the reflectvty peak s known from n stu measurements [16] and from large-eddy smulaton [18]. In Fg. 5, logvarance of estmated C n over consecutve 60-mn perods s compared aganst radosonde-based potental temperature profles. It s worth notng that much hgher varance occurs across the top of the convectve boundary layer (correspondng to the heght of the strongest potental temperature gradent) due to strong turbulence, and peak C n varance ncreases as the potental temperature jump across the nverson ncreases. 5. Concluson In ths paper system performance of FMCW radar detecton of atmospherc targets at S-band frequences have been dscussed. In partcular, the effects of non-zero Doppler veloctes and fnte coherence of the atmospherc echo on both spatal resoluton of FMCW radars and on Doppler estmaton are presented. Parallax errors n reflectvty and near-feld operaton for S-band FMCW radars are also consdered. Addtonally, for the clear-ar atmosphere measurements, the S-band radar s senstvty to Bragg and Raylegh scatterng and the effect of Raylegh scatterers on vertcal profles of mean radar reflectvty have been nvestgated. Due to fne spatal and temporal resoluton capablty of FMCW radars, t s shown that Bragg scatterng from refractve ndex turbulence can be dscrmnated from Raylegh scatterng by usng correlaton coeffcent based post-processng. Expermental data collected by the hgh-resoluton atmospherc FMCW radar s used to perform analyss of S-band radar sgnatures of atmospherc targets and to quanttatvely test theoretcal predctons on the convectve atmospherc boundary layer.

7 RADIOENGINEERING, VOL. 19, NO. 1, APRIL Fg. 5. The log-varance of estmated C n over four consecutve 60-mn perods (left), and correspondng potental temperature profles measured by radosonde (rght). References [1] STRAUCH, R. G., CAMPBELL, W. C., CHADWICK, R. B., MORAN, K. P. Mcrowave FM-CW Doppler radar for boundary layer probng. Geophyscal Research Letters, 1976, vol. 3, no. 3, p [] RICHTER, J. Hgh-resoluton tropospherc radar soundng. Rado Scence, 1969, vol. 4, no. 1, p [3] CHADWICK, R. B., MORAN, K. P., STRAUCH, R. G., MOR- RISON, G. E., CAMPBELL, W. C. Mcrowave radar wnd measurements n the clear ar. Rado Scence, 1976, vol. 11, no. 10, p [4] EATON, F. A., MCLAUGHLIN, S. A., HINES, J. R. A new frequency-modulated contnuous wave radar for studyng planetary boundary layer morphology. Rado Scence, 1995, vol. 30, no. 1, p [5] HIRSCH, L. Spaced-antenna-drft measurements of the horzontal wnd speed usng a FMCW-radar-RASS. Contrbutons to Atmospherc Physcs, 1996, vol. 69, no. 1, p [6] GOSSARD, E. E. Radar research on the atmospherc boundary layer. Edted by D. Atlas. Boston: Amer. Meteor. Soc., 1990, p [7] INCE, T., FRASIER, S. J., MUSCHINSKI, A., PAZMANY, A. L. An S-band frequency-modulated contnuous-wave boundary layer profler: Descrpton and ntal results. Rado Scence, 003, vol. 38, no. 4, p [8] INCE, T. On performance of S-band fmcw radar for atmospherc observaton. In Proceedngs of the IEEE 15th Sgnal Processng and Communcatons Applcatons. Esksehr (Turkey), 007, p [9] DOVIAK, R. J., ZRNIC, D. S. Doppler Radar and Weather Observatons. nd ed. San Dego: Academc Press, [10] WYNGAARD, J. C., PENNELL, W. T., LENSCHOW, D. H., LEMONE, M. A. The temperature-humdty covarance budget n the convectve boundary layer. Journal of Atmospherc Scences, 1978, vol. 35, no. 1, p [11] TATARSKII, V. I. Wave Propagaton n a Turbulent Medum. New York: McGraw-Hll, [1] OTTERSTEN, H. Atmospherc structure and radar backscatterng n clear ar. Rado Scence, 1969, vol. 1, no. 4, p [13] HANSEN, R. C. Mcrowave Scannng Antennas, vol. 1. Ed. by Hansen, R. C., Los Altos (USA): Pennnsula Publshng, [14] SEKELSKY, S. M. Near-feld reflectvty and antenna boresght gan correctons for mllmeter wave atmospherc radars. Journal of Atmospherc and Oceanc Technology, 00, vol. 19, no. 4, p [15] KAY, S. M. Fundamentals of Statstcal Sgnal Processng, Volume 1: Estmaton Theory, New York: Prentce-Hall, [16] WYNGAARD, J. C., LEMONE, M. A. Behavor of the refractve ndex structure parameter n the entranng convectve boundary layer. Journal of Atmospherc Scences, 1980, vol. 37, no. 7, p [17] FAIRALL, C. W. A top-down and bottom-up dffuson model of Ct and Cq n the entranng convectve boundary layer. Journal of Atmospherc Scences, 1987, vol. 44, no. 6, p [18] MUSCHINSKI, A., SULLIVAN, P. P., WUERTZ, D. B., HILL, R. J., COHN, S. A., LENSCHOW, D. H., DOVIAK, R. J. Frst synthess of wnd-profler sgnals on the bass of large-eddy smulaton data. Rado Scence, 1999, vol. 34, no. 6, p About Author... Turker INCE receved the B.S. degree from the Blkent Unversty, Ankara, Turkey, n 1994, the M.S. degree from the Mddle East Techncal Unversty, Ankara, Turkey, n 1996, and the Ph.D. degree from the Unversty of Massachusetts, Amherst (UMass- Amherst), n 001 all n electrcal engneerng. From 1996 to 001, he was a research assstant at the Mcrowave Remote Sensng Laboratory, UMass-Amherst. He worked as a desgn engneer at Aware, Inc., Boston, from 001 to 004, and at Texas Instruments, Inc., Dallas, from 004 to 006. In 006, he joned the faculty of Computer Scence at Izmr Unversty of Economcs, Turkey, where he s currently an Assstant Professor. Hs research nterests nclude electromagnetc remote sensng and target recognton, radar sgnal processng, bomedcal sgnal processng, neural networks, and global optmzaton technques.