![[~~I~M]Mr~Mli~I~Limlil~I~Llilil~~~ ~](http://data.docslib.org/img/ca9fa2669fcc8ed5fc79956e8d250e8e-1.webp)
-- - . . : " [~~I~m]Mr~mli~I~limlil~I~llilil~~~3 4589 000019829 ~' U.S. DEPARTMENT OF COMMERCE. John T. Connor, "'...... aury
ENVIRONMENTAL SCIENCE SERVICES ADMINISTRATION
Robert M. White. Administrator
Weather Bureau. Geor,ge P. Cressman, Director
TECHNICAL NOTE 46·NSSL.26
Prob i n9 Air Motion by Dopp Ie rAna lysis of Radar,Clear Air Returns Roger M.Lhermitte NSSL, Norman, Oklahoma
NATI9NAL SEVERE STORMS LABORATORY REPORT NO.26
WASH'INGTON, D.C. May 1966 The program at the National Severe Storms Laboratory involves the cooperative participation of many government agencies and other groups. The work reported in this paper\'lasgreatly assisted by sub stantial support from the Federal Aviation Agency ------through interdepartmental agreement No. FA65 WAr -91 .
. ':",'" .~ . . -.' ~ ','
...... , Oklahoma Climatological Survey
TABLE OF CONTENTS
Section Title Page
Abstract 1
1. Introduction .. 1
2. Doppler Radar Method 2
3. Intensity of Target Back Scattering 5
4. Doppler Spread 11
5. CAR Horizontal Motion Estimate 14 6. Estimate of Vertical l1otion 22 7. Study of a Low-Level Jet from the Doppler Radar Data 23 8. Doppler "Wind" Speed Variance and the Scale of Horizontal Eddies 29
Correlation between Target Motions at #, Several Levels 31
10. . Conclusion 33
Acknowledgments 33
Appendix·· 34 References 36 ..
PROBING AIR MOTION BY DOPPLER ANALYSIS OF RADAR CLEAR AIR RETURNS
Roger M. Lhermitte National Severe Storms Laboratory Norman, Oklahoma
ABSTRACT A Doppler radar has been used in central Oklahoma to probe the motion of invisible targets usually referred to as "angels fI • The large c].ensi ty of targets detected on certain days suggests the presence of a dense atmospheric "planktontt drifting with the air. Uniform motion for all the targets in the area surveyed by the radar beam is confirmed by.the systematic pattern of target radial motions as a function of radar beam azimuth. Target hori zontal motion direction and speed are derived from the radial . velocitY-,.;lzimuth patterns and interpreted as horizontal wind. The small vertical motion of targets is also estimated f·rom the. '. data. This technique is applied ·to the analy~is of wind variance and the study ofa low-level jet.
1. INTRODUCTION It has been known for years that radar echoes are· often ob served from . clear air when. no targets can be seen by the naked eye .. The invisible targets have been called "angelsll but this paper re- fers. to them as '·'c ." . There 'is no doubt that in some instances CAR has been def;i':' niteiy· associated Wi.th migrating birds. On the other hand, it has also been demonstrated that turbulent, layers in clear air create radar return (Hardy at a1. [13J) .', . '. . " . " .. . Regardless ot the nature of the targets,lf they gre smalL 2 and have a low inertia, their motion relative to the surrounding air should be negligible. If the radar return is due solely to the at mosphere itself, as in the case of localized high variance of the index of refraction, air motion and apparent t.arget motion should be identical. Therefore, continuous observation of CAR target veloc ities should lead to an effective probing of air motion in the al titude range wh~re the targets· are detected. It has been found that CAR is often detected, in central Okla homa, in an atmospheric layer which extends from slightly above the ground to an altitude which ranges between'a few hundred meters and 2 km. Detailed observations of CAR motion have, therefore, been conducted with an "X" band Doppler radar. The Doppler radar pro vides a very quick estimate of· the radial motion of any detected target and, with an appropriate scheme of azimuth and range scan ning, horizontal and vertical components of the motion at several altitudes can be derived from the observation of the radial speed of a large number of targets. . . / The Doppler radar has been operated almost continuously during i several months and CAR motion has been effectively observed during , more than 1,000 hours, at several altitudes ranging from 300 to 2 km. ; \ The intensity of the C~R signals has also been recorded. Although , the data have not been completely analyzed yet, this paper presents an interesting case study of the motion of CAR during the 30-hr. \~ period from 0700 CST Ju·ne. 26, to 1300 CST June 27, 1965. This wa.s .. a clear summer day. in central Oklahoma. Thermal convection was followed by a nocturnal lOW-level jet stream. j Although some characteristics of the back scattered signal are discussed here,our main purpose is to relate the target motions to ~ the wind. The origin of the radar returns will b~ explored later wi th the aid of data collected during several months of operation. ·At this time, the works of Browning and Atlas [7J and Hardy, et al. j [13J can be noted for discussion of CAR origins. 2. DOPPLER RADAR METHOD Some past attempts to derive winds from CAR motion have been based on the use of automatic tracking radar to measure target vel ocity (Roelofs [23J). On some occasions the horizontal target speed was derived by relating the dUration and altitude of individ;;' ual radar echoes to thebeamw.Ldth and wind speed assuming the scat terers to be point targets transported through the stationary beam with the wind (Plank [22J). While these studies have generally concluded that the targets are small relative to the beam and appear to be wi nd borne , no :firm conclusions could be reached as to their . adequacy as wind tracers since the motions of some targets were 9losely related to that of the. 'wind and others were not. This vari ability may be attributed to the fa.ct that related wind measurements . were made at different times and locations, and that 'CAR motion was determined from only a small number of measurements. 3 The Doppler radar techniques present~d in this paper offer an improved means of observing CAR motion and determining its correla tion with the wind. Such techniques require only a few milliseconds to obtain accurate Doppler frequency estimates. Moreover, with'an adequate data acquisition scheme, statistics of motion can be deter mined for all the targets around the radar. The atmospheric volume explored by this technique is defined by an area of several square miles and a vertical extent of approximately 2 km, If the radar beam is fixed, the number of targets observed during a certain time depends on both their advection and their density. However, with radar beam scanning, the number of targets observed during a certain time does not involve advection, and is only a function of the vol ume sca.nned. Scanning provides observation of a gr.eater number of targets and, therefore, improves the reliability of the statistics of motion derived from the observations. ~t must be noted that the scanning speed is limited by the fact that the target must remain in the radar beam for at least a few milliseconds, in order to avoid the production of spurious. Dop pler'frequeneies related to the Fourier transform of the signal time function. On the other hand, the probing technique is optimized when the total time for exploration is no longer than that required to observe a fresh supply of targets. For probing the horizontal air motion, the radar beam is scanned in azimuth at a fixed elevation angle, 9.. The altitude at which Doppler observations are made is determined by sampling the signals in a narrow range gate at range R and altitude R sin 9 • This is equivalent to exploring a circuJ.ar region at an altitude and horizontal radius defined by the selected range and the radar beam elevation angle. The radial motion which is derived from the Doppler frequency shift is represented by the projection of the target motion vector on the axis of the radar beam, assuming it to be narrow. Fqr example, assume that the targets are at the same alti tude and mOving in the same direction with identical speeds. The target radialv$locity along the beam, VR, is resolved into horizontal and vertical components Vh and Vz according to: (1) . where 9 is the elevation angle, and t3 is the difference between the azimuth of the wind vector and the azimuth of the radar ·beam. Equation (1) and the"associated'method is similar to that presented by Lhe~tte and Atlas [19J, Lhermitte [17], Boucher et al. [6J, for the study of precipitation particle motion. The work contained in this paper is based on CAR speed meas- 4 urements obtained using the above method in a study of atmospheric motion in central Oklahoma. This scheme has been found to be ade quate when a large number of targets is observed during a single azimuth scan. An experimental 1!X" band pulse Doppler radar, which has been described elsewhere (Lhermitte & Kessler [20J) has been used to ob serve and record target radial velocity. The essential radar char acteristics are: peak power = 6 kw.; receiver noise figure = 7 db.; 0 antenna gain = 58 db.; antenna pencil beam width = 0.65 ; ~ulse repetition.rate adjustable from 400 c.p.s. to 10 kc. sec.- , and pulse duration adjustable from 0.25 sec. to 2 sec • . The system is fully coherent with a frequency or phase stabil ity leading to a Doppler resolution greater than 0.01 m sec.-l but limited in practice to 0.2 m. sec.-l by the frequency analyzer capa bility discussed below. The signal, which contains information con cerning the phase (target position) and amplitude (target radar cross section), is gated in radar range arid applied to a multi-channel I frequency analyzer whose output represents the target Doppler spec ) trum in real time. The 3-db. bandwidth of the filters, which act a velocity gates, is 0.05 m. sec.-I, and their spacing is 0.2 m sec.-1 It is interesting to note that the filter frequency characteristic has a steep slope such that the signal ou.tput is attenuated by 40 db. for velOCity deviation of ± 0.1 m. sec.-l from the central frequency of the fi~ter. This is a very important feature which allows great \ accuracy in observing the motion and motion variance of the targets._ l Or;e hundre~ filt:rs are used to cover a velocity range of 20 m. ~Ic. , w~th the f~rst f~lter .selectable at 0, 20, 40, 60, or 80 m. sec. For th: work presented here, the fr~~uency analyzer covered the vel- ocity ~nterval from 0 to 20 m. sec. . ... As is well known, the maximum radial velocity vlhich can be ob served without ambiguity by a pulse-Doppler radar increases with pulse repetition frequency (PRF), but a high PEP limits the maximum target range which can be observed without ambiguity. Thus a Dop pler radar capable of measuring high velocities can not separate targets at long ranges from those'nearby. ,This problem has no im portance in the present case because all echoes have been received from nearby targets. During all the observations discussed in this paper, .the radar PRF is 4 kc. sec.-l This provides a non-ambiguous maxi~~range of approximately 35 km. and a maximum non-ambiguous target radial velocity of 30 m. sec.-l with the Doppler processing scheme used.1 A higher PRF would provide performance exceeding.that of the 100-channel frequency analyzer. It should be noted, however, that the·elevation angle of the radar beam also determines the J!lax imum horizontal speed which can be measured. With·a 60 0 elevation ,1The frequency range of unambiguous measurement is limited to PRF/2 for the Doppler signal processing used in this work. See Lnermitte [18] for more details. 5 angle, the 20 m. sec. -1 capacity of the frequency analyzer is attained for horizontal speeds of 40 m. sec.-l As mentioned above, azimuth scanning increases the number, of targets observed during a given time and the reliability of esti mates-of horizontal wind direction and speed. This procedure also allows the radial velocity of the targets to be displayed as a func tion of their azimuth. This is accomplished by applying the output of the frequency analyzer to the modulation electrode of a cathode ray tube, whose rectangular scanning axes are controlled by the frequency scale and the radar beam azimuth. In this way, the dis- played position of any target is controlled by its radial velocity and azimuth (VA display or 'VAD) • During azimuth scanning, a pat tern or target radial motion as a function of azimuth is reproduced directly on the display. This scheme does not provide observations of individual targets if the target 'concentration is large, but gives an adequate estimate of the average speed of numerous tar gets and the width of their speed distribution. , The VA display i's illustrated in figures la and lb, where one notices the large number of targets which contribute to a velocity azimuth pattern. Only the absolute value of the radial speed is dispIayed in the present case, with no discrimination of the Doppler sign'indicated in equation (1). Therefore, the negative portion of VR, due to the negative sign of the cosine term, is folded over. This effectively doubles the velocity range covered by a single frequency analyzer. The theoretical cosine pattern can be easily recognized in all the di'splays which are obtained at different alti tudes. Notice the two maxima which cor~espond to the downwind and upwin<;:l points, and the cross wind zero radial velocity; from these pOints, target horizontal speed and direction can be estimated. Ver tical motion can also be estimated by assuming that any difference between the two maxima is due to the radial component associated with a uniform vertical air motion. One also notices a spread of the radial motion, as well as departures of the mean radial motions from the true cosine pattern indicated by equation (I) ,but usually only at the lowest levels. The nature of the pattern, and the informa tion on air motion which can be extracted from i tare discussed in greater detail in the following sections. 3. INTENSITY.OF TARGET BACK SCATTERING , The range gating system used, toacquire'dat~ permits the ra dar receiver gain to be 'controlled automatically by the amplitude of the signals received. The automatic gain control therefore re';; duces the amplitude fluctuationsof~he signal applied to tJ1e in put of the Doppler spectrum frequency analyzer, 'arid optimizes the operation of the analyzer by matching the amplitude range of the signal to the dynamic range of the an~lyzer. In this way, spec trum harmonics due to signal distortion are ~voided. When the antenna beam is scanned continuously according to the scheme discussed previously,a large number of targets is 6 20 18 16 , "j I u U U Q) Q) Q) III III III E E E >- 10 > > I- I- I- u U U 8 o o 0 -J -J 6 -J 6 W W W > 4 > 4 > 2 2 Ou--J__ ~ __L--L __ L-~ 0 240 180 120 60 0 300 240 180 120 60 0 300 240180 120 60 0 300 Azi.(degrees) Azi.(degreas) Azi.(degrees) 171 m. 293 m. 394m. -68 dbm. -78 dbm. -73 dbm. 20 , 18 18 -, 16 I U '. Q) 14 ~ 14 III III ....E 12 E 12 } >- 10 > .1- I- U 8 u 0 o \ -J -J 6 w 6 w > 4 > 4 \ 2 2 0 0U-~ __-L __ L-~ __~~ 240 180 12060 o 300 240180 120 60 0 300 Azi.(degrees) Azi.(degrees) 590m. 685 m. -75dbm. -92 dbm. j u j Q) U III. •III ....E. E >- >- t: I- u u 0 0 -J ..J W W > > 240 180 120 60 0 300 240180 120 60 0 300 Azi. (degrees) Azi. (degrees) Azi. (degrees) 780 m. 876 m. 940 m. -93dbm. -95dbm. -98dbm. Figure lao - Velocity-Azimuth Displays showing the CAR radial velocity . at several altitudes. Radar beam elevation angle, 20°. Radar site Norman, Okla. Time 2023 to 2031 CST, June 26, 1965. Signal mean intensity is indicated in -dbm. 7 .. u I. CD U CD en lit E E >- > ~ t: u u 0 o ...J ...J ILl IIJ > 4 > OU-__~~ __~ __L-~~ 240 ISO 120 60 0 300 240 ISO 120 60 0 300 60 0 300 A zi. (degrees) Az i. (degrees) Az i. (dOQfUS) 41Sm. SISm. 740m. -S4dbm. -83 dbm. -89dbm. i" ,... U I. CD U en CD ." E E >- > ~ > ~ ~ u u u 0 0 0 ...J ...J ...J ILl LIJ ILl .. > > > 240 ISO 120 50 0 300 240 180 120 60 0 300 240 ISO 120 60 0 300 A zi. (deorees) Azi.(dagrus) Azi. (degrees) 866m. 987m. 1111 ffi. -S5dbm. -88 dbm. -86dbm. IS , , ~ 14 u'. u en • •en E E E > > > ~ ~ ~ u u u o o o ...J ...J ...J IIJ IIJ IIJ > 4 > > 2 240 ISO 120 60 0 300 240 ISO 120 60 0 300 240180 120 60 0 300 Azi.(degrees) Azi. (degrees) Azi.(degrees) 1233m. 1360m. 1570m. -87dbm. -S6dbm. -90dbm. Figure lb. - Velocity-Azimuth Displays showing the CAR radial velocity at several altitudes. Radar beam elevation angle, 60°. Radar site Norman, Okla. Time 0528 to 0537 CST, June 27, 1965. Signal mean intensity is indicated in -dbm. 8 examined. It has been observed that during intense CAR activity the density of these targets may be more than one per beam-width and perhaps more than 300 to 400 during complete azimuth scan, cor responding to a high target density of about one per 1,000 cubic meters. This is approximately 10 times larger than the target den sity reported by BroWning and Atlas [7] in Massachusetts in Septem ber but agrees with the direct insect counts by Glick [llJ in the southern United States. We assume a point target characteristic, which seems jus.tified by the narrow Doppler spectrum observed from these targets. Then every target generates a signal which varies in amplitude as the target enters and leaves the radar beam as a result of scanning. If the scanning speed is rapid compared to the motion of the targets, the echo power PI' varies with time in proportion to the antenna gain function and the radar equation as (2) I "}I where Pt is the transmitted power, A is the radar wavelength, R the ( target range, ~ is the target radar cross section (assumed constant), .:.~ Go is the antenna gain in the beam aXiS, and 9 is the angular posi tion of the target in elevation angle with respect to the beam axis. \ 90 , {30 respectively are the 3-db. poin.ts for elevation and azimuth angles and.1L is the angular speed in azimuth of the antenna. This assumes a Gaussian angular shape for the radar beam which closely II represents the actual beam shape of the antenna used in this work if the side lobes are neglected. Since the frequency analysis scheme applies to th~ whole Signal time function and includes the Four~ertransform of the signal amplitude, as well as Doppler, f~e ~ quency components are generated by the envelope of the signal time function. This problem is obviated by scanning so slowly that spurious frequency components are outside the Doppler frequency range of interest. The Signal at the output of the radar receiver fluctuates con stantly as targets enter and leave the radar beam, and at any time may represent the contributions of one·or mO:r:'e targets. Since it is difficult, in the case of large target concentration, to charac terize CAR activity in terms of individual target cr9ss-sections, . it·is·appropriate to observe the mean of the received signal related to the contribution of several targets. This signal, which contains limited fluctuations, is also used for automatic receiver gain con trol and is continuously recorded. It must be noted that a conse quence of the averaging process is that the received power is pro portionalto both the back scatter cross section and· target concen tration. The average signal is thus proportional to the effective scattering volume defined by radar pulse length and the area scanned during the effective signal integration time, which is several sec onds for the work reported in this paper. Therefore, the average 9 signal intensity is proportional to the inverse square of the radar range as it is for.other distributed targets. The average signal due to the contribution of several targets has been continuously recorded as a function of antenna azimuth. Systematic variations of the average can be attributed to local changes of target density or to anisotropy of target shape and cross section. For the data reported in this paper, it has been. observed often that the maximum signal intensity occurs at right angles to the motion vector. The average intensity obtained during single azimuth scans is a measure of the signal intensity at a particular altitude and time. Arithmetic averages of this quantity have been made for periods of several hours at steps of altitude and range. The results are plot 0 0 ted in figures 2 and 3, for two elevation angles, 20 and 60 • I JUNE 26.1965 JUNE 26.1965 -70r--r.~~r+-r+------+----~--4--- -70~·--+-~4-4-~------~----~~---- CD0942 TO 1206 CST 02342 TO 0314. CST @1217 TO 1700 CST @0330 TO 0644 CST @1713 TO 1804 CST @06~8 TO II ~7 CST -75r-~~~~~~~~ __~~~~--~- -75~-+-4-4-4~~~-----4----~--~--- @1906 TO 2100 CST E .0 -0 ~ -80r--P~~~~~~~---4----~--~- en z w I- ~ -851---+---+~-+-+-~+--~J.. ...J Z C)"' en -90r--r~~-4-r~~--~~~--~--~-- j -100 '--...... ~~~--'-...L.-___--l~_~~Io.....L._ -IOQL..,o... ;,.;.J,..--'--'--'-..l....L-_----II..--...... J.-3.....J..-_ 400 600 800 1000 2000 400. f?00 800 1000 2000 4000 RANGE (meters) RANGE (meters) Figure 2. - CAR signal mean intens -. Figure 3. Same as Figure 2 exce·pt 0 ity, at Norman, Okla., as a beam elevation 60 • function of the radar range. See text for definition of sig- nal mean. Radar beam elevation angle 20 0 • 10 One sees that the 1/R2 law is obtained within 1 or 2 db. with the 60° elevation angle, for a range interval between 500 m. and 2,000 m. However, for the 20° elevation angle during the day, the average relationship is close to the 1/R3 law. The difference with respect to the 1/R2 law can be explained by a decrease of the target concentration as a function of altitude, which is consistent with observations' by Chernikov [lOJ. ' Important time fluctuations of CAR activity were observed at all altitudes. These variations of CAR are shown in figure 4, where the intensity of the 1/R2 range-normalized back scattered signal is ,plotted as a function of time and altitude. One sees that the CAR activity was at a maximum about noon and decreased to a minimum just before sunset. Slightly after sunset, the CAR activity increased sharply at all altitudes and stayed high until after midnight. Observations of the radar ftAft scope revealed that this enhancement of CAR activity during the night was due mainly to an increased number of targets rather than to increased radar cross-sections. 1 After mi~n±gh~the CAR activity decreased slowly and was at a 'minimum at low levels immediately after sunrise. At this time the / I radar cross-sections of CAR increased with altitude to 1600 meters, in contrast to its behavior the previous mid-day. \ I I I I I I I RECEIVED POWER, YR2 INORMALIZED AT R. 500 METERS 1.6 ISZI -90 dbm TO -84 dbm 1.5 ~ -84dbm TO -78dbm 1.4 ~ -78 dbm TO -72 dbm B -72 dbm TO -66 dbm ...E S,R. 1200 1800 2400 0600 1200 , JUNE 26 JUNIi 27 CENTRAL STANDARD TIME Figure 4. - Mean intensity of range normalized CAR signal as a function of time and altitude during the situation presented in this paper. Sunset (SS) and sunrise (SR) are indicated on the time scale. Note·the sharp increaseqf CAR activity after sunset, II No apparent correlation was found between the radar cross section and density of targets and the turbulent air motion dis cussed below. Increases of the CAR activity about sunset have also been reported by Ottersten [2lJ for "dot angels" which are siinilar to the t~rgets reported in this paper. . 4. DOPPLER SPREAD The Doppler data obtained on CAR velocity always reveal a no- . ticeable spectrum width. The total spreai is always large j,n the low levels (approximately 3 to 5 m. sec.- ) and ty~ica.llY decreases with altitude to become approximately 0.5 m. sec.- at the high levels •. Such a spread of velocity is accurately observed in the VAD patterns since the frequency resolution obtained in the processing and display of radial velocity is better than 0.2 m. sec.-l (equiva lent velocity spacing between filters of the frequency analyzer). On the other hand, the contribution of Doppler equipment frequency instabilities to the spread is negligible since the observation of Doppler from trl,le point targets doe.s not reveal any noticeable spectrum width. ';['he Doppler spread is always due to the existence of several scattering centers (targets) moving at different speeds. In the case of point targets having constant shape and size, if the target den sity is so small that only one target is observed at one time, there is no Doppler spread. However, the observed velocity may change from target to target and the whole pattern will have a Doppler spread •. If the target density is large and uniform, several targets are observed at once, there is an effective Doppler spread due to the distribution of their speed, and the targets are no longer seen individually, i.e., distributed target scattering. Therefore, the transition between spread due to the velocity change from target to target and an effective Doppler spread, is merely a matter of the target density. In the case of targets moving with the wind and the existence of a large wind shear, there is a velocity spread due to the wind variation as a function· of altitude, i.e., across the· ver tical depth of the radar beam. This has been discussed by Lhermitte and Atlas [19J in an article on the interpretation of the Doppler spectrum from precipitation particles. In that 'article, it is shown that the contribution of wind shear to the Doppler spread is represented by the projection of the wind shear vector on the axis of the radar beam. This implies that the Doppler spread resulting from wind shear must bea linear function of the cosine of the azi ffiutnangle and should appear in the VAD patterns. In fact, this is . fairly noticeable and a case of strong wind shear is shown in fig ure 5. The effect of wind shear on Doppler spread is also discussed. by Gorelik et ale [12J and Atlas [lJ. . During most of the period reported in this paper, however, the spe,ctrum width was independent of the radar beam azimuth. The observed spread might be tentatively attributed to the sampling of small-scale turbulence which produces a velocity distribution among the targets which trace .t;helocal air motion. 12 -I V .,.,. E 8 >- ~ 6 6 u 0 ..J 4 4 LU > 2 2 , 0 o~ __~~ __~ __~======i I, 240 180 120 60 0 300 240 180 120 60 0' 300 j Azi CdeQrees) Azi. (deQrees) I \, Figure 5. - Effect of Wind shear on the velocity-azimuth pattern. Left 'photograph - Altitude 740 m, time 0520 CST. Strong wind shear of approximately 8 m. sec.-1/IOO m. indicated by the max 0 0 I imum Doppler spread in azimuths 05.0 and 230 • Right photograph - Very small wind shear. \ In the case study which is reported in this paper, it was ob served that the Doppler spread was mostly due to instabilities of the radial motion' from target to target. Average's of the Doppler spread have been computed and the results are shown in figure 6. One sees that the Doppler spread always decreases as a function of altitude. It is greater after noon time and decreases a few hours after sunset. There is only a moderate increase during the night in a region where large wind speed was observed. Figure 7 is a scatter diagram showing l-hr. averages of Doppler. spread and the standard deviation of the wind speed during the same period of time, which will be discussed below. Both the Doppler spread and the wind "speed variance decrease with altitude, and this provides a certain degree of correlation between these two quantities. However, it was observed that during the night, the Doppler spread, whic}{ is smaller than during the day, still decreases uniformly wi th altitude even if the wind speed variance becomes greater. It must be noted that the Doppler spread is always greater at, low altitudes even in the case of very low wind speed. Therefore,a better knowledge of the physical characteristics or physical nature of the observed tar gets is needed to understand and interpret correctly the meaning of the Doppler spread. 13 1.6 t----t-----+----l--...:.---.l-----~- JUNE 26,1965 CST CD 1205 TO 1414} ELEV.A.TION ®2009 TO 2100 " ANGLE 20° 1.4 r------;t-+~-__l- @2341 TO 0222 } ® 0329 TO 0420 ELEVATION ANGLE 60° l @0434 TO 0520 . L 2 t-----If---\--7--I1-- " " 1.0 E ~ lL.I C :l.... 0.8 I- «-l 0.6 0.4 t----I------f--~-~----'--.3iri---_4- o~.. ------~------~------~------~~------~-- o 2 "3 4 5 RADIAL VELOCITY SPREAD,m sec.-I Figure" 6. - CAR Doppler "spl;'ead estiirtates'ave~~g~d during time shown plotted qS a function of altitude. Norma:I1. , Okla., June 26 ,1965. 14 1.5 z 0 • 876 m I-- + 780 m 2.5 3.0 3.5 4.0 SPECTRUM WIDTH Figure 7. - Comparison between Doppler spectrum width and standard deviation of the computed wind. Norman, Okla., June 26, 1965. 5. CAR HORIZONTAL MOTION ESTIMATE Figures la and Ib show typical velocity-azimuth displays ob- . tained from CAR targets at two elevation angles and at several alti tudes. The cosine function predicted by equation (1) is well dupli cated everywhere, and departures are noticeable only for the data' acquired below an altitude of approximately 300 m. Deviations from the cosine function indicate locally variable air motion and are associated with turbulence in the low layers of the atmosphere. The Doppler spread has been discussed in the preceding section; although i·ts origin is not clearly shown, all the data treated here show the Doppler spread to be evenly distributed around a very well defined radial motion mean. Above an altitude of 300 rn. the mean always exhibits the perfect cosine shape predicted by equation (1). These patterns show that the CAR targets have a very uniform motion over large areas and for long pe:clods' of time. It is therefore dif ficult to conceive of patterns like'"figure 1 being generated by tar gets not moving with th.e wind at their altitude. The theory that 15 the targets are tracers for the wind is reinforced by the short-term stability of their Doppler computed horizontal velocity, and the longer-period variations with time and altitude which are consistent with elementary me"teorological inferences. In this paper mean Dop pler CAR motion and horizontal air motion are considered identical, and horizontal components are computed by applying equation (1) to patterns like those shown in figure 1. Equation (1) predicts that the radial velocity is a cosine function of the radar beam azimuth angle, ~, if all the observed targets are moving uniformly. Let the maximum positive Doppler velocity be U (upwind, cos ~ = 1) and the extremum negative velocity be D (downwind, cos ~ = -1).1 Then from equation (1) U = Vh cos' 9 + Vz sin 9 (4) D = -Vh cos 9 + Vz sin 9 It is clear from (1) that zeros are observed midway between the ex trema U and D. ~Vhen Doppler sign is not provided in the' signal processing scheme, the extrema luI and IDI are shown as two maxima as in fig ure 1. When Vf = 0, equation (4) shows that the two maxima are un equal, but if the targets' true motion is uniform, it follows im mediately from (4) that the average of 101 and 'DI correctly identi fiesthe horizontal motion. Thus = I + IDI (5) Vh 'U2 cos 9 In this analysis, the extrema, tul and IDt are considered to be rep resentative of all the radial motion information in the VA display. This is obvious from the cle~n patterns obtained above 300 m. Be low this altitude, when local variations of the wind are present, the best cosine fit is estimated from the whole pattern. ~e high density of targets encountered in this case provides accuracy of 0.5 m. sec.-~ or better for the estimates of the Doppler mean. Computations of the horizontal motion based on (5) have been made at the ten altitude levels where Doppler observations were made. The observations step from one altitude to the next, and the time interval between successive samples at the same altitude lSince approaching targets are associated with increased frequency of the back-sc.attered .radar energy, it is appropriate to assign pos itive velocities to approaching targets, negative velocities to re- ceding targets. 16 . is 12 min.- corresponding to air motion of 7 to 15 km. for the range of speeds encountered. The results are shown in figure 8 (daytime) and figure 9 (nighttime). One sees the trend and also some varia tions between successive. ,samples at the same alt;i.tude. Part of. the variance is due toa random error in estimating the middle point of .the Doppler spectrum and, therefore, U and D. However, this error 25 - 20 / ~ ~ /5 ----~ .. r-.,. V """' f--"""'- 876m. --- ... l- 20 ./ - -...r l./ ~ I 15 ~ r.v- ~ ...... - 7 r-- --- 780m. \ --.J ...... 20 V -I .-. ./ r--..../" ~ .,u /5 f-'" ..... -- ~ _/ -- ., "" ~ 685m. J E ..,,- >-.·20 V I,..--J ~ t /5 ~ ~ IV u ~ ./ '-./'" V o "" r- ~90m. ..J .."...... ~ 20 ...... r-~ --...... ,.... ~ V- zo '/5 .... 7 ~ V--~ 497m. ~ /'....- ~ ~ /5 A ~ '-Vv-rv--. t-"", i--" V ...... -"" '" 1394m. /0 ~ ..... "-./~ I~...... J I\/" ./ /5 V , -:.: [79 V - - ..... 293m. /0 V " . ,.., ... A A , A. /5 v -.... ~ -- \;.J ~ ./V\.. ~ r--... 171m.1 ~ 10 - I ·1000 /200 /400 /600 /800 2000· CENTRAL STANDARD T/ME Figure 8. - Computed Doppler "wind" speed sampled at Norman, Okla. at a rate of five times an hour at eight selected altitudes .. June 26, 1965. Time 1000 to 2100 CST. ------~------~------( 17 25 .-..- ~ -....6 ~ ~ r-...... 20 .... --. .../ 1I611 mJ r-----" V 25 '-- ~ '-- ' ...... ~ -...... / t---..L ~ / 20 ------[" - 11~IOm.1 " - ~ .1 ,,------, . / - f--/'- --- 20 "-- '--I-' ---- 11360m·1--- .~ 25 ~ ~ rv ..,.,.- 20 '-\ ~ ~ U233m.J ~ ~v 15 " 25 -...... --f- ~ " "\ r--.. IrJ III II m.1 /' u 20 " OJ' !V III i'--. E 15 25 .....-:\ ".. /\. >- -...... / - V 1"--" ...... - Ig81m.! ..... --... u 20 .It.. 0 ...J 15 ~\ .-...... >ILl a ~ ...... z 25 "'" , - "-V \ --- l866 mJ !: 20 \--.,/ 15 ~ " ~- 25 f'.. [" .-" ...... L'-- \ '-- '- ."' 1740m.! ~L'\ /' 20 v r--,"\. 15 r- 25 .- ~ ~ 20 ~ ~ 1-0.. -""-. ~ ...... L618m.1 1'-/ . ... .A. 15 \ ~-. A ...... "'" 20 .-- ""'''-..r-'v 15 1'-/ f-.., , -... /- 1461m.1------"-J ~ J 2400 0200 0400 0600 0800 1000 1200 CENTRAL STANDARD TIME Figure 9. - Computed Doppler "w:i..nd" speed sampled at Norman, Okla. at a rate of five times an hour at ten selecteeJ altitudes. June 27, 1965. Time 0000 to 1200 CST. l8 variance is estimated to be much less than 0.2 m. 2 sec.-2 (standard deviation 0.4 m. sec.-I), and the remainder must be due to realvari ations of the target speed. Note also that some of the wind speed features are repeated at several altitudes, sometimes with a time shift. Such correlated variations of the wind at several altitudes a're noticeable -in the ;ind observations provided by tall instrumented towers (Izumi [16"]). " The Doppler data have been compared with wind soundings made at 1800 CST on June 26 and at 0600 CST on June 27, at Will Rogers Airport 20 mi. north of the radar site. The wind soundings and computed target horizontal motions' are shown together in figures lOa, b, c, d. Several Doppler "wind" profiles are plotted with related rawinsonde observations in order to illustrate the variability of the wind and make the comparison more objective. The agreement on wind direction' is always within a few degrees. For the wind observed in the late afternoon on June 26, notice that although the Doppler wind variance is several m. sec.-I, the I mean Doppler wind profile is everywhere within 1 m. sec.-l of the rawin data. For the data ta~en just aft~r sunrise the next day in , ,a region where a high wind was observed (low-level jet discussed be 1I low), the agreement between target speed and wind speed is still '..1 good but the wind speed profiles are shifted in altitude, relative to rawin profile, by approximately 200 m. The computed target hori zontal speed is extremely steady at this time as shown by the pro files plotted in the figure and the spread of the Doppler spectrum in the VAD patterns is less than 0.4 m. sec.-I; there is no differ ence in radial speed between the two maxima of the VAD pattern and the whole pattern has a perfect cosine shape. It is difficult to accept as fact the idea that all the radar targets have a uniform motion (within 0.5 m~ sec.-I) systematically different from that of the wind in all the region explored by the radar during several hours. Since the wind sounding was recomputed from the basic RS data and possibl~ computational error removed, the only possibilities left to explain this discrepancy are radar or radiosonde altitude errors of undetermined origin, or a true difference in the wind profile at locations 20 mi. apart. Perhaps, for example, standing waves in the low-level jet produce such differences. Figure 9 shows that the computed wind varies little from sample to sample during the night at the altitude of the low-level jet. However, the variance of the estimate of Vd from sample to sample' :is usually larger than the mean horizontal and vertical wind gradients. The average Doppler velocity has been computed during I-hr. periods to reduce this small sca.:!-e variance and reveal in figure 11 the meso ,scale features of the wind. The pattern of wind speed and direction shown there is based on all of the 1800 CST wind data points obtained at the 10 selected altitudes. The vertical motion is also shown in figure l1. 19 2.0 TIME; 1700 TO 1840 CST 1.8 JUNE 26 1.6 - 1.4 E 1745 CST RAWrN ' -.lC 1.2 ... . . L&J :. 0 1.0 . :::> • •• • t- 0.8 t-- -l « 0.6 r'0 ..... 0.4 I . e._. __.J .•.. 0.2 • DOPPLER WIND •.' ••.. • 4 6 8 10 12 14 16 18' 20 22 24 26 28 HORIZONTAL SPEED em sec') • DOPPLER WIND . Figure lOa. (top) --Comparison 1.4 - 1745 CST RAWIN~ between speed of Doppler "wind" at Norman, Okla. 1.2 l- and rawin data at Will :E Rogers Airport, Okl~homa ,x 1.0 I- City, Okla., June 26, 1965. z 'i- r--. I- 0.8 I- Figure 10h. (left) - Comparison :z: • \(!) • beb~een direction of Doppler "0.6 l- • ,. w - wind and'rawin data • :z: • • • 0.4 l- • • ' . JUNE 26 • TIME: 0.2 - • • '. 1700 TO 1840 I I 0.1 • 3 • 160 ' 170 180 190 200 DIRECTION IN DEGREES 20 During daylight there is almost no vertical wind shear but the wind speed increases steadily at all altitudes with an average time change of 0.5 to 1.0 m. sec.-I. During the night, a well defined maximum of wind speed, the low-level jet, occurred at 800 m. alti tude, this is discussed below • .2.0 1.8 • 05 13 TO 0525 CST + 1.6 + 05 26 TO 05 38 CST o 05 39TO 05 51 CST 1.4 6) .0552 TO 06 04 CST E fJ. 06 05TO 06 18 CST .:.: 1.2 i IIJ. 0545 CST RAWIN....-'" 0 1.0 ::> I-- I- 0.8 ....J 1.6 1.4 E MEAN OF . .¥ 1.2 DOPPLER "WIND" DATA OJ 0 1.0 ::> I-..... I- 0.8 ..J O~~~~~~~~~~~~~~-L~~~~~~~-J 180 185 190 195 200 205 210215 220 225230 235240245 DOPPLER WIND DIRECTION (DEGREES) Figure lOde Doppler "winct"-direction at Norman, arid rawin data at fJ.Jil.l Rogeps Airport. 2l 7 2. //, /' •• :.- 1.6 _.- - . -- .- - -- ~'l...~ ""'- ~ :...... v( If /" .~ r-... ~ 5 •• 1--_ ",0. 2. \ 7- ): 1.4 i ~ ~ \1\ I 22 '" ) v::: :?': ~ 2' ~ \'"' \ r VA ~ 1 ISOLINES OF HORizONTAL 24 "'- i-- I/, 1".. 2- ~ '/// V .\ \\ J ~ - WIND SPEED IN In ...... ,.c;-' ,\' r-'" J~ 1//1// V" .1- -'- J rl Z j( _\ 'I " I, 2'!.. :/V ./!fIJ '/, 7 ~ 1.0 .- I '/ '-' -/ E IT :7" /' to fJ/. 'I \ :! 0.9 - / 171 -' - "ijj g.0.8 '\ ''', !•• I~ .l U . , --/, ~ If, '/ .- T" " ~ ~ I J -I \. ~ ~ %-: 'II' n- .- ~ 0.7 "'- :.J J i- I ...... ) \\ \ '- :---- :--- - :§§: ~ ::a: ~.".... /' - - ~ 0.6 - , ( 1.\ :-: '/'j--~ % r "..".- ,I 0.5 1/ "- - '"( ! I l '- ;:::::: ,...;.-:% ./ 0.4 I 1 - ::---: -'l \j J ! \ ~ v, ;:-::: :::-:: ;::::::- :::-..::::1v ,...... - - o.~ "'- '-.i --1 - 0.2 ::::- '- ,/ i e O. Ir,o .- f-- ...... "- / "- ~ ....--±.- _i... --~ ::. ~-1-- - -::.::, ,...,r',. - 9 '" •• 1200 1800' 0 •.•. 2400 0 .. o 7 "'060070- 1200 2fO I, _._1-, --I- 8 1- . r-;- ~- "~ V f-- ••~-~.. .- .. _ -~ .. .. - .- I.7 I----:- -- 10' = = r:-:::- . -,...... ( -- '-' ~ . - , . .- ~- - - ··-r~ . _ ... __ ~t--. r--! 1.6 -.1- ~~ , "'0 i ~i 100-_ 5 .e. 1'\ '\, I 1.4 -:- .IS0LINES OF WI~D DIRECTION tN cIe.re',L r---:', .eo .-205, ~ ~-I'O _ .. ~ "7 .~ ~~ - \ - 1\ }g., i\. r\; It. 2 - \ ) I I V .I ...' ...... 2; ~ ~ \ v '0, / - 1.0 .00 100 \. = "" 110 f-' E , 71 ./ ;;;:; ~ ItO 'Ie~ "- zoo I..... ~ ~.9 .0 /"/ 17.-- "- zoo OJ J I po ~'70 ...... i-- t- ...J g 0.8 ~ t::-- \. ''-... - 1/ 1/ .• 00 1,,1 :--..;: ...... ~0.7 '7 \ I ~ ~ / ..J 1!iI~la5 I ~ I I ( , ...... '\ " 0.6 '- 'r-.. 100 7 \~ V I I '\ \ t"'" HI' )~. ~ ItO - I'-..... It' ~ 0.5 \\ '\, II 0.4 1\\ \ \ ~\ '\ J J '7. 0.3 I I 1 \1 I ol'll Ott) 0 ITO! Ie. 0.2 ---1 -2!!,!!!! .. ~ ; r 1200 1800 2400 0600 1200 JUNE 26_ JUNE 27 CENTRAL STANDARD TIME Figure ll. - Altitude-time presentation of iso-contours ~of horizontal mean wind speed (top) and direction, and estimated vertical motion (bottom), computed from the Doppler data averaged durin~ period of an hour~ 22 6 • ESTIMATE OF VERTICAL MOTION Equation (4) implies: V == lui -: In/ .. z 2 sin 9 , (6) in· this scheme, Vz is positive when the motion is downward (see foot note 1). Use of equation (6), however, is predicated on uniform tar get motion in the observed region. For the work reported in chis paper, random or systematic differences between the horizontal com ponents of U and n are often as large as Vz , and are a significant source of uncertainties with respect to Vz computations. These un certainties can be reduced. by an averaging procedure, based on the derivation which follows. ) Consider the magnitude of radial winds, lui and Inl correspond !~ ing to upwind and downwind locations. 'Fol10wing equation (1), we have, . I u J = U cos 9 + U sin 9 \ h z f ( 7) Inl = nh cos 9 nz sin 9 where Uh is the magnitude of the upwind component and Dh the magni tude of the downwind component which are considered greater than the Uz and nz vertical motion components. The pair (7) implies that Vz is derived from: + lui - In, r~ - DJ UZ nz 2 sin 9 = t 2 ~. cot 9 + 2 (8) The left hand side of (8) is just the calculated vertical speed Vz defined in (6). Equation (8) when averaged, shows that the.computed average vertical motion, V , is affected by contributions from two sources: a term due to th~ average difference between the true hor izontal winds at the upwind and downwind pOints, and a term which is the mean of the true vertical target speeds at upwind and downwind points. Computations based on averages should faithfully reproduce the average value of Vz on1Y if there is no mean horizontal gradient at the horizontal wind. On the other hand, local features might pro duce a systematic perturbation in the distribution of horizontal winds near the radar and a resulting systematic error in calculations 'of Vz • Systematic differences of Uh and Dh would also be associated with the existence.of a gradient in the large-scale distribution of the horizontal wind. 23 The magnitude of Uh - Dh might be estimated from synoptic wind charts or from the observed trend of Vhat the radar station. The latter estimates based on temporal trends involve the additional as sumption that wind changes reflect advection of a frozen-in pattern. In this case (9) 1 where dVh/dt is in_me sec.:..l hr. -\ L in km. and Vh is in m. sec.- For L = 2 km. and V = 15 m.sec.-l a change of wind speed of 1 m. sec.-lhr.-l gives Uh - Dh = 0.03 m. sec.-I, a value typical of the present study. It is evident that the magnitude of Uh - ~ can be reduced by examining the Doppler signal in an annulus of smaller diameter, L • . Running means of Vz have been computed for hourly periods, i.e., with five pairs of upwind and downwind samples and with no attempt to correct for a possible gradient of the true horizontal wind. The results are illustrated in figure 11. We are happy to note that the correction suggested by equation (8) is substantially smaller than typical magnitudes within the mesoscale Vz pattern, and has no serious consequence for the general interpretation of the results. Although some regions of the horizonta~ wind pattern are associated with wind changes as large as 3 m. sec.-I, this con tributes at most only .07 m. sec. -1 to the vertical motion estimate in this case. Our confidence that the average vertical motion pat terns reflect a close correspondence between air and target motion is strengthened by the vertical continuity of the patterns and by the regular variation ofVz in time over a period several times as long as that enclosing the running means. The pattern is' very complex during the day; perhaps this is due to st;"rong solar heating qf the earth t s surface. The typical period of variation through regions of~ising and descending motion is about 3 hr. Dur.ing the night the pattern OJ:' vertical motion is much more regular; the quasicyclical variations then have a period of about 6 hr. 7. STUDY OF A LOW-LEVEL JET FROM THE DOPPLER RADAR DATA As shown in figure 11, the wind during the night of June 26- " 27, 1965 had a strong maximum at an altitude typical of the low level jet described by Blackadar [2J and others [3, 4, 8, l6J. The Doppler "wind" profile as a function of altitude is remarkably simi lar to the wind profile published by Blackadar. The Doppler wind 24 data reported in this paper also correspond to the boundary layer phenomenon defined by Bonner's [5J climatological study of low-level jets. For instance, according to Bonner, the most frequent speed is between 50 and 60 kt. and the maximum speed found in this work is 54 kt. The altitude at which the maximum wino spe~d is observed (800 m.) is above the mean of the altitude distribution of the "southerly jet" observed at Oklahoma City (600 m.) but is at the mean altitude estimated at Fort Worth. The observation of the strong wind reported in this paper is associated with nocturnal in version which was still observed at the time of the sounding, June 27, 0545 CST). At this time the base of the inversion was at an altitude of approximately 400 m. and the top of the inversion layer, at 600 m.,was slightly below the altitude of the maximum speed. These results are consistent with conclusions of Blackadar, Bonner, and Hoecker [14J on the importance of the nocturnal inver sion in producing the low-level jet • .Theshape of wind profiles selected from the Doppler data, as well as their time stability, is ·illustrated by figures 12, 13, and 14 and also by figure 10c w~ch was shown above for comparison with the rawin data. The wind profile is fait'ly stable for long periods I of time and changes gradtiallyas indicated by wind isolines plotted in figure lIon an altitude ... tim~ basis. The wind maximum is always well defined with, however, a decrease of the wind gradients above \ the maximum which is noticeable at about 0500 CST. The altitude of I I 2.0 1.8 1.6 1.4 E ~ 1.2. lLI c 1.0 .....:::> .... 0.8 ..J ~ 0.6 0.4 JUNE 27 0.2 TIME; 0008 TO 0102 CST 0 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 HORIZONTAL SPE.ED (m sec-I) Figure 12. - Structure ·0·£ Doppler ilt..'lfud" profile during: the lOW-level jet. NOl:'man, Okla., June 27, 1965. Time 0008 to 0102 CST. 25 2.0 J.8 /.6 1.4 E ~ J.2 w 0 /.0 :::> t- t- 0.8 -oJ ex 0.6 0.4 JUNE 27 0.2 TIME ;0221 TO 0248 CST O~~~~~~~~~~~~~~~~~~~~~~~~~ 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 HORIZONTAL SPEED· (m sec-I) Figure 13. - Structure of Doppler "windl1 .prtofile during . the low-level jet. ~orman, Okla., June 27, 1965.· . r~. \\ \ \ .~ . i .. ~lL.. . ..~ .. . ~_~::::::f.':::-;-----=·~ .~~. JUNE 27 TIME;0420 ·TO 0512 CST. 15 16 17 f8 19 20 21 22 23 24 25 26 27 28 HORIZONTAL SPEED (m sec-I) . . .. ~. . Figure 14. - Structure of Doppler "windu profile during the low':"level jet. Norman, Okla., June 27,1965. 26 the maximum speed remains constant (near 800 m.) except for a tem porary decrease of altitude to 700 m. shortly after 0200 CST. As \ expected, the altitude of the wind maximum increases after 0600 CST; this can be due to a gradual appearance of turbulence in the low layers. At about midnight the maximum wind, at an altitude of 800 m. becomes very steady as seen in figure 9. Such wind stability must be due to stable synoptic conditions. This'is indeed shown by the sea-level pressure map at 0000 CST shown in figure 15. The geostrophic wind, Vg , has been computed every hour from the pressure data (reduced to MSL) reported by a selected number of weather stations in the region of the radar site. Although the sur face pressure reduced to sea level was used, Vgwas estimated for the air density at the altitude of maximum wina. speed ... Friction '"" forces can be estimated from the departure of the real wind' from the geostrophic wind. In our case,the pressure field is somewhat variable as revealed by the change of the computed.geostrophic wind, I Vg ; these variations are associated with an isallobaric wind com- . I ponent. The Brunt-Douglas wind (Brunt [9]) which includes the isal lobaric component but neglects substantial derivatives is given by: \ 0 , 95 Figure lS. Weather map in of Norman, Okla., June 27, 1965, 0000 CST. 27 u + i..v (12) where A - is the Coriolis parameter, p is the air density, and op/Ox, o2p/ oxot and op/oy, o2p/oyot respectively are the pressure gradient and pressure tendency along E-W and N-S axes. Use of this equation provides a first order explanation of ageostrophic wind components. The synoptic wind, computed from equation (12), has been estimated every hour by a graphical evaluation of the vectorial variation of the geostrophic wind vector during 1 hr. It must be noted that e~ti mates of the isallobaric wind component require more accurate pres sure reports than do estimates of Vg since the pressure gradient variations -during 1 hr. are usually much smaller than the gradient itself. Therefore smoothed Vg data have been used to reduce the scattering of the computed synoptic wind~ The direction and speed of the synoptic wind V , (equation (12)), geostrophic, Vg , and maximum Doppler wirid, Vd, have ~een plotted in figure 16 as functions of time. We notice that, in the case of such non-stationary pressure fields, the isallobaric correction on Vg is not negligible. _ The Vg speed shows a scattering of about 1 m. sec.-l which is consistent with the estimated 0.2 mb. accuracy of individual pressure reports and the 300 km. average spacing between stations. 28 26 24 22. SPEED 20 I ..~ 18 e + DOPPLER WINO MAXIMUM. SPEED AND 16 DIAECTION. o I&J @ COMPU·TED GEOSTROPHIC WINO. SPEED I&J AND DIRECTION. 230 Go (I) • SYNOPTIC WINO o q"f'P>-'® 220 (I) z I&J ~ ., ft~-Ji'.~ 210 - I&J ®'"@i' 11/ ~ ~ .!-'fl';Z...... ~ II:: C!) 8 .... + :\ 200 I&J ~,.~~..®-@"/ /~ 0 , /- +>+fHt.+ + 'to 6 \ \...... ++... ~+++ ~ 190 z -2 4 \...... ~+H++++++ *,C DIRECTION 180 t +,,~,. \ / I&J 2 ..'+I 170 ~ JUNE 26,1965 JUNE 27,1965 0 O_~~~~~~~~~~~~~~~~~~~~~~~ 160 10 12 14 16 18 20 22 00 02 04 06 08 10 12 14 16 18 TIME, CST Figure 16. - Time variations of Doppler "wind II speed and direction compared to geostrophic and synoptic winds. 28 During the daytime, there is a large discrepancy (approximately 5 to 8 m. sec.-I) between V and the Doppler wind. According to Blackadar, this is due to tRe presence of turbulence in the low lay- ers, probably associated with thermal convection and enhanced fric- tion of the air with the ground. The air mass was quite unstable in the low layers during daytime and remained so in the first 300 m. at the time of the 1800 CST temperature. Also, the presence of turbu- lent motion reaching high altitudes can be deduced from the complex nature of the vertical motion field shown in figure 11. The Doppler wind increases slightly during the afternoon, becomes stable between 1500 and 1700 CST, and then increases greatly at 1730, 2 hr. before sunset. The rapid increase of the maximum jet speed coincides with the disappearance of temperature fluctuations (± 0.5°C.) observed on a thermograph located at the radar site. The same discontinuity in temperature fluctuations is observed at other stations of the NSsLl .mesonetwork. This turning point of the maximum Doppler wind speed .i seems to be due to the combination of a substantial increase of the l synoptic wind and a decrease of friction. The difference between ~ synoptic wind and Doppler wind becomes gradually smaller until sun- .~ set at 1945 CST. The angular difference between the synoptic wind and the Dop pler wind vectors, is greatest at 1400 CST (approximately 25°). Note in figure 16, the temporary change of the Doppler wind direc tion from 180° to 170° about sunset; this is followed by a steady increase .toward the synoptic wind direction indicating a marked de crease of friction forces. Change of the geostrophic wind direction generates a Significant isallobaric wind component which turns the synoptic wind to the right while increasing its speed. It is inter- esting to note how well this detail is reproduced in the Doppler wind function. The synoptic wind remains gr~ater than the Doppler wind until midnight. However, the fact that the Doppler wind becomes geostrophic in speed and even slightly supergeostrophic around 0200 CST, seems to be caused by a decrease of the synoptic wind which is more rapid than a corresponding decrease of the Doppler wind. In fact, the maximum of Vs noticeable at around 2300 CST is followed by a maximum of Vd abo~t 2 hr. later. There is a time lag of approximately 2 hr. between the maxi mum of Vs and the maximum of Va. The time lag is probably due to the inertia of the. air mass in responding to synoptically induced variations of the wind. rhis is implied in Blackadarts analysis of the low-level jet. Note that the Doppler speed becomes super geostrophic only when the synoptic wind decreases, and it is ob vious that if the 0600 CST rawin data are used for a climatological study of the low-level jet, most of the interesting features of the previous history of the wind will be lost. The DopplerJwind coincides with the synoptic wind for only a few hours between 0300 and 0600 CST. This may be related to the time at which the noc,turnal inversion reaches its maximum altitude. 29 The time variatiens ef the Deppler wind vecter shew a typical' cleckwise retatien which has been previeusly reperted by Smith and Welf [24J and Heecker [14J. Analysis ef the 700-mb. and 8s0-mb. maps at 1800 CST June 26, and 0600 CST June 27, shews that the, gee strephic wihd directien., at 1.5 km. and 3.0 km. ef altitude, was 210° except at 1.5 km. at 1800 CST when it was 205°. The field ef average Deppler wind directien (figure 11) shews the variatien ef the altitude at which the Deppler wind' has a geestrephic directien. This may,be interpreted in terms ef the depthef the frictien layer. During daytime there is no. Deppler data abeve 1.1 km •. but the alti tude at which the Deppler wind directien reaches the geestrephic wind directienis estimated to. be greater than 2.km. This altitude decreases gradually and reaches the altitude ef the maximum wind speed (850 m.) between 0600 CST to. 0900 CST. This is ccnsistent with the time variaticns cf the winds plctted in £igure 16. The pattern ef estimated vertical air mcticn from 2200 CST to. 1000 CST June 27, sheuld also. be ncted. There is upward mcticn when the Dcpple'r wind vectcr retatestcward the directicn cf the syncptic wind and downw~rd moticn when the directicn_ cf the Deppler wind is staticnary. The mcticn up resumes when the Dcppler wind mcves again to. the right cfthe gecstrcphic wind. Hcwever, additicnal analysis ef vertical air meticn estimates is needed~ 8. DOPPLER "WIND" SPEED VARIANCE AND THE SCALE OF HORIZONTAL EDDIES , The variatien cf the ccmputed hcrizcntal meticn can be analyzed by ccmputing the sampled variance ot2 cf the wind speed at all the altitude levels and times at whicn the ebservatiensare made. The results are pletted in figure 17 fcr the time period between 031 CST to. 1759 CST when the trend ef the wind was small. The variance changes cnly slcwly with altitude and. shews a slight maximum at an altitude cf 600 m. In spite cf'cur selecticn of a period with small trend, ~t2 still includes a trend cempcnent.and is nct representative cf in stabilities at the smaller time scales shewn in figures 8 and~. To. eliminate the ccntributicn cf lcng-term time ch~nges to. the variance, a shcrt-term variance cf the speed estimate, ~s = (Vh - VL)2, was cemputed with respect to. the lccal mean VL during adjacent hcurly in tervals. This is justified if the mean is essentially staticnary 2 during hcurly periods. Average cf Us must be made fcr all the avail able times tc increase the ccnfidence cf the estimate. It can be 2 shcwn that ~s can be expressed by: . 2 0'" 2 = Cf. 2 ( 13) s crt L where ~t2 is the tctal variance and ~L2 the variance of the ccmputed heurly meahs, which is assumed to. represent the variance cf the trend. 30 2 The results of the computation of as are plotted in figure 17. One s~es that as2 is relatively high in the low altitude levels (1 m. sec.-2), decreases drastically between 290 m. and 390 m., in creases slightly at 600 m., ~nd finally decreases to less than 0.25 m. 2 sec.-2 at 1 km. ·It should be noted that the sharp decrease of (]s2 above 290 m. coincides with a complete disappearance of departures from the theo retical cosine function of the VAD patterns. The size of local wind disturbances which shQuld cause the VA display to depart from a per fect cosine function has been estimated by considering the azimuthal extent of distUrbed portions of the pattern and the distance of ob servation. This size has been foUnd to be about 100 to 200 m. It seems therefore, that the excess of ~s~, (0.7 m. 2 sec.-2) observed below 290 m. may be related to the sampling of eddies of this size. Other information on eddy sizes can be derived from equations V7). It is shown in the Appendix, that if the variance of vertical vel ocities is small compared to the variance of horizontal velocities, equations (7) imply that (14) 1.4 o crt TOTAL VARIANCE OF COMPUTED MEAN WIND FROM UPWIND AND 1.3 DOWNWIND SAMPLES. + SMALL SCALI; VARIANCE FOR MEAN WIND DURING ONE HOUR PERIODS. 1.2 • SMALL SCALE VARIANCE OF THE UPWIND OR DOWNWIND SAMPLE. • VARIANCE COMPUTED FROM DOPPLER SPREAD CT~. (l1svy l.I 1.0 0.9 + 0.8 I ·z\. UJ +", . ." \ c 0.7 ::::> + • '\ I- O.S I- ~+".e ...J. //\ « 0.5 of:: • • 0.4 \ "'\ 0.3 ~. 0.2 j \\ 0.1 TIME; 0931 TO 1759 CST 0 0.1 0.2 0.3 0.4 0.5 1.0 2.0 3.0 4.05.0 10.0 2 2 VARIANCE Cm sec ) Figure 17. - Estimated variances ot the Doppler "windll as a functio~ of alti~ude. 31 where f.J£) is the correlation coefficient between horizontal win Vc: Vi - Vi.· Vj ~j assesses the least square linear prediction of the wind at a certain level from the·wind at another level, therefore derining the explained variance. 2 2 at ftj where ~t2 is the total variance at th~ level considered. The unex plained variance is ~x 2 = Ot2(l - Pij ) and is related to the vari ance contributed by random eddies whose size is smaller than the spacing between levels and random eddies which are large and tilted. However, tilted eddies are improbable since the average wind shear is small. Although the physical significa:nce of O'x 2 is. not assessed in great detail here, it seems that a measure of the .vertical turbulence 32 is given by the increase of O'x 2 as a function of the.spacing be- twe,en. two levels a~ a given2mean altitude. A~ shown in figure .16 the mnd speed var~ance, O't , changes only slightly as a functlon of altitude. The unexplained variance has been computed at several mean altitudes and for different spacing between levels; the results are shown in figure IS. At altitude levels 'of approximately 600 m. all the unexplained variance (0.3 m. 2 sec.-2) is due to the contri- bution of the 100 m. spacl.ng or less. This variance is approximately the same as the 'short-term variance O's2 computed above. It seems, therefore, that O's2 is related to a variance which is not correlated for vertical spacing greater than 100~. Below 600 m. the unexplained va2iance incY)~~ses with spacing 'and O'x reaches values greater. than . rrs . at the same lev~l which involves the participation qf the noncor- related trend to CT • It must be noted that the space correlation (Ii between the U ana D components discussed above.showed that sub- " stantial correlation was observed for longer distance. Thus the !j turbulent eddies are anisotropic, and have greater lengths in the J horizemtal plane. . .\ I .. I 900 - 800 f- , • en ... -~ 700 .'+-GI - . ~ SEPARATION 300m GI + '@J-'(i1 E 6.00 - •/ \ ~®~EPARATION 400m -w c 500 - \. T~ . "--®~(i1.... . ::::) . .~ --:;~ ... 400 - ~ + /$ ... 200 m -1 .--.~.~SEPARATION « 300 r- • • 200 - . '., '. SEPARATION 100m 100 f- , , .,' I , , ., 0 I 0 "0.5 1.0 2 -2 UNEXPLAINED VARIANCE (msec .) Figure lS. -Unexplained variance O'x2derived from iinear prediction . of the Doppler horizontal motion at one level from the saine motion 2 at another level. ax is plotted as a function of the mean level for d;i:fferent spacin~ for the 'hon-correlated levels • . ' 33 10 • CONCLUSION Continuous probing of the .wind in the planetary boundary layer illuminates important processes taking place there. The time history of mesoscale phenomena in relation to the horizontal wind and its vertical shear have paramount interest.. Continuous probing has been difficult above about 1500 ft., the maximum altitude covered by tall instrumented towers. The location of a tower is often governed by extrameteorological considerations, and such massive structures may affect the winds being measured. A wind-probing technique based on Doppler radar requires only tiny targets which are carried with the wind. The radar· can be in- stalled almost anywhere and the method is flexible and accurate it I natural targets are plentiful, as at Norman, Okla. during spring, I summer, and fall. The potential of the method has been demonstrated . by continuous operation of the Doppler radar for more than three .1 months including 1,000 hr. of effective observations of target vel- ocity and signal intensity. It has not been shown conclusively whether the targets are particulate matter, insect~ dead or alive, or if the targets are due to other discontinuities of index of re- fraction. However, the fact that the scatterers behave like point targets of small radar cross section suggests 'that the scatterers are atmospheric "plankton", i.e., particulate matter or insects drifting with the air. Browning 'and Atlas [ 7l have reported simi- lar observations in Massachusetts and concluded that their targets were insects. Random deviations of target motions from their mean velocity are indicated by the Doppler spread and are systematically greater in the low atmospheric levels and during daylight. This is con firmed by the analysis of data taken almost continuously over three months •. "It is interesting to note that the same behavior of the spectrum width is observ~d with slow-falling precipitation particles detected at such low elevation angles that the variance of the fall .speed of the particles gives no contribution to the Dop~ler spread. The derivation, in this paper, of sma'll vertical air motions from observed vertical target motions remains somewhat uncertain since the targets are not positive.1.y identified. However, this res ervation does not apply to simi~r analyses of horizontal winds, especially when the winds are strong. ACKNOWLEDGMENTS The author is indebted to Dr~ Edwin Kessler and Dr. David Atlas for reviewing the manuscript and making helpful conunents. Mr. J. Fank hauser provided assistance with the synoptic analysis of the meteoro logical data. Mr. J. Dooley and Mr. M. Faruqui assisted in the com putations and reduction of the Doppler wind data; Mr. D. Sirmans and Mr. J. Jennings acquired the Doppler data and opera,ted the radar. 34 APPENDIX Derivation of equation (14) Addition of the pair of equations, (7) yields (AI) and subtraction yields (U - DT-~ cos 9 (l1J1 -- (A2) The variance of (U + D) is U + D =(U + D)2 - (U + D)2 (A3) And, from (Al) Oj~I+IJ)1 = cos"e[u~ + ])~ +ZUHDH -(UH)2~(DH)~~ Z UH D~J . + .sih2e[v~ +])~ - ZV~])~ - (u~)~- (Dr."'/, + Z U'C1>~1 . (A4) + Zeos e sin e [UH Uc - UH])-e +1)1-\ U~ - .])1-\ ])2; - UH Uoc -: UH D~ + DIi , V=c -.])1-1 De] It s'eems probable that the last term in (A4) vanishes. Then (A4) can be rewritten (AS) 2 iii A$stiming , CJ."u - a:. J e - J)'!: 35 Also, -recall that COY. x!:i =- e'K'j OX CT) ,where f is the normalizedcor-: relation coefficient. Then (A6) where £ , as in th~ text, is the diameter of the annulus surveyed by the radar. A similar development shows that 2 (J. 2 .. = Zeru. 2. co.s 2"Ee 1- ("\-\ .(t) ~ + 2 0:- sin 2 e -~1-+ e:oL Ce.)~. IUI-ID\'" ~-r= (A7) With :z 2 0-: ~cr- . Ivl + 1111. 101- Il>l (A8) .:l .2 Cl-IUI 4-IDI+ <)"101-11>1 Equation (A8) is iden.tj,cal to equation (14) in the text. REFERENCES ... 1.. Atlas, D., "Advances in Radar Meteorology, t! Advances in Geophysics 10, Academiq Press, 1964, pp. 318-478. 2. Blackadar,A. K., "Boundary Layer Wind Maxima . and Their Significance. for the Growth of Nocturnal Inversions, n Bulletin of the American Meteorological Society, vol. 38, No.5, May 1957, pp. 283~290. . . .. . 3. Blackadar, A. K. -etal., "Structure of Turbulence and . Mean Wind Profiles With;in the Atrriospheric Boundary Layer, It Pennsylvania State University, Dept. of Meteorology, Uni,,:, versity Park,Pa., FinalReport on ContractNo.AF19(604)- 52:31, Oct. 1960. . . 36 4. Blackadar, A. K., "The Vertical Dj;stribution of Wind in a' Baroclinic Adiabatic Atmospheric Boundary Layer,!! presented at the 211 National Meeting of the AMS, Pennsylvania State University, University Park, ,Pa., Jan. 1963. 5. Bonner, William D., "Statistical and Kinematical Properties of the Low-Level Jet Stream, t1 Satellite Meteorology Research Project Research Paper No. 38, Jan. 1965, 54 pp. . 6. BouCher, R., Wexler, R., Atlas, D. and lhermitte, R., "1-1eso Scale Wind Structure, Rev~aledby Doppler ,Radar, rr Journal of Applied Meteorology, vol., 4, No.5, 1965, pp. 590-597. 7. Browning, Keith A. and Atlas, D., rrVelocity Characteristics of some Clear Air Dot Angels." (Manuscript to be submitted for publication.), 8. B'uaj-itti, K. and Blackadar, A. K., "Theoretical Studies of Diurnal Wind-Structure Variations in the' Planetary Boundary Layer," Quarterly Journal of the Royal Meteorological So ciety, vol. 83, No. 358, Oct. 1957, pp. 486-500. 9. Brunt, David, nPhysical and Dynamical Meteorology, tf Cam bridge University Press, 1952, 428 pp. , 10. Chernikov ,A., tfRadar Study of Echoes from, a Clear Sky," Trudy, No. 48, 1963, pp. 56-97, Tsentra1 t naia ,Aerologiches kaia Observatoria,Moscow. (Translation available from A.M.S.) ll~ Glick, D. A., "The Distribution of Insects, Spiders,Mites in the Air,tf Technical Bulletin No;. 673, U.S. Dept. of Agriculture, 1939, lSI pp. ' . 12. Gorelik,. A. G., Iv. V. Mel'nichok and A. A. Chernikov, UTheStatistical Characteristics of the 'Radar Echoes asa Function of the Dynamic Processes and Microstructure of the, Meteorological Entity,"Trudy, No. 48,1963, :pp. 3-54, , Tsentral'naia Aerologicheska:la Observatoria Moscow. (Research Trai:1s~tionT-R-479 (Aug. 1965), Air Force Cambridge Research Labs,Bedford, Mass.) . , 13. Hardy,}(. R., D. Atlas,and K.M. Glover, tfMulti-Wayelength BacksCCitter from the Clear Atmosphere," Journal ,of' Geo~, physical Research, vol.71,1':Io. 6, 1966, pp.1,537-:-l?5,2. 14. Hoecker, W. H., nComparative PhYSiC~l Behavior of'Southerly Boundary~Layer Wind Jets,U Monthly Weather Review, vol.·93, , No.3" Mar. 1965 ,·pp.133-144. . " , ' 15. ' Hpecker, W. H., tf1'hree Southerly Low-Level Jet Systems Delineated by the Weather Bureau Special Piba1Network of 1961, tfMonth1y Weather 'Review, vol. 91, Nos. 10-12, Oct.- Dec. 1963, pp. 573-582., ' 37 16. Izumi, Yutaka, "The Low-Level Jet," Air Force Surveys in Geophysics, No. 140, Proceedings of the Symposium for Aero space Vehicle Design, 1962, pp.' 218-223. 17. Lhermitte, R., TfNote on Wind Variability with Doppler Radar," Journal of the Atmospheric Sciences, vol. 19, No.4, 1962, pp. 343-346. 18. Lhermitte, R., TfWeather Echoes in Doppler and Conventional Radars," Proceedings of the Tenth Weather Radar Conference, Washingtol), D.C., 1963.,-pp. 328-329. '19. Lhermitte, R. and Atlas, D., ffPrecipitation Motion by Pulse Doppler,ff Proceedings of the Ninth Weather Radar Conference, Kansas City, Mo., 1961, pp. 218-223. 20. Lhermitte, R. and Kessler, E., "An Experimental Pulse Doppler Radar for Severe Storm Investigations,Tf Proceedings of the 1964 World ,Conference on Radio Meteorology, Boulder, Colo.; 1964; pp. 304-309. ' ' , 21. Ottersten, H., "Occurrence 'and Characteristics of Radar Angels Observed with Vertically Pointing Pulse Radar," Proceedings of 1964 World Conference in RadibMeteorology, Boulder, Colo., 1964, pp. 22-27. 22. Planck, V... 'G., "A Meteorological Study of Radar Angels,tI Ge'ophysical Research Paper No. 52, Air Force Cambridge Research Center, Bedford, Mass., 1956" 117 pp. 23. Roelofs, T. H., ','Characteristics of Tra ckab Ie Radar Angels," ResearchRepor~ RS137, Ithaca, New York, .Cornell Univer sity, Center for Radio...--Physic~ and Space Research, 1963, 51 pp. . . . : 24. Smith,T. B. and Wolf , M.A., ItFurther Analysis of WINDSOC Data, JI Meteorology Research, Inc., Altadena, calif. Final Report to U. S • Army Chemical Corps, Dugway Proving Ground, Contract DA-42-007-CML-504, Nov. 1961. 25. Tolbert, C., Straiton, A., Britt, C. and Gerhardt, J., "Measurement and AnalysiS of Atmospheric Echoes from Milli "meter Wavelength, JlProceedings of the Seventh Weather Radar Conference, American Meteorological Society, Boston, Mass., 1958, pp. E-9 to E-16. ' " USCOMM-ESSA-OC,