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Time change of the tropical inversion layer and of turbulent statistics Rossignol, Dominique Jacques 1973

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TIME CHANGE OF THE TROPICAL INVERSION LAYER AND OF TURBULENT STATISTICS by DOMINIQUE ROSSIGNOL D.E.A., University of Paris, 1968 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of Physics and the Institute of Oceanography We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA JANUARY, 1973 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission fo r extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by h i s representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department The University of B r i t i s h Columbia Vancouver 8, Canada Date flu,uf K 14.7 ABSTRACT Measurement of turbulent fluctuations of wind temperature and humidity to determine the momentum, sensible heat and latent heat surface fluxes were made in Bimini Island, in Apr i l - May 1971 over Grand Bahamas Banks. The temperature spectralshape and WT cospectral shape showed strong time dependency. The temperature and humidity turbulent fluxes were dissimilar some of the time as in the case of B.O.M.E.X. This dissimilarity and time dependency of the spectra and cospectra depend on the structure of the vertical profile of deeper layers which i s determined by the evolution of the tropical inversion layer. i i i TABLE OF CONTENTS PAGE ABSTRACT ± ± TABLE OF CONTENTS i i i LIST OF FIGURES i v LIST OF TABLES v i ACKNOWLEDGEMENTS v i i INTRODUCTION 1 DESCRIPTION OF THE EXPERIMENT 4 EQUIPMENT 6 DATA ANALYSIS 8 TIME TRACES H SPECTRA 1 3 COSPECTRA 1 8 T - Q CORRELATIONS 22 RADIOSONDES 25 SYNOPTIC SITUATION 30 DISCUSSION OF THE EVOLUTION OF THE PROFILES 36 CONCLUSIONS 40 BIBLIOGRAPHY 42 APPENDIX 43 LIST OF FIGURES iv Figure 1. Map of experimental location 2. Photograph of mast 3. Flow chart of recording system 4. Time traces 5. U , V , W spectra 6. T , Q spectra 7. T , Q spectra , and T-Q correlation. One diagram for each case 8. WU , WT , WQ cospectra 9. WT semi log plot 10. WU , WT , WQ cospectra One diagram for each case 11. T-Q correlation 12. Bimini and Miami radiosondes 13. Temperature time cross section 14. May 6 at 00 synoptic ground level weather map 15. May 6 at 06 synoptic ground level weather map 16. May 6 at 12 synoptic ground level weather map 17. May 6 at 18 synoptic groun- level weather map 18. May 7 at 00 synoptic ground level weather map 19. Potential virtual temperature profiles — ~2 20. WU versus U 21. WQ versus UAQ Page 3 5 7 12 14 16 17 19 20 21 23 26 27 31 32 33 34 35 37 47 48 ' LIST OF FIGURES (cont) Figure Page 22. WT versus UAT 49 23. a w / u * v e r s u s Z/L 50 24. cr t/T A and 0^ /0.^  versus Z/L 50 25 -30. WT and WQ cospectra on semi log plot for 51-55 each, run 31 -50. Spectra and cospectra on log-log plot for 56-75 each run v i LIST OF TABLES Table Page I S t a t i s t i c a l results 10 II S t a t i s t i c a l results 45 III Air temperature and sea temperature used for 46 the computation of the bulk coefficients v i i ACKNOWLEDGEMENTS The writer expresses his indebtedness to his thesis advisor, Dr. M. Miyake, for helpful advice and guidance in the completion of this thesis. He i s also grateful to a l l the students of the Institute of Oceanography, U.B.C., among whom John McDonald and Douglas Davison deserve special mention. Mr. Don Hume made the experiment easier on the f i e l d . Miss Daphne Friesen helped in analyzing the data. I INTRODUCTION One of the most intensive meteorological f i e l d measurement programs over a trade wind region was performed during the B.O.M.E.X. experiment in the Barbados, in June and July 1969. In particular turbulent surface flux measurements were taken from a buoy FLIP and from an aircraft. The results of the aircraft measurement program were analyzed by Mark Donelan in his Phd. thesis. His conclusions were as follows: "The fluxes of moisture and momentum have similar single-peaked k-cospectral distribution below 50m and the most predominant of the scales responsible for the transfers have about the same wave length in both fluxes. By contrast, the k-cospectra of the sensible heat flux often contain two peaks of opposite sign. The positive peak i s at smaller scales than are the peaks of the other fluxes, while the negative peak occurs at larger scales." The same conclusions were given by Gordon McBean in his thesis, where he analyzed part of the FLIP flux measurements. "The results from B.O.M.E.X. pointed out the large differences in the distribution of temperature variance at large scales between the subtropics and mid-latitudes." Some of the FLIP data were also analyzed by S» Pond, and the results showed the particular behaviour of the temperature fluctuations in the tropics. One possible explanation of this particular behaviour of the temperature was the role of the radiative transfer, enhanced In tropical regions because of the high level of moisture content in the ai r . Studies of effects of radiation in a turbulent f i e l d showed that i t was not to be neglected ( Townsend 1958 ). Other po s s i b i l i t i e s for such a behaviour are the effects on an upper boundary condition, such as an inversion layer, or the role of the convective organization , which is induced mostly by the buoyancy forces due to high moisture content. This was the state of knot/ledge when we staged an experiment in Bimini to look specifically into the characteristics of the turbulent f i e l d and the temperature fluctuations over a trade wind ocean. Radiosondes were launched every six hours while the flux measurements were performed, so that i t was possible to compare the flux results with the mean atmospheric profiles. The study w i l l consist of three different parts. In the f i r s t part the turbulent spectra and cospectra are analyzed. It i s shown that their characteristics change with time within 24 hours. Then the study of the radiosondes shows an evolution in the profiles of temperature and humidity. The third part consists of a comparison of the two evolutions, which shows how the turbulent f i e l d i s modified by mesoscale atmospheric disturbances. The f i r s t paragraph describes the experiment i t s e l f , the experiment s i t e , and the instruments used for the turbulent flux measurements. Figure 1 - map showing the geographical location of the experimental 4 Description of the experiment The measurements described here were performed during a joint experiment with the Sea Air Interaction Lab of NOAA Miami, the University of Miami and the University of Hamburg in May 1971. The purpose was to investigate the structure of the Atmospheric Ekman Layer. The University of Hamburg measured the wind profiles by balloon tracking, using two f u l l y digitized and automatically recording theodolites. The SAIL group organized the joint experiment and installed wind, temperature and pressure sensors on several islands in the site. While the University of Hamburg was measuring wind profiles by balloon tracking, the University of British Columbia group measured the turbulent energy transfers at the surface of the ocean. The site chosen was a small island, Bimini, in the Bahamas, situated at 79°15' longitude and 25°40' latitude. The flux measurements were taken from a fixed mast standing in the sea at 50m from a small f l a t coral reef: Turtle Rock. The mast was situated at the southern part of Turtle Rock on the East side. Its location can be seen on Figure 1. The easterly winds had a fetch of 100km at least over shallow water before measurement s i t e , in a l l directions ranging from E.N.E. to S.S.E. The mast was 5m high but was on the average only 3m above the sea surface because of the tide ( lm variation ). A photograph i n Figure 2 shows the arrangement of the sensors on top of the mast. A l l the instruments were fastened to a pipe which could be orientated so that a l l the sensors were facing the mean wind direction. 5 Figure 2 - photograph of mast with instrumentation 6 This experimental site f u l f i l l e d together several requirements for accurate flux measurements. The mast was a fixed platform over water and the trade wind had a very long fetch over the ocean, however the f l a t coral reef changed the nature of the waves and water currents. Equipment A l l the instrument used for this experiment have already been described in other articles. Their capability of measuring turbulent fluxes have been discussed by Miyake et a l . ( 1970a, 1970b ) and Miyake and McBean ( 1970 ). Some of the sensors used for this experiment were : -A horizontal G i l l anemometer used to give estimates . of the mean wind speed and direction in situ. -A three dimensional sonic anemometer (Kaijo Denki) was measuring the instantaneous wind speed. This instrument measures the wind velocity by the time difference between two sound pulses propagating in opposite direction along the same path length. -A Thermistor (Veco 41 A 401 C) was used to measure the temperature fluctuations. It was mounted on a Disa hot wire support which was clamped on the sonic anemometer frame. This allows having the two sensors as close as possible, so that the cospectrum estimates between the wind velocity and the temperature were not affected by the spatial separation. -A Dew point hygrometer ( Cambridge systems, model 137-C3 ) was used to provide a calibration of the fast response humidity sensor. 7 w a v e s d e w P c i nt gin a n e m o m . s o n i c a n e m o m e t e r v o l t a g e c o n t r o l l e d o s c i l l a t o r tape record er d i s c r i m i n a t o r s i x c h a n n e l s c h a r t r e c o r d e r t h e r -m i s t o r Figure 3 - flow chart of recording system -A Lyman Alpha humldiometer ( Electro-magnetic Research Corporation ) measured the high frequency humidity fluctuations. It senses the water vapour content by measuring the absorption of the Lyman Alpha radiation across about 1cm path length. Since the frequency response of the instrument i t s e l f i s of the order of 1000 cycles, i t i s only limited in response by the path length. The sensor was placed in a small protective box, with two aperatures opened as close as possible to the light and the detector. This mounting device allowed us to obtain humidity fluctuations up to a frequency of 8 Hz before the noise level became important. A wave sensor was mounted at sea level on the mast. A l l e l e c t r i c a l signals were frequency modulated and multiplexed. They were recorded on one channel of a Hewlett-Packard tape recorder, model 3690. At the output of the tape recorder, we connected a discriminator which allowed monitoring of the different channels on a chart recorder. A diagram of the recording scheme is represented in Figure 3. Data Analysis The length of each run analyzed i s on the average 30 min. long. Each analogue tape was f i r s t digitized at 50 Hz. with the PDP 12 at I.O.U.B.C. In this process the channels were digitized sequentially. The d i g i t a l tapes were divided into f i l e s which contain one run each, i.e. about 9 x 10"* data points. The d i g i t a l tapes obtained ware f i r s t checked for possible parity errors, and then analyzed. The Fourier coefficients of each channel were 9 computed using the Fast-Fourier Transform. Then the spectra and cospectra ware computed. To extend the Foruier analysis to lower frequency, a program averages each data block and takes the Fourier Transform of the new time series obtained. The spectra and cospectra are plotted out in a log-log scale; the frequency axis being Log(fz/U), where f frequency z = the height of the measurement, U the mean wind. On the other axis i s plotted Log f(J)(f). Some of the plots are obtained i n semi log axis: Log (f z /u) versus f<j>(f). The fluxes are calculated by the total integral under the cospectrum : for example, i f W i s the fluctuation of vertical velocity and T the fluctuation of temperature: where (J)WT(f) represents the cospectrum between W and T. As pointed out by McBean in his thesis, the spectral correlation coefficients are of importance in the study of the transfer mechanism. They are given by: In the case of the temperature and the humidity, they indicate the similarity which exists between the temperature and moisture behaviours as a function of the frequency. The s t a t i s t i c a l results obtained from the spectral and cospectral <|>T,j,(f) = spectra of the T quantity <J> (f) = spectral estimate of the Q quantity. 10 cr •J * — c to to 1 CT^ -~ I D c OC B 3* 3 D to D O t o O E 3 ^ a o o rH to | CT t>0 |S E 3 O -a in T rH rH CM «a <3 c> CM c\ m CM CO co m sf co <• co rH rH rH rH m in m o p» vO 1/1 vO -a- •a-' « rH in m o VO \o 00 0  vO o o o o o CM CM CO CO vO r-i CO CO rH rH O o o O o O vO IT) CO o rH rH rH O 00 o m O VO m CO in ' .* • CM m VO o 00 CM CM CM rH rH -a CM CM <T O CM co co CM CM o o p^  m vO r~ r~ -a CO o oo 00 rH co O o m On c\ o Ov rH rH rH ~3 00 CO CO CO <r CO CO CO CO CM . CM CM CM CM m m o •a -a m VO -a CO o o O o o co o m o CO o CM CO rH CM CM o r-i r-l rH rH rH —^ m m m m m *a »a -a •a- m co -3 in vO r>-H H H Eh I t>0 0) IS I •B 3 c r O oo CO I o o CJ rH I c r o o l » P I r H CO CM 0  o Ov o VO CO <-4 o r— crv CO CO CM r~ 00 o 00 VO CO o . -a- o CO •a- CO rH rH rH 1 CM CM CO CM CM m co to CO -a tn o rH -a CO CM CM CM CO CO CO -a o o o O © O o o o o CO CM CO m o CO o m r-! CM rH o c rH CM rH CM CM o O C o o o O o o o o CM CO vO O •a-•a- CM CO vO VO CO CO O CO vO CM O m o -a o oo VO o rH m VO O rH CM •a -a rH rH rH rH vO VO CO CJ o o vO • vO VO VO m m f~ o CM CO CO CM CM CM CM CM CM CM 0) O m o VO O CO m r«. CO IO B •a- CO •a- CO m m P~ vo vo VO o o o m o o o o o O l-i o o o rH m rH m •a m o o CM CO CM rH CM rH rj *a •H rH rH CM CM o O o o rH rH rH rH rH rH rH rH -H — —^ m m . vn in vn m m m — —^ —^ Q vO vo vO vo vo vO r» O f-* ON o rH CO -a m CO o rH rH rH r-l rH . rH —t rH CM cv o. M rH rH t-H rH rH rH r-< M rn r j H H H H H H H f- fH H Table I S t a t i s t i c a l results 11 estimates are summarized in Table 1. A more complete discussion of the results i s given in the appendix. The following discussion deals with ten consecutive cases . recorded in a total time span of 24 hours : from May 6 at 10 AM to May 7 at 10 AM. Since we want to discuss the evolution of the turbulent structure of the flow, we w i l l start to look at the time traces. The change in convective organization i s directly v i s i b l e on the time traces. Time traces The time traces for two different runs, are displayed in Figure 4. They show the horizontal velocity from the G i l l anemometer, the thermister temperature and the humidity fluctuations from the Lyman-Alpha output. By comparing f i r s t the two temperature traces of the two runs ( TI10, TI13 ), one can see that there i s more low frequency variation in the f i r s t run than in the second run. By low frequency variations we mean time scales longer than about the 50s. If one compares the temperature trace to the humidity trace in the TI10 run, one can see that the two traces are correlated, and that an increase in temperature corresponded to an increase in humidity. This cannot be noted on the TI13 run. While the humidity trace shows large fluctuations of the order of the 50 s n o t h i n g can be seen on the temperature trace, which looks like a differentiated signal. The humidity fluctuations can be said to be of "sawtooth shape", indicating some kind of convective organization of the order 12 F A S T HORIZONTAL VELOCITY SLOW UP VERTICAL T VELOCITY i-r.-s , _ _ DOWN 1 1 0 ^ ^ ^ ^ ^ .. ^ / ^ ^ / ^ TEMPERATURE - p ^ V ^ ^ j l ^ ^ COLD DRY HORIZONTAL ^ . . T J ^ V W , ^ ^ ^ ^ . SLOW . UP VERTICAL 7.Jli , jj(i,Ji. im/s VELOCITY DOWN 13 :  WARM TEMPERATURE u COLD HUMIDITY :S-KS " WE 1 Figure 4 - time domain traces of horizontal wind, ver t i c a l wind ve-locity temperature and humidity fluctuation Upper diagram recorded at 12:00 (TI 10) Lower diagram recorded at 19:05 (TI 13) 13 of 150 m scale length: the humidity slowly rises u n t i l i t f a l l s suddenly, and rises again. Those features correspond to very sharp peaks of temperature change in the time trace. The TI13 run is very similar to what have been found by S. Pond ( 1971 ) during the B.O.M.E.X. experiment. The TI10 run i s different and shows a different kind of temperature and humidity correlation, denoting a different kind of convective organization. The study of the time traces does not provide a l l the information we need. It i s necessary to look at the spectra and cospectra of the temperature humidity and wind velocity to obtain more precise data on the structure of the flow. We w i l l now analyze the spectra of the wind components, of the temperature and humidity. Then we w i l l look into the characteristics of the different cospectra which measure the different turbulent transfers. To achieve the study in the frequency domain, we w i l l need to look at the T-Q correlation coefficients at different '-frequencies. Spectra Wind spectra The spectra of the downwind U, cross wind V, and ve r t i c a l velocity W are plotted on Figure 5, on log-log axes. At high frequencies they follow the Kolmogoroff -5/3 law, but the extent of the i n e r t i a l sub-range i s different for each component. The -5/3 slope of the U component ranges from fZ/U = 7 to fZ/U = 10 \ the V component from fZ/U = .3 to fZ/U = 7 and W from fZ/U = .5 l _ O G ( F Z / U ) normalized downstream, cross stream, and vertical wind component spectra - the straight lines have a slope of -2/3 corresponding to the -5/3 Kolmogoroff law. 15 to fZ/-U = 7. For larger scales, the U component has more energy than the V component, and the W spectra decrease . For scales of the order of 1 km, the V spectra show a peak which does not appear in the U-component. This feature was stated as a result of B.O.M.E.X., but i t was not clear i f this peak was real or caused by the effect of FLIP rotation. Since i t appears on our results, i t indicates that i t is a characteristic of the turbulence in the trade wind. Temperature and humidity spectra The spectra of the temperature and humidity fluctuations are plotted on Figure 6. The dissimilarity between the spectral shapes i s f i r s t to be noted. The temperature spectra show a decrease in -1 -2 energy between fZ/U = 10 , and fZ/U = 10 . This corresponds to eddy sizes between 100m and 1 km. For lower frequencies, the temperature spectra show a great v a r i a b i l i t y in the temperature fluctuations associated with each scale of motion. On the other hand the humidity spectra have energy with scales of motion associated with eddy sizes between 100m to 1 km. Their shape can be compared to the U-component spectra. On the other side of the spectra, the humidity shows a -5/3 law from fZ/U = 7 to fZ/U = .25. It is more d i f f i c u l t to define the i n e r t i a l subrange of the temperature spectra because i t appears between the instrumental fall-^off at higher frequencies and the decrease in variance characteristic of the trade wind situations for the lower frequencies. On Figure 7, one can see each individual spectrum of the temperature and humidity r r - 3 -2. 4 7 > 1 L O G ( F Z / U ) Figure 6 - normalized temperature and humidity spectra. The straight lines have a -2/3 slope. 17 1.0, 0.0. -1.0- • 10, ao--10-to, ao--to-to-. 0.0--to-to,. « cr -t.0J JO ^ to-, o-o-•©• ao--i.oJ CD ao--1.0-to-> 0.0- . -to-tO-j 0.0--to-to-ao--to-tO-j ao--to-tO-i 0.0--to-10-] 0.0--to-to-0.0--to-o ^— to-. X 0.0-o -10-t-& 0.0-LOG -10-10-j 0.0 -to to 0.0 -to-1.0 0.0 -1.0 to 0.0 -1.0 z o UJ or or O u Q 3-,.o c -CO UJ or 3 0.0 cr UJ 0_ -to UJ . „ Z O 0.0 < _J Ul or or O U to >-Q 2 o.o Z) I "O §-»• UJ 10 or ft00 Q_ LU H -to -*0 -10 -20 -1.0. 0.0 tO 2.0 -4.0 -3£ -2.0 -1.0 0.0 tO 2.0 LOG ( f Z / U ) -4a - 3 a -2.0 - i a o.o "to 2a - 4 a - 3 x 3 -2.0 -ijo 0.0 to 2a Figure 7 - normalized temperature and humidity spectra, and T-Q correlations, showed in sequence, to point out the time dependence of the temperature spectra and T-Q correlation. 18 fluctuation, together with the temperature and humidity correlation coefficient. On this diagram the va r i a b i l i t y of the temperature spectrum can be seen more easily. The only constant feature i s the —1 —2 decrease of the temperature variance for fZ/U between 10 to 10 For lower frequencies there are not two spectra which resemble one another. The constant feature can be related to the ver t i c a l temperature profile. As we w i l l see later ( Figure 12 ), the mean temperature profile below the inversion i s neutral, and the height of the inversion i s about 1 Km. This explains why eddy sizes between 100 m and 1 Km do not contribute to any temperature variance. On the other hand, the humidity profile decreases with height, so that every eddy scale produces humidity fluctuations. Cospectra The cospectra WU, WT, WQ are shown on the same diagram on Figure 8, r-plotted on a log-log scale. The low frequency part of the WT cospectra i s blanked out, since the negative estimates cannot be seen on a log-log plot. The WU and WQ cospectra have similar shape at high and low frequencies. The WT cospectra are plotted on a semi-log scale on Figure 9 to point out the variable importance of the downward heat transfer. , A l l the cospectra are displayed separately, each case on a different diagram, on Figure 10. This arrangement allows one to discuss their variation with time. They are also represented on a semi-log scale at the end of the thesis. This particular type of diagram lets us determine exactly the extent in frequency of the upward transfer, and the intensity of the downward flux. On a l l these diagrams, i t i s to be noted that the WQ and WU cospectra are similar and their signifigant scales of transfer are the same, while WT has a narrower bandwidth of upward transfer. Since the shape of the 19 p k -e-0.0'r -1.0 - 2 . 0 L • • -e-L l . o o O.Or -1.0-- 2 . 0 --e-o _J O.Or . -1.0 -2.0 » • •: v. . 4. • I< t" 40 -3.0 -2.0 -1.0 0.0 1.0 2.0 L O G C F Z / U ) Figure 8- Normalized cospectra between vertical velocity and ho-rizontal velocity, vertical velocity and temperature, ver-t i c a l velocity and humidity. The low frequency part of the WT cospectra i s blanked out since i t i s not relevant because of the negative estimates. 20 4-1 3-H 2 H H OH - 2 H - 3 ^ 7. 7 .. 5 T k 1 ' ... * i 2. 1 h%* A , - 4 - 3 - 2 -1 0 LOG(FZ/U) 2 Figure 9 - Normalized WT cospectra plotted on semilog axis to show the negative estimates. Each number i s a d i f -ferent run. 21 T I 0 9 0 . 0 , -1.0 . - 2 . 0 -- 1 0 • - 2 . 0 . 0 . 0 _ - t . 0 -- 2 . 0 . TI IO 0 . 0 . -1.0 . - 2 . 0 . - 1 . 0 . -2.oL 0 . 0 , - 1 . 0 -- 2 . 0 -TITI 0 . 0 , - 1 . 0 . - 2 . 0 . 0 . 0 . - 1 0 -- 2 0 -0.0, -1.0 --2.0L T H 3 0 . 0 , - 1 . 0 . - 2 . 0 . 0 . 0 , - 1 . 0 • - 2 . 0 . . 0 . 0 , -1.0 . - 2 . 0 . •TIM 0 . 0 X u. o Q T115-1 0 . 0 , - 1 . 0 - 2 . 0 TI16 0 . 0 - 1 . 0 - 2 . 0 li-te S X u. o Q 0 . 0 - 1 . 0 - 2 . 0 O O - 1 . 0 - 2 . 0 0 . 0 V o * •&• oo r X -i.o r u, o q _J 0 . 0 - 1 . 0 - 2 . 0 TI17 0 . 0 0 . 0 - 1 . 0 - 2 . 0 0 . 0 - 1 . 0 - 2 . 0 TI18 0 . 0 0 . 0 - 1 . 0 - 2 . 0 0 . 0 , -1.0 -- 2 . 0 -T I 2 0 - 1 0 . 0 - 1 . 0 - 2 . 0 . 0 . 0 - 1 . 0 - 2 . 0 -AD - 1 0 - 2 f l - 1 . 0 0 . 0 1.0 2 . 0 -10 - 3 0 - 2 0 -1.0 0 . 0 1 0 2 . 0 LOG (FZ/U) -40 - 3 . 0 - . 2 0 -1 .0 OO 1.0 2.0 Figure 10 - Normalized cospectra between vertical velocity and horizontal velocity, vertical velocity amd temperature, vertical velocity and humidity. They are displayed separately to point out the time dependence of the temperature cospectra. 22 cospectra changes from one run to another, we w i l l describe them separately. From TI09 to T i l l , the WT cospectra have an upward heat transfer at a l l scales, and the effective bandwidth is for 10 < fZ/U< 1, with a maximum transfer for fZ/U = 10 ^. The WQ cospectra have their -3 -1 effective bandwidth much larger (10 <fZ/U <f 10 ). The humidity transfer i s effectuated by larger scales than the heat transfer. For TI13 and TI14, the sensible heat transfer i s much different. A -3 -2 downward heat transfer appears at large scales ( 10 <fZ/U< 10 ), and the effective upward transfer i s reduced to smaller scales —2 ((5)10 <fZ/U< 2 ). The humidity transfer has s t i l l the same extent in frequency , the main flux being for ((3)l0~^ <fZ/U<(5)i0_1 ). From TI15 to TI20, the downward heat transfer i s much reduced, and there is almost -3 -2 no flux at large scales ( 10 <fZ/U< 10 ). The effective upward scales of motion are the same as for TI14 and TI13. The WQ cospectrum changes i t s shape for those cases. The transfer i s more effective at -3 high frequencies than for the previous cases ((5) 10 <fZ/U< 1 ) . Also i t appears as downward humidity transfer for some cases ( TI20 ). There i s no similarity between the moisture and sensible heat flux which can be deduced from those diagrams. The WT and WQ cospectra are different in their shape and their effective bandwidth of upward transfer. It must be noted that the WT cospectra are varying very much from one case to another, depending on the extent of downward heat transfer. T-Q correlations Figure U shows the T-Q correlations of the 10 cases plotted together. They show a great v a r i a b i l i t y for fZ/U< 10 ^. For the 23 o h-< DC O O I 1 f o --1 9 x V • '5, a « ' * 7 6» 7 % * 3 • 4 « 7 5 55 8 f 6 < V -4 3 - 2 0 L0G(FZ/U) Figure 11 - Correlation between temperature and humidity. Each case is represented by a different number. 24 lowest frequency estimates, many of them are either equal to +1 or -1, which indicates that there were two kinds of turbulent regimes at this scale: either T and Q are correlated, or they are anti-correlated. The temperature and humidity correlations are shown on Figure 7 with a separate diagram for each one of the 10 cases. The Q-T correlations are positive for high frequencies, and negative for some of the low frequency estimates. In this general pattern their individual shapes have as much var i a b i l i t y as the WT cospectra. We w i l l then describe them in sequence. From TI09 to T i l l , the negative T-Q correlations happen only for a few low frequency estimates ( fZ/U < (5)10 ). For TI13 and TI14, the extent of the negative T-Q correlations has the largest extent. T-Q correlations are negative for (4)10 < fZ/U <12)10 . For TI15 to TI20, the extent of the negative T-Q correlations fluctuates, and then resumes the shape of the f i r s t cases, i.e. the negative T-Q correlations exists only for a few estimates at very low frequency. It must be noted that the strong negative T-Q correlations are related to the presence of a downward heat transfer. The positive T-Q correlations are what i s expected for an upward heat transfer from the sea to the atmosphere. The negative T-Q correlation indicates that the air considered is warm and dry or cold and wet. Since one does not expect cold air to rise from the sea surface, i t means that there must be at large scales, some warm and dry air going downward. To obtain a better understanding of the different features described successively for the spectra, cospectra, and T-Q correlations, we need to have some information on the mean temperature and humidity profiles. From the shape of the spectra and cospectra we have studied, we 25 conclude that the turbulent f i e l d has two kinds of scales of motions: a small scale mixing which produces most of the sensible heat transfer, and a larger scale ( more than 1 Km ) characterized by downdrafts of warm and dry a i r , and also by a large variance of the V-component of the wind speed, which suggests some convective organization. This organization i s changing in time: the downdrafts are taking a variable extent in frequency, determining the domain of upward sensible heat transfer. The study of the spectra, cospectra and T-Q correlation showed a great time dependence of their characteristics. No more information can be obtained from the frequency domain which leads to an explanation of this change in time. We w i l l discuss next the results from the radio-sondes, and relate them to the synoptic weather map at the same time, and we w i l l show the presence of a weather disturbance which propagated over Bimini at that time. Radiosondes Soundings from the atmosphere were launched every six hours from Bimini Island. They are shown on Figure 12. The vertical scale i s the logarithm of the pressure, and the horizontal scale represents the potential temperature and the mean humidity in g/kg. Each diagram displays the radiosonde measurement, every six hours, starting on the 5th of May at 23:29, and finishing on the 7th at 06:20. The bottom figures show the radiosonde taken in Miami at the same time. The temperature time cross-section displayed on Figure 13 shows an atmospheric disturbance propagating in the temperature f i e l d at 850 mb as the presence Figure 12 - potential temperature and humidity profiles in Bimini and Miami 27 S r / a t ^ w / l t S n at both ends o f the d.agra. 28 of colder a i r at this height, which disappears and i s replaced by a homogeneous temperature gradient,. This disturbance can also be seen -on the sequence of radiosondes on Figure 12. . '•, Looking at the radiosondes, one can see that the inversion level i s going down un t i l 17:35, and then goes back up. The difference in level between 11:34, and 06:20, is of the order of 1000m. In the earlier case the inversion level i s 1500m, and at 06:20, the inversion level i s 2500m. In the following discussion we w i l l c a l l the layer above the inversion, the inversion layer, and the layer below, the subinversinn. At the beginning of the time series the subinversion layer i s neutral, indicating that the layer is well mixed from top to bottom. The very sharp gradient of humidity at 11:34 indicates that the water vapour cannot diffuse upward. This can happen i f a downward motion of the atmosphere prevents the upward mixing of temperature and humidity. The fact that the inversion level i s going down indicates a downward mean motion happening at this level. The subinversion layer receives moisture from the ocean, and since i t cannot diffuse upward, i t i s stored. This describes the situation u n t i l the 11:34 sounding. Then the equilibrium of the inversion layer i s broken, as shown by the 17:35 prof i l e . The potential temperature of the 880 mb point i s below a l l the potential temperature ascents. This low temperature can only be obtained by a diabatic process. It can be created by advection of cold a i r , or by a strong radiative cooling, or by evaporation by f a l l i n g rain. From the data we processed, i t is not possible to deduce which process i s involved. It i s also possible to assume that i t i s an erroneous measurement. Nevertheless the next sounding shows the dissipation of a well defined inversion level. A strong inversion forms which propagates downwards and prevents the mixing of moisture across i t . Then, at 06:20, the motion is completed and a new-inversion layer i s formed higher up. This describes the complexity of the motions occuring at the inversion level, at the same time as the flux measurements were taken at sea level. The time period of the subsidence of the inversion layer i s approximately 30 hours. It i s interesting to quote that the B.O.M.E.X. results indicate a variation in the moisture flux of the same period. The two phenomena- might be related. Another important feature has to be noted: the constant increase in humidity in the subinversion layer since the beginning of of the sequence. The last sounding i s much more humid than the others. The sea level mixing ratio goes from 12 g/Kg to 15 g/Kg in six hours, between the radiosonde of May 6 at 2321 and May 7 at 0620. The increase occurs not only at the sea level but up to 750 mb. This sudden change could be explained in terms of a boundary layer convergence, creating a humid tower. The same evolution i s noticeable on the Miami radiosonde data, although the amplitudes of the temperature and humidity changes are weaker. A subsiding motion of the inversion level lasts from May 5 at 23:03 to May 6 at 23:17. This sounding is very similar to the 23:21 Bimini sounding, showing a downward movement of the inversion which inhibits the upward mixing of moisture. The very low layers are affected by the night radiative cooling, as shown by the profiles at Miami taken in the morning at 11:00 on May 6 and 7. Since the radiosonde evolution showed a mesoscale atmospheric disturbance, we w i l l now look at the synoptic weather maps. 30 Synoptic situation The synoptic ground level maps of the area are shown on the figures 14 to 18. They represent the synoptic situation every six hours, starting on May 6 at 00 TU. One can recognize the steady easterly circulation which characterizes the synoptic circulation over the Atlantic ocean at this time of the year. On the last figure, corresponding to May 7 at 00 TU, one can see an anomalous pressure measurement taken by a ship near Bimini Island. We must note that this anomalous pressure measurement occurs at the same time as the weather disturbance seen on the radiosondes. According to the previous analysis of the radiosonds, we have described this disturbance as being formed of a subsident motion at the front followed by an upward mixing of temperature and humidity. We have to note also that the wind speed increased at the measurement site for the TI 16 run, which was recorded on the 7th from 01 AM to 0250 AM; the wind speed, which was previously of the order of 6 m/s, reached 7.5 m/s, and slowed down again to 6.5 m/s. The atmospheric disturbance we have just described is similar to the structure found by Zipser in the line Island experiment, for a cloud cluster (Zipser, 1969). This type of disturbance i s a travelling convective c e l l , and realises an upward mixing of latent heat by the mean of a "tower" of upward motion. We have shown that the inversion layer acts as a barrier to the upward transfer of latent heat, particularly in the trade wind where the wind f i e l d i s generally divergent. Nevertheless the general atmospheric circulation requires that the latent heat be transformed into kinetic energy in the tropical circulation. This transfer has to be effectuated by convective cells big enough to be able to break through the inversion layer to achieve the necessary upward transfer of latent heat.- It..-has 31 Figure 14 - May 6 at 00 TU synoptic sea level weather map Figure 15 - May 6 at 06 TU synoptic sea level weather map 33 Figure 16 - May 6 at 12 TU synoptic sea level weather map Figure 17 - May 6 at 18 TU synoptic sea level weather map Figure 18 - May 7 at 00 TU synoptic sea level weather map 36 been shown that the latent heat transfer in a tropical model of circulation is effectuated mainly by small immature cyclones: "the rare mature cyclone does not play a crucial role i n maintaining the energy balance of the general circulation". This transfer must be effectuated by mesoscale weather disturbances as cloud clusters or squall lines, which have the same structure as the disturbance we are discussing. The next step in the study i s to compare the evolution of this atmospheric disturbance with the results of the flux measurements. Discussion of the evolution of the profiles It i s noticeable that the shapes of the profiles are very much .time dependent, so that i t would be necessary to have radiosondes taken more frequently to be able to synchronize them exactly with the flux measurements. Nevertheless we can s t i l l get some conclusions from the four radiosondes a day. The study of the spectra, cospectra and T-Q correlations showed an evolution in time of their shapes. An evolution also appeared in the study of the mean profiles of the temperature and humidity. When we synchronize the two measurements, we note that the maximum negative T-Q correlations (cases TI 13, TI 14) correspond to the 17 35 sounding, when a downward motion of the temperature takes place. The large scale negative T-Q correlations correspond to big eddies bringing down warm and dry ai r from the inversion layer. This i s inferred from two facts: the presence of negative T-Q correlations, and from the fact that the inversion level disappears and mixes with the subinversion layer. The air from the inversion layer reaches the sea surface where i t i s detected by the turbulent sensors. The inversion layer i t s e l f i s a very stable layer; at the inversion level Figure 19 - Potential virtual temperature profiles of two cases in Bimini 38 the decrease in moisture does not compensate the increase in temperature froma buoyarcy point of view. This can be seen by the diagrams on figure 19, where the virtual-potential temperature i s plotted versus pressure. It shows that an inversion s t i l l exists in the v i r t u a l potential temperature. Since the air at the inversion level i s very stable, i t needs energy supplied by dynamical motions to be brought down to the surface where i t is detected. The subinversion layer must have an organized structure to allow for such descending motions of dry and warm ai r . What are the possible explanations for such a phenomenon. - Convective motions driven by the temperature i n s t a b i l i t i e s . This phenomenon would not produce a negative correlation between temperature and humidity at large scales. - Convective motions driven by humidity transfer. We have plotted on figurel9, the virtual-potential temperature profile. This profile i s very nearly neutral, and i t is not obvious whether or not convective motions can be driven by such a profile. - Internal waves at the inversion layer. They would require to be of considerable amplitude to be f e l t right down to the surface. The possibility of internal waves produced by the density s t r a t i f i c a t i o n i s excluded since the s t r a t i f i c a t i o n i s neutral. However, energy from waves at the inversion layer breaking at slightly earlier times might produce the phenomenon. - Dynamical i n s t a b i l i t i e s of the ECKMAN Spiral. These would produce long vortex r o l l s at an angle with the geostrophic wind, and the order of magnitude of such r o l l s i s of 1 km (Brown, 1970). In the sub-inversion layer the neutral s t r a t i f i c a t i o n would not interfere with those dynamical motions. Also the fact that the V-component spectra have more energy at scales of 1 km, than the U components, indicates that the motion / I ' I 39 a t tho32scales might be in long vortex r o l l s . Whatever process is producing the downdrafts, the main result i s t h e presence of them, and their role in modifying the turbulent boundary layer, and the turbulent transfers. Those downdrafts inhibit the upward transfer of heat, and enhances the upward transfer of moisture, since warm air i s able to achieve evaporation better than colder a i r . Those down-drafts are present at the same time as . the downward motion of the inversion level. We have shown that subsidence does not allow for upward transfer of moisture through the inversion layer and that the downdrafts enhance the transfer from the surface, but the moisture stays in the subinversion layer. Those downdrafts are responsible for the dissimilarity between the heat flux and the moisture flux at the surface. The presence of such downdrafts depends on larger scale disturbance, as we have observed from the radiosonde analysis. They exist only from TI 09 to TI 16ascharacterized by a negative T-Q correlation, and then they start to disappear when the subsidence also disappears. This shows how different scales of atmospheric motion can interact, starting at a mesoscale convective c e l l , which induces downdrafts of smaller scale, which themselves modify the latent and sensible heat flux. Since the release of latent heat in the upper atmosphere effectuated by a mesoscale disturbance depends on the moisture in the boundary layer which is 1 cm depends on the surface flux, one can see how the downdrafts can themselves influence the intensity of such a mesoscale weather disturbance. 40 Conclusions The purpose of this study was to investigate the turbulent fluxes over a tropical ocean, and to explain the dissimilarity which exists between the latent and sensible heat fluxes. We showed, with the help of the T-Q correlation coefficients, that the dissimilarity was created by downdrafts of warm and dry a i r . The scale of such downdrafts i s of the order of 1 km. Their presence can also be detected on the V-component of the wind speed spectra, in which there i s a peak at the low frequency end. It i s not possible from the data gathered during the experiment to deduce the exact origin of those downdrafts. Their role is to reduce the sensible _2 heat transfer to a band width which extends from f Z /U = 10 to f Z./U = 1., and to increase the latent heat transfer, since warm and dry air w i l l favor: evaporation. The analysis of the radiosondes showed that the downdrafts were associated with a mesoscale weather disturbance. The intensity of the downdrafts was greater in the subsident part of the perturbation. The var i a b i l i t y of the turbulent fluxes was related to the weather disturbance by the link with downdrafts happening during the subsidence and dis-appearing in the upward mixing. This shows how a mesoscale disturbance changes the characteristics of the surface fluxes by creating smaller scale downdrafts which reduce the sensible heat fluxes and enhance the moisture flux. The analysis of the radiosondes showed how the inversion level inhibit the transfer of latent heat above i t . Since the general circulation i s maintained mainly by the transformation of latent heat into kinetic energy, the necessary transfer of latent heat through the inversion 41 level has to be achieved i n tropical weather disturbances, such as easterly waves, hurricanes, cloud clusters and big cumulonimbus clouds. Those disturbances have enough energy to form a convective c e l l including a "hot tower" which allows the moisture content to break through the inversion level and diffuse upward. More experiments are necessary before the relationship between mesoscale processes and turbulent fluxes can be established. An extensive study of the v a r i a b i l i t y of the turbulent fluxes in the frequency domain between f Z/U = 10 ^  to f Z/U = 10 ^  has to be conducted in close relation-ship with the analysis of mean atmospheric profiles taken at the same time, during mesoscale disturbances. 42 BIBLIOGRAPHY Brown, R.A., 1970, A secondary flow model for the planetary boundary layer. J. Atm.^Sci. Vol. 27, No. 5, pp. 742-757. Donelan, M.A., 1970, An airborne investigation of the structure of the atmospheric boundary layer over the tropical ocean. PhvD. thesis, University of British Columbia. McBean, G.A., 1970, The turbulent transfer mechanisms in the atmospheric surface layer. Ph.D. Dissertation, University of British "Columbia. Miyake, M. , Donelan, M. , McBean, G. , Paulson, C , Badgley, F. , and Leavitt, E., 1970a . Comparison of turbulent fluxes over water determined by profile and eddy correlation techniques. Quart. J. Roy. Meteor. Soc. Vol. 96, pp. 132-137. Miyake, M., Stewart, R.W. , and Burling, R.W., 1970c, Spectra and cospectra of turbulence over water. Quart. J. Roy. Meteor. Soc. Vol. 96, pp. 138-143. Miyake, M., and McBean, G., 1970, On the measurement of humidity transport over land. Boundary Layer Meteorology, Vol. 1, pp. 88-101. Monin, A.S., 1970, The atmospheric boundary layer. Annual Review of Fluid Mechamics, Vol. 2, pp.225-249. Phelps, G.T., and Pond, S. 1971, Spectra of the temperature and humidity fluctuations and of the fluxes of moisture and sensible heat in the marine boundary layer. J. Atmos. Sci. Vol. 28, No.6, pp. 918-928. Pond, S. , Phelps, G.T., Paquin, J.E., McBean, G.A., Stewart, R.W. , 1971, Measurements of the turbulent fluxes of momentum, moisture and sensible heat over the ocean. J. Atmos. Sci. Vol. 28, pp. 901-917. Townsend, A.A., 1958, The effects of radiative transfer on turbulent flow of a s t r a t i f i e d f l u i d . J. Fluid Mech. Vol. 4, pp.361-375. Zipser, E.J., 1969, The role of organized unsaturated convective downdrafts in the structure and rapid decay of an equatorial disturbance. J. Appl. Meteor. Vol. 8, pp. 799-814. 43 APPENDIX » St a t i s t i c a l results Table I summarized the flux results; the values of the variances, u^, the different fluxes are given, as well as the st a b i l i t y parameter, Z/L. The range of the s t a b i l i t i e s varies from -0.09 to -1.04. We have ~2-represented on Figure 20 the stress as a function of U . It is noticeable that the drag coefficient has a lower value than already found in -3 BOMEX. Our average value i s .85 x 10 , while the result of previous -3 works ( S. Pond .1971 ) is around 1.5 x 10 . The reason for this low value may be the long fetch over shallow water ( around 15 feet ). The presence of large scale convective organized motions ("1 Km ) can produce large scale UW positive correlations, reducing the value of u^ . Similarly we have plotted on Figure 21, the humidity transfer versus UAQ. We -3 obtained an average bulk aerodynamic coefficient of 1.22 x 10 . This _3 result agrees with what has been found during BOMEX ( 1.23 x 10 ).WT versus .UAT is plotted on Figure 22 and no bulk coefficient can be deduced. ,r. We calculated the Bowen ratio B ( sensible heat flux/latent heat flux ). This coefficient i s shown in Table II. Its average value .16 i s larger than the BOMEX result ( .10 ). This difference may be due to the fact that our measurements were taken earlier in spring ( May ) than BOMEX ( June ) and more sensible heat i s transfered from the ocean to the atmosphere. Table II gives the variations of crw/u^, a^/T^, 0"Q/Q* with Z/L. According to Monin and Obukov's similarity theory, those ratios are only functions of Z/L ( Monin 1970 ). a w / u * must increase s t a b i l i t y , while O-fT^ and a /Q^  must decrease. We have plotted a /U^ as a function of Z/L 44 on Figure 23. It shows a tendency to increase towards more unstable cases. The value of Cw/U^  found is higher than the previous results ( McBean 1970 ). This i s due to the low value of U A which may indicate a highly convective motion. It varies between 1.5 and 2.4; McBean found an average of 1.53 with no tendency to vary with s t a b i l i t y . O^/T^ and °*q/Q* are also plotted as a function of Z/L on Figure 23. It shows a tendency to decrease as -Z/L increases. The results are in qualitative accordance with the i Monin Obukov's similarity theory, but no real functional dependence can be deduced, as one might expect from middle latitude measurements. ( Monin 1970 ) 45 Tape No aw XT T* a a. Q* B Z/Lj- Z/Lq TI 3 2.4 .40 .43 .14 .59 .44 TI 4 2.0 .52 .44 .15 .24 .15 TI 5 2.1 .47 .57 .16 .30 .19 TI 6 1.8 .55 .42 .10 .32 .23 TI 7 2.0 .44 .46 .09 .59 .45 TI 9 1.6 .81 .73 .17 .34 .16 TI 10 1.9 .55 .50 .20 .73 .30 TI 11 1.5 .58 .60 .20 .40 .•1*. TI 13 1.5 1.05 .97 .07 .17 .15 TI 14 1.6 1.05 1.20 .11 .18 .10 TI 15 1.5 1.00 .97 .18 .08 .02 TI 16 1.6 .94 1.02 .24 .07 .02 TI 17 1.6 1.00 1.10 .18 .06 .02 TI 18 1.6 .71 .80 .26 .09 .03 TI 12 1.5 .73 .88 .25 .12 .04 / Table II: S t a t i s t i c a l results Run N° T a i r T water UAT UAq TI03 24.4 26.6 7.6 54.9 TI04 23.8 25.6 9.4 66.0 TI06 23.3 23.3 0.0 56.4 TI09 27.2 25.6 -6.8 28.0 TI10 30.4 27.8 -9.1 40.2 T i l l 30.4 27.6 -13.2 32.0 TI13 26.1 28.8 9-7 39.6 TI14 26.1 26.6 2.5 35.0 TI15 26.1 25.8 -1.2 20.3 TI16 26.1 25.3 -6.0 33.7 TI17 25.6 25.6 0.0 40.2 TI18 25.6 25.0 -3.3 22.0 TI20 27.8 26.1 -11.0 26.0 Table III : Air temperature and sea temperature used for the computation of the bulk coefficient 47 To2 X > 4 ^ 6 J O B J O - V 2 2 -2 10 J U r n s £~ Figure 20. - WU versus U 2 Figure 21. - WQ versus UAQ 49 WT m s 1 k -p05 3 i I 1 1 1 — - r Hi .05 -3 0 10° UAT ms 1 k T 1 r 7 1 .05 Figure 22. - WT versus UAT 2.5 2D-12 H 1. •H-+ + + 1 1 1 1 1 1 .2 .4 .'6 .8 1.0 1.2 Z / L Figure 23 - values of -o /u. versus Z/L w * 1.2 1 . C H . 6 ^ . 2 H o • • o o * o Figure 24 - values of -a /T o o .2 .4 .6 .8 l b 1.2 - Z / L T / x A and -a^/Q^ versus Z/L 51 w TI09 THERHISTER TJ09 4.0 U =4.00 2 =3.00 DEC] =0.00481 + T+ -+- ,+ — i — -3.0 -2.0 -i.o 0.0 1.0 » TI09 M.PHR IYUAN TI09 U =4.00 2 =3.00 DECI =0.00430 . ++ . 1 -2.0 4.0 -3.0 -2.0 -1.0 0.0 r-1.0 2.0 52 4.0 3.0 2.0 A 1.0 A 0.0 -1.0 -2.0 A " TUO THERHISTER TUO 4.0 U =3.50 2 =3.00 0EC1 =0.00557 t + + A -3.0 -4. a •H-" TMO RLPHf) LTTHflN TI10 U =3.50 2 =3.00 DEC! =-0.00304 " 3 0 - 2 - 0 - i . o ^ o T o r o : o " 3-° -2.o. ^ I T o CU5 TO" 2.0 4.0 3.0 2.0 1.0 0.0 -1.0 A -2.0 A -3.0 V T i l l THERMSTER T i l l 4.0 A * U =3.50 Z =3.00 DEC1 =0.00453 • 1 -1— •4.0 -3.0 -2.0 1.0 0.0 1.0 V T i l l flLPHn LYHRN T i l l U =3.50 2 =3.03 0EC1 =0.00259 2 " .0 -3.0 ^2.0 -1.0 0.0 ].o To 53 4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 4 TI13 -?.0 THERHISTOR TI J. •<4.0 4.0 -, 3.0 H 2.0 H 1.0 0.0 -1.0 -2.0 4 -3.0 + t f ^ j " U =3.50 ' Z =3.00 DEC] =0.00144 w Tits lTURN flLPHH Til3 } ++  + + + U =3.50 Z =3.00 OECI =0.00321 + + -3-0 -2.0 -l.o u.O l.o 2 . 6 f.O in V T114 THERMISTOR T J 1 4 . U =5.00. 2 =3.00 OECI =0.00179 ++ + + -3.0 -2.0 -1.0 0.0 V TI14 LYMAN BLPHfl TIM r~ 1.0 U =5.00 2 =3.00 DECI =0.00503 • + + 2.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 0 -3.0 -2.0 -1.0 0.0 1.6 2 .6 54 4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 SONIC V 7 1 1 5 1 THERMISTOR TIIS-' i .0 n + + =s.eo 2 =3.00 OECI =0.00275 .0 -4.0 -3.0 -T.Q -ITo 0~7o ~ 7 X SONIC V T I1 5 - 1 LTMAN ALPHA TI15-1 + + + U =5.80 2 =3.00 OECI =0.00215 2.0 '.0 -3.0 -2.0 -1.0 r~ 0.0 1.0 5.0 n 4.0 H 3.0 H 2.0 1.0 UJ Q U J Q . cn 5K -1.0 -2.0 THERMISTOR TI16 TI16 •H-+" i f U =8.00 2 =3;00 OECI =0.00678 V T116 ALPHA LYMRN T116 + + + + + T U =8.00 2 =3.00 DECI =-0.0043 4 ; 0 -3.0 ^ 0 ^KO 0~0 T o 2.6^-0 -3-0 -2.0 -1.0 0.0 1.0 2.0 LOG(FZ/U) LOG(FZ/in 55 o U J D 5.0 -i 4.0 3.0 2.0 1.0 0.0 T H E R M I S T O R TUB TI18 U =6.30 Z =3.00 DECI =0.00537 CJ UJ Q L i n -1.0 -1 -2.0 -4.0 — i 1— -3.0 -2.0 -1.0 0.0 r -1.0 V TUB LTMAN ALPHA TI 18 U =6.30 Z =3.00 DECI =0.00313 It + + 2.0i . o -3.0 -2.0 -1.0 0.0 1 1 1.0 2.0 4-.0 n 3.0 2.0 H 1.0 0.0 SONIC V TI20-1 THERMISTOR TIZO-1 A. U =6.00 Z =3.00 DECI =0.00672 4.0 T + "4- + -i.o H -2.0 H -3.0 -4.0 -3.0 -2.0 -1.0 0.0 r~ 1.0 1 -J. 2-0,' SONIC V TI20-1 LYHAN ALPHA TI20-1 U =6.00 Z =3.00 DEC I =0.00343 4+ r — 1 1 r->.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 56 TI09 P4O10 2 I & 0 0 DEW bMioooO 1.0 n 0.0 -I -1.0 -\ -2.0 -3.0 -4.0 1.0 0.0 1.0 2.C -5.0 TI03 U =4.00 2 =3.00 DECI =1.00000 + + + + + -4.0 -3.0 -2.0 -1.0 0.0 l.o 2.ol TI09 TI09 U =4.00 2 =3.00 DECI =-1.00000 1.0 - i 0.0 H -1.0 -2.0 -3.0 -4.0 t 1 I I 1,1 II , _t= n _ 1.0 o.o i .o 2T0 - ~" r TI09 U =4.00 2 =3.00 DECI =1.00000 -t- + 4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 57 ALPHA LYMAN T109 .0 T .0 W U =4.00 H =3.00 OECI =1.00000 THERMISTER TI09 •1.0 •2.0 •3.0 •4.0 H + •5.0 -4.0 -3.0 -2.0 -1.0 r-0.0 1-1.0 1.0 o.o H -1.0 -i -2.0 -3.0 n -4.0 U =4.00 2 =3.00 OECI =l.CC0Do 2.C 3 -5.0 -4.0 I 1 1 r--3.0 -2.0 -1.0 0.0 t.O 2.0 .0 1 .0 H •l.o H •2.0 H -3.0 -\ -4.0 -5.0 V TI09 ALPHA LYMAN TI09 U =4.00 Z =3CflO OECI = idboooo + + -t- + + * 1.0 1 o.o A - l . o H -2.0 -3.0 -4.0 -4.0 n -5.0 —I 1 1 r--3.0 -2.0 -1.0 0.0 1.0 2.0 -4.0 V TI09 THERMISTER TI09 U =4.00 Z =3.00 OECI =1.00000' 4+ + + ++~ ++ f f - ' - I ' l l , , ,_ -3.0 -2.0 -1.0 0.0 1.0 2.G 58 TUO THO i.o 1.0 H -1.0 -2.0 H -3.0 H -4.0 H U =3.50 2 =3.00 DECI -1.00000 1.0 n 0.0 -1.0 -2.0 -3.0 -4.0 A L) =3.50 2 -3.00 DECI -1.00000 +++ + + + ++ -5.0 H r 1— -4.0 -3.0 -2.0 . V 1.0 i 3.0 -1.0 TI10 r-0.0 1.0 . -5.0 - I — To - 4 0 -3.0 — i — -2.0 -1.0 0.0 T110 r~ 1.0 -1.0 -\ -2.0-^ -3.0 -4 0 -5.0 , U -3.50 2 -3.00 0EC1 -1.00000 1+ ++~ ++ -+- +++ 1.0 -i 0.0 - i -1.0 -2.0 -3.0 -4.0 H — i 1 1 — i " ~"T 4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 n TIIO u = 3.50 2 =3.00 DECI =-1.000 J - -1 t -H >-h , 1 ' H M l -<J 0 -3.0 -2.0 -1.0 0.0 1.0 2 \ 5 59 ALPHA L*HnN TI10 THERMISTER TIIO 1.0 T 3.0 -l.o A -2.0 A -3.0 A -4,a A U =3.50 Z --3.00 OECI 1.00030 -5.0 4 --4.0 —T 1 1 1 r--3.0 -2.0 -1.0 0.0 1.0 1.3 1 0.0 -l.o A -2.0 -3.0 A -4.0 U =3.23 Z =3.00 OECI = 1 . 0 0 0 0 , -5.0 . r - 1— 1 , P--3.0 -2.0 -1.0 0.0 1.0 1.0 0.0 -1.0 -2.0 A -3.0 -4.0 A V TIIO ALPHA LYMAN TIIO U =3.50 Z =3.00 OECI =-1.0000C +4+ + -5.0 -4.0 -n -3.0 -2.0 -1.0. 0.0 1.6 1.0 0.0 -1.0 -2.0 -3.0 -4.0 * TIIO THERMISTER TIIO 1 -5.0 2.0 -4.0 U =3.50 2 --3.00 DEC1 = 1 . 0 0 3 0 + + -3.0 -2.0 "'•0 0.0 1.0 2.J 60 1.0 0.0 1^.0 -2.0 -3.0 A -4.0 -5.0 + + -3.0 T i n U =3.50 2 =3.00 OECI =1.00000 -2.0 -].0 0.0 1.6 1.0 0.0 -l.o A -2.0 A -3.0 -4.0 A • 1 2.0 -5.0 + + T i l l U -3.50 Z =3.00 DECI =1.00CC 4.0 -3.0 -2.0 -1.0 0.0 1.0 2 T i l l o.o A -i.o H -2.0 -3.0 -4.0 -5.0 J( , , , r--4.0 -3.0 -2.0 -1.0 0.0 U =3.5C 2 =3.00 DECI =1.00000 + + 1.0 0.0 -1.0 -2.0 •o A •4.0 A -5.0 V u T i l l T i l l M =3.50 2 =3.00 DECI = 4 . 0 0 T+ •HY ft 1.0 2.0 H S-T+ 4 0 -3-0 -2.0 ^ o~o" 1.0 2. 61 RIPH3 LTM3N Til." 1.0 o.o A -J.0 h -2.0 h -3.0 A -4.0 h -5.0 •J --a. 50 Z =3.00 OECI -1.00000 THERMISTES T i n 1.0 o.o -1.0 -2.0 -1 -3.0 -4.0 h -4.0 i I 1 r--3.0 -2.0 -l.C 0.6 7 T 2^0 "50.<, o + + 0 =3.SO Z =3.00 OECI =I.O00C —r- 1 • 1 r--3.0 -2.0 -1.0 0.0 r~ 1.0 1.0 0.0 -l.o A -2.0 -3.0 A -4.0 -5.0 V T i l l RIPHR LYMRN T i l l 0 =3.50 Z =3.00 OECI =1.00000 + + + + 1.0 -i o.o H -1.0 H -2.0 -3.0 A -4.0 T 1 "++-H _ 5 3 0 -3.0 -2.0 -1.0 0.0 1.0 2.1 V T i l l THERMISTER Til] U = 3 . 5 0 Z " 3 . 0 0 ' OECI = 1 . 0 0 C + + H 1-1 r- 1 1 1--4.0 -3.0 -2.0 -1.0 0.0 1.3 62 Tl 13 1.0 3.0 H -2.0 -3.0 -4.0 A 4. ++ U =3.40 Z :-3.00 DEC1 =1.30000 -5.0 -\ 1 r --4.0 -3.0 -2.0 — i — -1.0 r -0.0 — r -1.0 1.0 -i 0.0 -1.0 -2.0 A -3.0 -4.0 2.0 -5.0. T113 U =3.40 2 . =3.00 OECI =1.0000 ~i 1 1 r •4.0 -3.0 -2.0 -1.0 0.0 1.0 2 TI13 1.0 -, 0.0 -1.0 A -2.0 -i -3.0 •4.0 A 'J =3.40 2 =3.00 OECI =1.00000 -5.0 J -•• + + + + + " + + -4.0 -3.0 -2.0 i — r -1.0 -, 0.0 -1.0 -2.0 A -3.0 -4.0 V 0 • TI13 TI13 +++ U =3.40 2 =3.00 OECI = - 1 . 0 0 0 +++ I -1.0 0.0 l.o 2.0 -5.0 i -4.0 i r -3.0 -2.0 -1.0 0.0 —H+4-H 1.0 2. 63 ITHfiN filPHS TI13 1.0 T ).o A -i.o A -2.0 3.0 -J 4.0 2 =3.03 OECJ =1.00000 THERMISTOR TI13 1.3 0.0 - i.o A -2.0 -3.0 -4.0 -J 5.0 -4.0 -3.0 -2.o -JTO OTO TO U =3.40 2 =3.00 DECI =1.00000 + + + . 1 -s.o . 0 2.0 -4.0 V T113 IYHHN RLPHH T113 U =3.40 2 =3.00 DECI =1.00000 1.0 2.0 •3.0 A -4.0 1 + + + + I.O 3.0 -1.0 -2.0 H -3.& -4.0 5.0 r — -4.0 * 1 — , 1—i 1 1 1 1 -3.0 -2.0 -1.0 0.0 1.0 2.0 -5.0 -3.0 -2.0 -1.0 0.0 \ V TI13 THERMISTOR TI13 -i r 1.3 2.C U =3.40 2 =3.00 OECI =1.0003: + +t H f- f -hH Hr—t- i r- -T-Ht+ -4.J -3.0 -2.0 -1.3 0.0 1.0 2 64 'J =5.00 * -3.00 DECI =1.00000 TI14 -t- + .1.0 0.0 -1.0 -2.0 A -3.0 -4.0 H -3-0 -i.O -J.o 0.0 TIH 1.0 2.0 U =5.00 2 =3.00 DECI =1.00000 -5.0 U -S.OO Z -3.00 DEC! =1.OOJC 1.0 0.0 -l.p -z.o H -3.0 -4.0 4 —I ! 1 1 r--3.0 -2.0 -1.0 0.0. -4.0 -3.0 -2.0 — i 1 r -1.0 0.0 1.0 2. V t f TI14 T114 U =5.00 Z . =3.00 DECI ---] .oco; -tf-. ft, r~ 1.0 i "5.0 4-H—K-tr-W •T—1-1 1- r— 2.0 -4.0 -3.0 . -i.o -].o 0.0 i.o T H E R M I S T O R n:4 1.0 1 J.o A U -5.i)0 Z -=3.00 OECI -=1.00003 •I.O •2.0 A -3.0 -4.0 H •5.0 -4.0 1.0 0.0 -1.0 -2.0 -3.0 -4.0 T - I r— , . -3.0 -2.0 -J.O 0.0 j.o 2.0 -5.0 U -5.DC Z -3.00 OECI --l.Of, -4.0 -i r--3.0 -2.0 -l.o o.O l.o 1.0 0.0 V TI14 t-Ynai PLP.MO m i U =5.00 2 =3.00 OECJ =1.00000 -i.o A -2.0 + -3.0 -4.0 H -5.0 ill I -4.0 -3.0 -2.0 -1.0 0.0 1.0 -i o.o A -i.o H -2.0 H -3.0 -4.0 A W TI14 THERMISTOR Til 4 U =5.00 Z -3.00 OECJ =i.ojoor: •+ + + 1.0 2.0 5.0 - j — i — H — j — l — H — » , 1 -4.0 -3.0 -2.0 -1.0 0.0 l . J 66 SONIC N TI15-1 1.0 n 0.0 -I.O -2.0 A -3.0 A -4.0 SONIC V TI15-1 -5.0 4 U =5.80 Z =3.00 OECI =1.00000 1.0 I 0.0 A -1.0 A -2.0 H -3.0 -4.0 A -4.0 - l -r -3.0 -2.0 -1.0 SONIC V TI15-1 0.0 1.0 U =5.60 Z =3.00 OECI =i .ooo; ++ + 1 -5.0 2.0 -4.0 . .0 1.0 - i . o A -2.0 A -3.0 -4.0 A -5.0 U =5.80 1.0 Z =3.00 DECI =1.00000 0.0 -1.0 A •+• +4. +++ 1 1 1 r--4.0 -3.0 -2.0 -1.0 0.0 r -1.0 -2.0 -3.0 -4.0 2.0 -5.0 i i -3.0 -2.0 — i — -1.0 r-0.0 1-1.0 SONIC V TI 15-1 SONIC U TI15-1 =5.80 =3.00 DECI =-i.oc: u rv r -4.0 -3.0 -2.0 — i — -1.0 1 MHiM-0.0 1.0 67 i.o. 0.0 -1.0 -2.0 -3.0 A -4.0 LYMAN ALPHA Til5-1 U =5.80 Z =3.00 t.O OECI =1.00000 0.0 -1.0 V + -2.0 -3.0 -4.0 -5.0 -4.0 ^3.0 -2.0 -1.0 oTo lTo 2^0 - s-° f.O I.O 1.0 •2.0 -3.0 4.0 SONIC V TI15-1 LYMAN ALPHA TI15-1 U =5.80 | Z =3.00 I OECI =1.00000 1.0 -, + + 5.0 -4.0 l i1 0.0 -1.0 -2.0 -3.0 -4.0 - ~ i I 1 — | , 11 -3-0 -2.0 -1.0 o.O 1.6 2.6 -5.0 THERMISTOR TI15-1 U = 5 . 8 0 Z = 3 . 0 0 OECI = 1 . 0 0 0 . 4.0 -3:0 -2.0 -1.0 0 .6 1.6 2 / SONIC V TI15-1 THERMISTOR TI15-1 U. =5.80 Z =3.00 DECI =1.0000: H — I il I i l l — r + - -1 r -4.0 -3.0 -2.0 -1.0 0.0 1.0 68 jj 2.C 1.0 0.0 -1.0 TUG TI 16 Q -2.0 £» D J -3.0 -J -4.0 4 U =6.65 Z =3.00 DECI =1.00000 + + i — r -4.0 -3.0 -2.0 LOG(FZ/U) -i r 0 A o A .0 A 3.0 4.0 U =5.65 Z =3.GO OECI = 1 . 0 0 0 : -1.0 0.0 i.o 2.0 "4.0 T- 1 r -3.0 -2.0 -1.0 LOG(FZ/U) 0.0 1.0 2. 2.0 . -, i.o A 0.0 J J * - i . o < I . o D J -3.0 -2.0 -4.0 -H T116 U =6.65 Z =3.00 2-° DECI =1.00000 i . o H o.o —I 1 1 r--4.0 -3.0 -2.0 -1.0 0.0 -1.0 -2.0 -3.0 1.0 2.0 1-4.0 V u TI16 T116 ********* U =6.65 Z =3.CO DECI = - 1 . 0 0 0 • i i ; \ i i r T '-H--4.0 -3.0 -2.0 -1.0 0.0 1.0 2 L0G!FZ/U) LOG(FZ/U) 69 ALPHA LYMAN TI 16 0.0 -1.0 -2.0 H -3.0 -4.0 A -5.0 A -6.0 U pi\0i Z j ptviji DEW tl-rjoi + +. U J a U J a. 5K U_ a o.o -i.o -2.0 -3.0 -4.0 -5.0 A » r -4.0 -3.0 -2.0 -1.0 0.0 L0G(FZ/U) W TI16 ALPHA LYMAN T116 0.0 -1.0 A -2.0 A J> 3 -3.0 A u Q -4.0 J 3 -5.0 1.0 U =1. Z = 1. OECI =-1 + + U J o -6.0 --4 0 . 0 — i -1.0H -2.0 -3.0 -6.0 T h ••! i I i -i r CJ UJ D_ £ -4.0 CD O -5.0 A •4.0 -3.0 -2.0 -1.0 0.0 1.0 LDG(FZ/U) THERMI5T0R TI16 U =1.00 Z =1.00 DECI = ! . 0 0 0 C i 1 1 <—r 0 -3.0 -2.0 -1.0 0.0 1.0 2. L 0 G ( F Z / U ) v —7316 THERMISTOR W46-*K00 [ ' 1 . 0 0 -6.0 -! N 1 III i -4.0 -3.0 -2.0 -M) 0.0 1.0 2. m r , ( F z/u) 70 i.O 1.0 A 2.0 3.0 4.0 5.0 D TI17 TI17 U =G.70 z ra . o o OECI =1.00000 1.0 0.0 -l . o A -2.0 -3.0 -1 -4.0 V U =5.70 Z =3.00 OECI = 1 . 0 0 0 0 • + + -4.0 -3.0 . -2.0 V -1-3 0.0 I.O 2.3 TI17 U =6.70 -5.0 -t— -4.0 •1.0 A -2.3 A Z =3.00 OECI =1.00000 -3.0 -4.0 -1 -+++++ + +  + -5.0 -, 1 r 1 r--4.0 -3.0 -2.0 -1.0 0.0 ~i7o 1.0 0.0 -1.0 H -2.0 A -3.0 -4.0 A - i -5.0 Ar>—I l M| i 1 i— -3.0 -2.0 V U- 1 -I.O o.o i . o 2.:-,. TI17 T i n U =6.70 Z =3.00 DEC1 =-1.00C h+-H+. •»- + 2-0 -*.0 --3.0 -2.3 -1.0 0.0 1.0 71 ITHRN RIPHfl TI17 i-0 -i 1.0 -1.0 -2.JH -3.0 -\ -4.0 -5.0 U =G.70 2 =3.00 j.o OECI =1.03000 0.0 THERHISTCR TI17 -1.0 -2.0 -3.0 -4.0 -i U =6.70 2 =3.00 OECI =1.0000: + + -4.0 -3.0 -2.0 -1.0 0.0 To 2~0 -5.3 T r -4.0 -3.0 -2.0 -1.3 0.0 1.0 2.C i H •o H v T i n LTHRN fiLPHP) TI 17 + - t — I — H r U =6.70 2 =3.00 OECI =1.00000 4^ 0 ,-3.0 -2.0 1.0 0.0 1. I.J 0.0 -i -1.0 -2.0 -3.0 -4.0 A V TI17 THERHISTOR TI17 U =6.70 2 =3.00 ~ OECI =l-.0O00C + + 0 2.6 -5-0 4- ->+++-H 1--4.0 -3.0 -2.0 -l!o o T 1.0 2.0 72 0.0 -1.0 n + + *--4.0 -5.0 run TI13 u --C. I '3.1 OECI - - l . t -4.0 -3.0 -2.0 -j.o -i r CO ].o o UJ a o UJ Q_ co u. l . u 0.0 -1.0 -2.0 T -3.0 4 o -5.0 U =6.20 . i -3.0J 0EC1 = 1 .JCJ'Jv -4.0 -3.0 -2.0 -I.O 0.0 r-1 .0 2.i H i e j 1.0 o.o -J -1.0 - i -2.0 4 -3.0 A U =6.30 2 =3.00 OECI -1.00000 .0 3 J -4.0 -5.0 4.0 -3.0 -2.0 - l io 0.0 1.0 2.0 "-4-0 -3^0 ' -2.0 - l lo 0 . 6 •0 4 1.0 J.O 3.0 A i.O 3.0 TUB TJ18 U 2 DECI • + V \ T+4. ^6.30 •3.C0 • - ] . 0 0 C H — M i l l t - r -»-H 1.0 2. 73 LTMflN ff-PHH TI18 iHEKnisrou r n o o -t .0 U =6.30 2 -=3.00 DECI =1.00000 --*-+H-+ 1— 1 1 r--A\0 -3.0 -2.0 -1.0 0.0 U J a a U J Q -</> X CO o 1.0 2.0 1.0 0.0 -{ -1.0 -2.0 H -3.0 A -»• -4.0 H -5.0 U =6 . 30 7 O . U O DECI = 1 . C 0 0 i -4.0 + + + + •Hi —i 1 1 1— -3.0 -2.0 -1.0 0.0 1.0 1.0 0.0 A - i . o A -2.0 A -3.0 A •» -4.0 H -5.0 W TI18 LTHfW PLPH3 TJ18 + t U =6;30 2 =3.00 DEC! =1.00000 H—HTH-H r >.0 1.0 2.0 3.0 A 1.0 H -> 5.0 THERMISTOR TUB TJ18 U =6.30 •Z =3.00 DECJ =1.000C "fit TH 1 R -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 -4.0 _ 2 Q -1.0 0.0 1.0 74 SONIC U TI20-1 .0 n •1.0 -i •2.0 4 •3.0 4 -4.0 H + t. U =6.50 Z =3.00 OECI =1.00000 SONIC V TI20-I 1.0 0.0 -1.0 -2.0 4 -3.0 4 -4.0 -5.0 -I 1 , 1 1 1—: , -s.o -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 -4.0 U =6.50 Z =3.00 OECI M.GCC -3.0 -2.0 -1.0 0.0 1-1.0 2.0 SONIC V TI20-1 1.0 0.0 - i . o H -2.0 =L -3.0 4 -4.0 H -5.0 J =6.50 Z =3.00 OECI =1.00000 + + - i r 1.0 0.0 -1.0 -2.0 -i -3.0 -4.0 SONIC V TI20-1 SONIC u TI20-1 U =6.50 Z =3.00 OECI =-1.000: + + + -H-'ft , -5.0 -\— I,I i --4.0 -3.0 , -2.0 - l ! o oTo 1~3 2^6 -4!o -3!o -2!o —T • 1 HH-tf -1-0 0.0 1.0 2.( 75 LYMAN ALPHA TI20-1 1.0 o.o H - i . o H -2.0 -3.0 H -4.0 H -5.0 U =6.50 2 =3.00 OECI =1.00000 THERMISTOR TI20-1 ++• 1.0 0.0 -1.0 -2.0 -3.0 -4.0 ' - 4 ' - 0 - 3 : ° - 2 - ° - » ' ° o l i l T o ~*'°-a.o I^o" - i l o o.o To U =6.50 2 =3.00 OECI =1.000; + + 2. 1.0 0.0 -1.0 --2.0 -3.0 -4.0 H -5.0 SONIC V TI20-1 LYMAN ALPHA T120-1 U =6.50 2 =3.00 OECI =1.00000 ++ •H-t * ~i—H i r -4.0 -3.0 -2.0 -1.0 0.0 •4-t-f-1.0 1.0 0.0 -1.0 -2.0 -3.0 -4.0 SONIC V TI20-1 THERMISTOR TI20-1 U =6.50 2 =3.00 OECI =1.00CC 4-++ , -5.0 T o "4-o -+-T-+--3.0 -+—r— -2.0 0-0 1.0 2.c. 

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