os io a Pte: Vad yee. oa ™ 1 wh a” we Bas the ¢ rs ail oe i 4 eA”, a, " Met nhl Cm , on reso Ne, we + ys e a ar ww N, Rr ao ne oa S| Bro a. 7 =~ rs f rw 5 Ta) fr J » Sa, a ees, ‘ i ii, Ne a, rau vii p was 1, Set ee ef a ee wie Fee a i Ns Pe ae, lie ge GT rent an A cpm | ENA INN . oF od sud a a Mt crn alien ot ae hae mtn ne Ppl ia Ve’ SS . ore Sens Oe) yd ene 8 nai ein ; pee ee &, 1 ERTICAL AND HORIZONTAL = THERMAL STRUCTURES IN THE SEA FACTORS AFFECTING UNDERWATER SOUND TRANSMISSION ARE MEASURED BY USE OF A TOWED THERMISTOR CHAIN E.C. LaFond and K.G. LaFond 29 July 1966 Research and Development Report U.S. Navy Electronics Laboratory l “ y Af ‘ + 6 af j ated a Od wv aan Fo “wot vat aia f" yy ——— “— is: i ey paw Wee ee | uy . wy, o ES | ey taba Ee a Wo: \S%9) | so DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED THE PROBLEM Investigate oceanographic factors pertinent to the behavior of underwater sound and to surface and subsurface navigation. Specifically, study the thermal structure of the upper sea layers by use of a towed thermistor chain. RESULTS 1. Detailed temperature structure data on the upper 800 feet of the sea south of Baja California, acquired by the U.S. Navy Electronics Laboratory (NEL) Thermistor Chain, revealed vertical and horizontal motion, large scale turbulence, and possible Doppler effects. 2. The sea temperature structure was found to vary widely and may be characterized by (1) smooth thermoclines where the isotherms had vertical oscillations with wavelengths generally greater than 2400 feet; (2) normal thermoclines of varying wave- length that averaged from 1400 to 2400 feet; (3) rough thermo- clines with steep isotherms and most wavelengths of less than 1400 feet; and (4) irregular thermoclines of large vertical shifts and major turbulent-type oscillations. 3. Irregular thermoclines were found to be related to fronts in water-mass boundaries caused by intermingling of the Gulf of California Water with the California Coastal Current Water and Eastern Tropical Pacific Water. 4. The isotherm slopes, determined from over 65,000 data samplings, showed a median of absolute values of vertical slope to be 0°25', and the 70th percentile of absolute values of slope to be 0°51'. The steepest isotherm slopes were found just south of the peninsula of Baja California. 5. The slopes were steeper during a tow to the north or south, which implied that off southern Baja California and in the mouth of the Gulf of California the wave crests in the thermocline were oriented more in an east-west direction. 6. The significant peaks in the power spectrum of isotherm depth of encounter were so distributed at different frequencies that no single frequency was dominant. il 7. The slopes of the log frequency vs the log of power spectrum averaged nearly -5/3 or in the turbulence range. Small deviations from the -5/3 slope occurred around 0.15 cycle per minute (cpm) (0.66 mile) in both the deeper and shallower iso- therms and around 0.30 cpm (0.33 mile) in the shallower isotherm. ” RECOMMENDATIONS 1. Continue development of the thermistor chain to improve the quality, accuracy, and reliability of data. 2. Investigate the use of additional sensors (in conjunction with temperature) on the thermistor chain for measuring current, turbidity, sound velocity, and salinity. 3. Use the thermistor chain to study thermoclines and associated internal waves and investigate the effects on thermo- clines of islands, shoals, coastal configurations, tides, known currents, upwelling, water-mass boundaries, storms, and seasons. 4. Examine in detail with the thermistor chain to determine the most persistent areas of smooth, normal, rough, and irregular thermoclines, and conduct sound transmission studies in, and adjacent to, such features to evaluate their effect on sound trans- mission. ADMINISTRATIVE INFORMATION Work was performed under SR 104 03 01, Task 0580 (NEL 140461) by the Marine Environment Division. This report covers the period February 1962 to February 1966. It was approved for publication 29 July 1966. The authors wish to express appreciation to P. G. Hansen, who led part of the cruise on which the data were collected, and to O. S. Lee, G. H. Curl, and J. L. Cairns for reviewing this report. Much of the processing and analysis of the data was started by E. L. Smith and Mrs. A. T. Moore. Thanks are also due to Mrs. R. Brown for the programming and machine computation, and to LT John Baldwin and the personnel of USS MARYSVILLE for making possible the collection of data. REVERSE SIDE BLANK iil Pa a A e7 RET (3 ; yey ’ a Bras blk, war TAY repgh,. ¥ PF fea ied ae eal ihe ts Urmme OM WET he rad nee oe te pee Bb Oa) = Pas Ate Vani ‘eb lie: So (OG glee ade yale , Syahatt ae eR jo eda Mie inthe a aang cotta Mt hit (hue isn te Seige ae iv rays ie SR Whit ee TO Lem Lh. ett i t that dep raalni a sii yy) TORR sy ROM tele , RAS state” * SetiaahY pales ae ity ORG 4a pela uvndin OF i hen ' nt ay “end wt owik - ; Vis aherey , pat A bi iY the Fopegedai tar PE pain ioe phy eutelens em Paes Mipyilet ry a Male i Bree oe siuhr ioe AWTS dK ie duces ni ator vibes 4 @ t Ce ey N cma! nding anne ye ah Sony! Reakeoby Lente tes ine bee tad ee ar rT . wee pine | aga oA adh Lag i TP 1. =wy See nel Fiwi . eee A (on; Sy SR nately é pnahp a a OAR 2 ives cone: ain PRS, a, a Ss CONTENTS INTRODUCTION... page 1 EQUIPMENT... 2 OBSERVATIONS AND DATA... 5) Procedure... Vertical Thermal Oscillations... © THERMAL STRUCTURES... 7 Common Type... 2 Temperature Inversion... 11 Cold Water Intrusion... 12 Ridge (or Dome)... 15 THERMOCLINE CLASSIFICATION... 16 Smooth Thermocline... 17 Normal Thermocline... 20 Rough Thermocline... 25 Irregular Thermocline... 29 TEMPERATURE STRUCTURE VARIABILITY... 32 Differences of Depth Values (Isotherm Slope)... 36 Autocorrelation of Depth Values... #& Power Spectrum of Depth Values... 4 Turbulence... 65 RECOMMENDATIONS... 72 SUMMARY AND CONCLUSIONS... 72 REFERENCES... 74 APPENDIX A: THERMAL STRUCTURES (figs. A1-A30)... APPENDIX B: ISOTHERM DEPTH DIFFERENCES (figs. B1-B52)... Bl APPENDIX C: ISOTHERM DEPTH AUTOCORRE LATION (figs, C1-C€52)... CZ APPENDIX D: ISOTHERM DEPTH POWER SPECTRA (SEMI-LOG) (figs. D1-D52)... D1 vi oo oO woamarnrtoaunwnrwDn 10 TABLES Depth factors for conversion of linear scale to true depth... page 8 Time and location of thermistor chain data samples used for analysis... 34 Cumulative distribution of slopes of isotherms .. .4 Autocorrelation (R,) of successive half-minute readings of isotherm depth... 49 Slope of log-log relationship between power spectrum and frequency... 67 Oy ILLUSTRATIONS The oceanographic research vessel USS MARYSVILLE and thermistor chain... page 2 Thermistor chain towing technique... 4 The pattern of thermistor-chain towing... 5 Two intersecting trains of internal waves... 7 Location of thermal structure examples... 9 Common thermal structure... 10 Thermal structure - inversions... 11 Thermal structure - cold intrusion area... 13 Thermal structure - ridge... 14 Location of sample sections of thermal structure data... 17 Smooth thermal structures... 18 Normal thermal structures ... 22 Rough thermal structures... 26 Irregular thermal structures... 390 Location of samples used in analyzing isotherm characteristics ...352 Sample of original data... 37 Cumulative percentage distribution of depth differences ... 38 Frequency distribution of slopes ... 40 Direction of tow vs average median vertical isotherm angle of shallow isotherms... 42 Direction of tow vs average median vertical isotherm angle of deep isotherms... 48 21 22 26 27 28 29 30 3d 32 33 34 35 36 37 38 ILLUSTRATIONS (Continued) Average 50th percentile slope of deep and shallow isotherms... 44 Geographic distribution of depth differences of shallow isotherms... 40 Geographic distribution of depth differences of deep isotherms... 47 Autocorrelation of successive half-minute readings of isotherm depth... 49 Geographic distribution - autocorrelation of successive half-minute readings of shallow isotherm... 02 Geographic distribution - autocorrelation of successive half-minute readings of deep isotherm... 53 Power spectrum from successive half-minute readings of isotherm depth... 55 Summary of direction of tow distributions of power spectrum of shallow isotherm... o7 Summary of direction of tow distributions of power spectrum of deep isotherm... 59 Summary of longitudinal distribution of power spectrum of shallow isotherm... Og) Summary of longitudinal distribution of power spectrum of deep isotherm... 60 Total power spectrum between 0.05-0.30 cpm... Geographic distribution of integrated power spectrum of shallow isotherm ... 63 Geographic distribution of integrated power spectrum of deep isotherm... 64 Power spectrum from successive half-minute readings of isotherm depth... 66 Average power spectrum of 25 shallow and 25 deep isotherm depths... 69 Geographic distribution of slope of power spectrum curve of shallow isotherm... 70 Geographic distribution of slope of power spectrum curve of deep isotherm... Gal REVERSE SIDE BLANK 62 vii ra mB) hi pray i J _ i A ; on ; oahu rlt 40 # rots Sit retire hd rear sth ental | as bs oe rae i ‘oO VMS 45 ar ig? RD iy ap ii boing pit ivy $ cin TS wae Teed “is ari a es: _— i teh sia Le apart Ne a we hehe Ate ni ti cae H H Ng si} ir ‘ neyadye a Ae i INTRODUCTION The U.S. Navy Electronics Laboratory thermistor chain, deployed from the oceanographic research vessel USS MARYS- VILLE (EPCE(R) 857) (fig. 1A) measures and records vertical sections of sea temperature structure from the surface to a depth of 800 feet. The first thermistor chain cruise by USS MARYS- VILLE was made in June 1961, and the results derived from it and six succeeding, data-collecting voyages have been pub- lished.!: 2: 3.4.5 The eighth chain cruise, which covered the coastal waters from San Diego, California, to Mazatlan, Mexico, investigated the nature of vertical and horizontal variations in sea temperature structure off southern Baja California and across the entrance to the Gulf of California. To detect the area of a possible water-mass boundary, the thermistor chain was towed in a complex, fan-like pattern ex- tending south of Baja California. This region, probably the most favorable in the northeast Pacific Ocean for acquiring data on thermocline roughness, is characterized by three types of water impinging on each other: (1) the California coastal current, rel- atively cold and of low salinity; (2) the warm, high-salinity, trop- ical, east Pacific water; and (3) the warm, high-salinity Baja California coastal water that wedges into the California current near Cape San Lucas.® Each water mass has its own definitive thermal structure as well as modifications resulting from differ- ential advection and large-scale turbulence. The data gathered by the thermistor chain were examined for oceanographic processes and types of thermoclines. Two se- lected isotherms, used to investigate depth change or slope, were subjected to autocorrelation of successive depth measurements, and the power spectrum of isotherm depth was determined. : Bess we : ae, ‘a i» 5 Pee iis so isan wh x iki i Figure 1. (A) The oceanographic research vessel USS MARYSVILLE with thermistor chain deployed. EQUIPMENT The NEL thermistor-chain ” assembly of drum, hoist, links, and weight weighs 37,500 pounds. The deck units consist of the hoist, chain, generator, and the drum on which the chain is wound (fig. 1B). The chain is composed of flat links 1 foot long, 10 inches wide, and 1 inch thick. A 2, 300-pound, torpedo-shaped weight at the end of the chain tends to maintain it in a more vertical position during towing, and represents the maximum depth of observation. One hundred pairs of insulated electrical leads fit through grooves inside the flat links, and the electrical wires (harness) are connected to the temperature sensors at 25-foot intervals (fig. 1C). The upper ends of the electrical leads are connected to a recorder located in the ship's laboratory, where signals from each of the 34 sensors are scanned electronically. The scan cycle time is 12 seconds. The order of sensing is from the surface to the deepest sensor, or thermistor bead. The chain, inclined backward at an angle, moves forward with the ship, and the sensing takes place in an approximately vertical 8 i. CHAIN ee 4 HOIST CHAIN GENERATOR FOR HYDRAULIC | SY STEM Figure 1(B). Thermistor chain assembly suspended from the fantail of USS MARYS- VILLE. HARNESS (120 INSULATED WIRES) CONNECTOR TEMPERATURE SENSOR STEEL CHAIN LINK PLASTIC FAIRING Figure 1(C). Chain link, fairing, harness, and temperature sensor. line. The signals, interpolated electronically, are used to record only the depth of whole-degree-centigrade isotherms on 19-inch- wide tape, which equals, in data acquisition, that derived from the lowering of a bathythermograph every 120 feet at a ship's speed of 6 knots. The surface temperature, recorded by the uppermost thermistor bead, and the depth of the deep extremity of the chain, recorded by a pressure sensor, are printed on the same tape. The oceanographic research vessel, towing the thermistor chain sus- pended nearly vertical from the fantail, cruises forward and ac- quires sea temperature structure data to a depth of 800 feet. Two- dimensional coverage, depth and distance, is thus achieved (fig. 2); however, time, a third dimension, must also be considered. The small change in depth at the end of the chain, caused by the forward movement of the ship, is disregarded in the following analysis. ALA LAST § PFSGDGD GSS SDSS SSS SSSISLISFISSS Figure 2. Thermistor-chain towing technique used to acquire a two-dimensional measurement of sea temperature structure. OBSERVATIONS AND DATA Procedure On the eighth cruise of USS MARYSVILLE with the therm- istor chain, the ship followed a course about 60-80 miles off San Diego south to near Cape San Lucas, Baja California. The vessel traced a fan-like pattern that extended 100 miles from the Cape and terminated in deep water off Mazatlan (fig. 3). The return trip traced a similar, more widely spaced pattern extend- ing out 170 miles. Advancing at a speed of approximately 6 knots, the chain recorded temperature from the surface to a maximum depth of 750-800 feet. Before an analysis of the isotherm recordings derived from Cruise 8 is presented, certain features of sea temperature struc- ture should be described. BAJA CALIFORNIA MEXICO 20° 113° OW 106° Figure 3. The pattern of thermistor-chain towing on Cruise 8 and the identification of thermal structure data sections. | Vertical Thermal Oscillations The thermal structure off Cape San Lucas was investigated on a number of cruises ®° using bathythermographs and revers- ing thermometers, and the studies revealed the existence of ther- mal fronts.* However, the nature of the detailed vertical changes in the isotherms had not been measured with the thermistor chain. Definite density boundaries in the sea should exhibit certain frequencies and modes of oscillation. It is pointed out!" that a given density boundary may have its own normal oscillating fre- quency (the Vaisala frequency). Strong winds may create convec- tion cells and eddies in the upper layers of the sea, and the re- sulting circulation will lower the thermocline more in one area than another. Vertical oscillations in the thermocline can be in- duced by fluctuating winds at the air-water surface, which can also generate waves on the thermocline. Tidal and other forces that impel water movement around land boundaries and topograph- ic features can also start oscillations in the thermal structure. There is, however, reason to believe that the vertical variations in the isotherms observed with distance can be internal waves moving in one or more directions and causing reinforcement or cancellation of the individual waves (fig. 4). The progressive nature of these oscillations in shallow water has been established by studies conducted from anchored ships and from the NEL Oceanographic Research Tower. ” The detailed recording of isotherm depths indicates the complicated character of sea temperature structure and empha- sizes the complex nature of the ocean in its temperature-related chemical properties and biological populations. *The term thermal front is defined as the leading edge of aborder separating unlike water masses. The boundary is frequently ill- defined, transient, and associated with motion causing a relative vertical displacement. Fronts are commonly observed in the region between water masses with marked gradients in temper- ature, salinity, and other properties. The frontal zones are important in sound transmission because of their strong horizon- tal and vertical gradients in sound velocity. Figure 4. Two intersecting trains of internal waves. THERMAL STRUCTURES Temperature changes at either the surface or various depths may be caused by several factors, such as (1) the advection of water of a different temperature; (2) radiation from the sun; (3) mixing by the wind; (4) tidal currents; or (5) internal waves.!3 Since such forces may occur simultaneously, it is difficult to de- termine their individual effects, but a detailed, two-dimensional data section, obtained by the thermistor chain, can frequently in- dicate the contribution of each factor to the processes taking place in the sea. The thermal structure presented here is more properly the "structure of encounter" or ''depth of encounter of isotherms." The vertical scale is depth, but the horizontal scale may be con- sidered as either time or distance. The amplitude of the vertical changes in isotherm depth is correct in either sense, but after 4 hours of continuous recording, changes will have occurred at the beginning of the section. The structures represent a spatial plot rather than a time shift, since the advective and vertical oscilla- tion movements caused by internal waves in strong thermoclines occur more slowly than does the movement of the ship across the section. The detailed thermal structure data to be presented can be described as vertical sections in the sea in the same sense as oceanographic sections derived from serial station data. The vertical scale is not entirely linear, since the thermistor chain assumes a slight curvature between the vessel and the weight at the end of the chain. For exact depths the linear depths on the analog record of thermal structure can be multiplied by the factors given in table 1. TABLE 1. DEPTH FACTORS FOR CONVERSION OF LINEAR SCALE TO TRUE DEPTH Depth factor * Linear Recorded Scale (for 100-foot intervals) 0 100 0. 930 200 0.955 300 0.980 400 1.005 500 1. 030 600 1. 055 700 1. 080 750 1.105 The thermocline normally occurs where the ratio of linear depth to true depth is nearly unity. For practical purposes the linear scale is accurate and is used throughout this report. *Smith, E.L., Determination of Towed Configuration and Sensor Depths of the USNEL Thermistor Chain, U.S. Navy Electronics Laboratory Report, 1966 (in preparation). The four examples presented in the following sections de- scribe thermal structures recorded along sections of continuous tows made off the western and southern coasts of Baja California (fig. 5). All sections in figures 6-9 represent straight-line tows of nearly 4 hours duration, or about 24 miles. Dee N sso Qi BAJA : POSITION 1 CALIFORNIA \o ee ~ ; = MEXICO (FIG. 6) 26° POSITION 2 NS (FIG. 7) Ase 4 q SS b t 2 ReStTION 3 ~ LAPAZ ~’ 93° (FIG. 8) CAPE MAZATLAN SAN P Tone OSITION 4 ae" (FIG. 9) ale 20° WIZ W ee SS} ae Wise Wz iii WiC? 10s Ok Tare 10¢ Figure 5. Locations of four measured examples of thermal structure. Common Type The first example (fig. 6), taken 50 miles off Baja California at Position 1, is the isotherm recording made while the thermistor chain was towed at a speed of about 6 knots. The vertical scale, magnified about 100 times compared to the horizontal scale, causes the isotherms to appear much steeper than in actuality. Only seven whole-degree isotherms, 16° to 10°C, occurred in the upper 10 SEA SURFACE | SURFACE! LAYER | STRONGEST (MAIN) sso THERMOCLINE INN a A 22 Na a 8 ey ae = * vane WM Net Cera 0 rts, ‘ond ¢ daca Peeper Ne Nee RA? 1 ~vafl ir T ~100 FT /-— 1 3 MILES Figure 6. A common thermal structure (Position 1, fig. 5). 800 feet. Throughout the depth was an upper mixed layer with no whole-degree isotherms from the surface down to about 200 feet. Close vertical spacing of isotherms directly under the mixed layer revealed a sharp thermocline. Below this was a gradual widening of isotherm spacing. This, the most common type of vertical temperature structure in the upper layers of all oceans, is present in 85 percent of the Pacific.!4 Horizontally, the most obvious feature is large undulations of the main thermocline. These were about 12 miles long, 50-100 feet high, and probably associated with the tidal cycle. The height of the long wave decreased with depth (fig. 6). The deepest iso- therm (10°C), occurring in a weak vertical gradient, fluctuated widely and showed no definite long-wavelength cycles, as do the 16°C isotherm and others in the sharper part of the thermocline. Small vertical oscillations appeared generally at a rate of 2 to 4 per mile, but 5 or 6 per mile were noted. Such oscillations, with amplitudes from several to around 20 feet, are present in all the isotherms in the thermocline, and are largely in phase with one another throughout the strongest part. Amplitudes of the small vertical oscillations increased inversely with the strength of the vertical temperature gradient. At greater depths (11°C and 12°C isotherms), the amplitudes were as high as 30-50 feet. Accurately observed isotherm depths in all oceans show similar vertical changes with distance and time. Temperature Inversion The second example (fig. 7) was recorded 90 miles south- east of the first example, where the water was warmer and the thermocline details changed. The deeper isotherms showed a radically different pattern. The surface layer in the southern part (left) was 150 feet thick, shallower than the previous sample, and mixed. In the northern part (right), a weak gradient containing one isotherm was above the main thermocline, and the temperature inversion below the thermocline was unusual. Since the surface current and surface layer were moving from north to south, it can be assumed that some of the water in the thermocline was also SEA SURFACE * 4 MAIN he ae , \ 19°C THERMOCLINE —*—CURRENT DIRECTION © d ea Jorn A ALI ie < m, 'S”-SHAPED PATTERN Le e+ 3 MILES Figure 7. Temperature inversions below the main thermocline (Position 2, fig. 5). iil 12 moving southward and overrode the deep water (arrows, fig. 7). The deep water was either moving at a slower speed or ina northerly direction. The difference in speed was measured to be 0.7-1.2 knot, and the motion could create a weak shear or tem- perature inversion as shown by the '"'S'' shape of the 11°C and 12°C isotherms (fig. 7). These inversions were 150-200 feet high, fairly weak (about.1°C), and probably transient. The ''S' shape implies that the flow in the higher level of the inversion was counter to the ship's motion. The main thermocline, between 150 and 300 feet, contained smaller waves. The spectrum of their wave lengths was broad; some were only 600-900-feet long whereas others (upper right) were nearly 4 miles long, and averaged 2-4 per mile. The 12- mile wave on the thermocline was less distinct than in the first example, and the thermocline less sharp. It became weaker with depth, as in the previous section, but was more uniform before transforming abruptly into the large inversions. Cold Water Intrusion The third example (fig. 8), recorded on a southerly tow 180 miles southeast of the second example, featured in its surface layer a 6-mile region about 1°C colder than the adjacent water. Below the surface layer a sharp thermocline changed with in- creasing depth into a more gradual one. The upward bending of the 13°C isotherm indicated an intrusion of colder water that did not extend into the strongest part of the thermocline. The cold area appeared to be an intrusion lying at an angle to the section rather than an up-bending of the thermocline. The thermocline was made up of small, wave-like oscilla- tions, particularly between the colder areas, numbering 3 per mile as compared with an average of 2 per mile on either side in the preceding sections. This may be due to a Doppler shift in fre- quency that corresponds to an apparent change in wavelength caused by the relative motion of the ship, current, and wave propagation. If a Doppler effect is assumed, then wave propagation in the cold region would have a more northerly component than waves in the regions on either side. The cold area at a depth of 500 feet where the isotherm curved up appeared to be characteristic of this level. SEA SURFACE CURRENT fe COLDER AREA DIRECTION : ary COLDER ag “'Z"-SHAPED PATTERN i ] ge Cy AREA Z we : mh LATS, Figure 8. Colder thermal area above and below the thermocline (Position 3; fig. 5). Here the ''Z''-shaped temperature inversion implied that the upper part was moving to the right or in the same direction as the tow, whereas the ''S''-shaped inversion of the second example implied that the upper of the two layers was moving in a direction opposite to the tow. Ridge (or Dome} The fourth example (fig. 9), located just south of Baja California, is marked as Position 4 (fig. 5). This thermal struc- ture was characterized by a general ridge (or dome), and colder water was found at the surface where the isotherms curved up to intersect it. Maximum bowing occurred on the uppermost iso- therms, but some doming was detectable to a depth of 500 feet. The sloping isotherms of the ridge imply a geostropic current, which probably means the presence of a current boundary at the ridge. A net-divergency-type transport away from the ridge, as well as parallel to it, is evident. ; 13 14 EBORS SEA SURFACE Figure 9(A). A thermal ridge or dome, indicative of divergence (Position 4, fig. 5). A detailed examination of recorded thermal structure fur- nished information on other oceanographic processes (figs. 9A and 9B). The detail of long waves of encounter (fig. 9A) averaging 0.44 mile in length can reflect a natural geographical phenomenon or a Doppler effect. The smooth, 20-foot-high waves may be shorter than recorded if traveling in the same direction as the ship. If surface waves were influencing the depth of the sensors, the internal waves would appear as irregular marks, since each recorded scan would give an irregular outline to the curve (the scan would fall at all phases of the surface wave). Surface waves, because of ship stability and bead lagging, have little or no effect on the recording of smooth, sine-shaped internal waves. In a second enlargement (fig. 9B), the recorded isotherms are much different from those of only 1-1/2 hours earlier al- though the speed and direction of towing were the same. The fluctuation and rough appearance of the isotherms are attributed to short-length internal waves, or waves propagating in an opposite direction to the ship. The waves of encounter are so short that Figure 9(B). Recording of smooth (long wave) thermocline (vertical scale: 160 feet; horizontal scale: 2.6 miles. ae 16°C 0 (4. ; Oa, nb, ‘ ?, op Pw igo: | ' oh004 is q A é afl 6 Mum 15°C WP a ' * page SePeagyhy 1% t Ce oepml IC iy ay ifee: et epee Un} et a aay x Figure 9(C). Recording of rough (short wave) thermocline (vertical scale: 160 feet; horizontal scale: 2.6 miles). 16 the 12-second interval scan falls on all wave phases. If one scan falls on the wave crest and the next off it, 120 feet away, an abrupt change in the normally smooth isotherm is recorded. Other wave phases are also recorded on successive scans, and thus a rough appearance is created when short waves are encountered. Since the isotherms in the northern part of the section are more irregular and reflect higher-frequency internal waves than those in the southern part, the ship may have been alternately moving in the same and opposite direction as the internal wave propagation, thus producing a Doppler effect. The ridge may be considered a front, or boundary, with a sloping density structure rising toward the crest. Small internal waves propagating at an angle with the boundary may be refracted as they are on the continental slope and be propagated toward the crest from both sides. A Doppler effect can therefore be experi- enced when towing toward and away from the crest (left to right, fig. 9). Waves propagating toward each other can create mixing and result in isothermal water near the surface, as was measured over the crest. This may cause the large difference in wavelength measured on either side of the rise, and the mixed structure over the crest. Other causes for differences in thermocline roughness are the variability and patchiness of the ocean. Since wave frequency on the thermocline may vary widely over a short distance, addi- tional examples are presented in order to demonstrate the types of thermocline and their distribution. THERMOCLINE CLASSIFICATION Thermoclines may be categorized either by their oceanog- raphic processes or (somewhat subjectively) by the wavelengths of their smaller oscillations. To identify types of thermoclines, a total of 30 2-hour (12-mile) two-dimensional data sections were selected from the ship's track (fig. 10) and classified in four categories: smooth, normal, rough, and irregular (Appendix A). The variability of oceanic thermal structure is confirmed by the fact that each type of thermocline is found near the other. 7 21° 20° ee MEXICO BAJA CALIFORNIA \ \ MAZATLAN CAPE SAN We ee Ws 110° 109° 108° 107° Figure 10. Locations of sample sections of smooth, normal, rough, and irregular thermoclines. Smooth Thermocline Smooth thermoclines are isotherm undulations of a more regular form than average. Ata ship speed of 6 knots, the 12- second scan falls several times on a crest and several times in the trough. The wavelengths of the smaller oscillations extend more than 2400 feet, or fewer than 2-1/2 oscillations per mile. Two examples of smooth thermoclines are identified as S-1 and S-2 (fig. 10). The first is from the central part of the area (fig. 11A). The second (fig. 11B) comes from an easterly tow directly south of Cape San Lucas. Smooth waves vary consider- ably in wavelength of encounter, but average more than 2400 feet in length. \ 106° 17 18 SEA SURFACE ‘ 23° Neen, eee a pre pn ee . Ci serene os ee ti as ex ytouee OB >! sot a went, Me oe 4, t ee ow or ee we wade he t setae gmat ow, an bry Aa “un, a € be 7b a te i Sar ate Sh 14° S-] Figure 11(A). Smooth thermal structure (Section S—1, fig. 10). SEA SURFACE atte et * Po, age Mt ae Ot Moy es! a al 7 od ie ban Se, Limos) a Sma ye % net P se , ton . an adh "ee, D) 1 5 ss, ethan Ny Se NS an as rere re Sen, As eer sae, A cea ‘ 4 vert Ry pom en) oes eas i yn ° : , os n niynnent ai eae ; mK Nett on att ad Ae Weve ree aa hag titanate PO aa. 20° a, ane Nac a ts : en ate Si cauemeanen Ps Ae Ain See Coty Gee ct ous UN Pm sett ea son, sasaigggtitedte eee ee, << Re ae nimron 4 re CPA en od 2 “ at “ a laa eee " Sat, Soe ’ Pot = ws a ~ a, wn ne’. " 0 wr pe =f me 1 em eD ~epirtt ao? ™ ee aha, Peet z aig pate moe Nase Naame ett 8A ee ei br] 8° a Gir. . . eg cose fraamme y, eu fs ~ eo - D Nit Naas nome < 2 ee te ~ PD eS a ae oc pale en peer ee EIN oa Pei $-2 Figure 11(B). Smooth thermal structure (Section S—2, fig. 10). REVERSE SIDE BLANK i) ~» ition mire eta ae aie, ? an ares, apyipeTene er elf eek vie riiieecesicii aronre eeey ‘ - fe Normal Thermocline Normal thermoclines reflect an average condition, and their wavelength, although irregular, varies from 1400 to 2400 feet. Examples from the areas marked N-1 and N-2 (fig. 10) are pre- sented (figs. 12A and 12B), and are derived from the general area where smooth examples S-1 and S-2 were found. 21 SEA SURFACE [So ” 22 N-] Figure 12(A). Normal thermal structure (Section N-1, fig. 10). SEA SURFACE Tae me I j 24° ¢ Nae iene Ne shyt 5 Pw mete aa mica wey ~ i la AY ' \ ‘ is i A se ey ! 4 pee v Shae! ot! ue 4 Se toy aa Wetean ye ‘ UG N-2 Figure 12(B). Normal thermal structure (Section N—2, fig. 10). REVERSE SIDE BLANK 23 Rough Thermocline Rough thermoclines are the vertical oscillations that occur more rapidly than the 12-second scan can follow and yet produce a wave-like form. Scans of 120 feet apart may fall at different internal-wave phases and thus show an irregular wave structure. The wavelengths average less than 1400 feet or about 4 cycles per mile. Two selected examples, identified as R-1 and R-2 (fig. 10) and presented in figures 13A and 13B, come from the extreme northern and southern parts of the area. To reconstruct the in- ternal-wave forms, a few of the scattered points have been con- nected with a fine line. 25 SEA SURFACE a . 1 ee, Nien ate AN Ot 3 Ml R-] Figure 13(A). Rough thermal structure (Section R—1, fig. 10). SEA SURFACE Can ; “ ~ Set ; >, wt 4 NR ER gin 5 a ee > mo 2 = aad gate . ‘ Y oe Ot 4 Buy ree . : aie ; : , Shae ; ta. - rays + om, 0 ne 6 v oy wee s e ' nd “ ” ie Ne : “ eae nee 0 S. 4 4 “ ¢ Un Sn te ; : a ¢ 7 a o * 1 wap! oars “ * 5 oo ¥ y 6 ait ‘ " #0 58 ms ve R ‘ as. - bas i™, . ‘ a f ' 4, Sn) oo, Y : - ' ~, we 4 a ; . o ah DAO . ag WY can tat s. a 1 a mG wt ' i - vag: ae Bee ~ 100 FT Ran § 3 5 Sey MW OM De Sem. Sa H i aos at ; “ ca \ ee A H Sen ! So f a a ; me Oy 0 A ‘ae afl h ! See % ren Me i “ac ety oD A 4 ee if ’ I ¢ . Figure 13(B). REVERSE SIDE BLANK R-2 Rough thermal structure (Section R—2, fig. 10). ‘e = moo Ow | te 18 =~] remedial Vibe ee a Irregular Thermocline Displaced thermoclines are found in frontal areas where the entire thermocline has shifted or buckled and inversions have usually occurred. The vertical changes are larger than the usual 2-4 cycles per mile. Examples of irregular thermoclines, marked D-1 and D-2 (fig. 10), are presented in figures 14A and 14B. Both irregular thermoclines are characteristic of regions where two water masses impinge on each other. These frontal features do not re- main in a fixed position, but shift, dissipate, and reform. Although Doppler effects can apparently cause differences in the wavelength method of characterizing thermocline roughness, a natural geographic or time difference in thermocline roughness can also be a factor. The average roughness of 1400-2400 feet is equivalent to 23-4 minutes, or near the Vaisala frequency. bo We) SEA SURFACE Pave : mE 3 q ' : ah Ae, foe md 4 - hae ef ' oon lodod 0.6 omy. ie Sie! by “ “ Wit HS NS eet Kb Ne : 6 : wt wee + by " we “7, ’ ~100 FT 3 Ml of D-] Figure 14(A). Irregular thermal structure, or front (Section D—1, fig. 10). SEA SURFACE a, eh ORE OB emia acragrtiatar Mar SEED CE. ann 40 as me newt bra pom! Nal iy tr hee ‘ a oe = aan eae j pre me SN yD ; ' D N f Waa Wg ce ON ad ey eS go ve i " wl ta GI, Pas ae of efi , Ph, —12° WAS *: aS ee ee : & a Ae D-2 h g 1 Wewad See an pe Figure 14(B). Irregular thermal structure, or front (Section D—2, fig. 10). 31 32 TEMPERATURE STRUCTURE VARIABILITY In addition to the general classification of sea temperature structure by degree of roughness, a statistical analysis was con- ducted to determine isotherm depth variation and thus identify oceanic regions by their statistical differences. The analysis included isotherm steepness, which can be considered a measure of roughness. Each section of the continuous towing track was alphabeti- cally identified by 27 sections (A to Z, AA) (fig. 15), and the time and geographical position recorded (table 2). The selection of sample sections for analysis was made to obtain geographical coverage of an area during a period when the tow was continuous in one direction. The length and quality of the sample towing were planned to be adequate for reliability in statistical results. For geographical considerations, the midpoint of the sections is treated as a unit or data point. Prior investigations studied the variability of surface and subsurface sea temperatures; others developed procedures for the statistical analysis of physical properties applicable to tem- perature variability.15. 16 17.18. 19,20 In this report, three methods of studying isotherm depth variability are employed: (1) differences in depth values — isotherm slopes; (2) autocorrelation of depth values; and (3) power spectrum of depth values. 20 iss MEXICO BAJA CALIFORNIA MAZATLAN ee a2 Wie 110° 109° 108° 107° Figure 15. Alphabetically identified sample sections used in the data analysis of isotherm characteristics. Geographic centers of sample sections are marked. 106° 335 oh 6G al! 16 SESOT | 16° SS.d6 | SV6T-OVLO qe 8 d 1 °SG.90T | 19 08.66 ceoz-ooll | deh N 19 TO.80T | 17 06.6 ootz-oout | deat | T 1G EToBOT | 12° 62.8% | OOLT-O0ST gen T Ds iV GZo80T | 12° 9.86 | OOST-OOOT goa T £ 16°6F.80T | 12° GEES | OOOT-00E0 qo T I iG “9T.80T | 11 7S.d% | 0002-0080 H 0°OT 16° LG.L0T iz" 2202e 0080-00626 uee TE-0€ D iL SPo8OT | 16°06.6% | 00ZC-O00T Uer OE a OOFT | .0OG | OOFT | GT | aes | iV 9T.60T =ccovaeaooresu0er UueL 6G a OOGI 0G | OOCLI ! WGI o9L0 1S °SE.60T | 16°60.1% | 000T-0000 d OOS | 61 | O9TS | ET o98T 16° SOOLT | 10ST | 00VZ-0020 O OOGL | .61T | OOGT | WGI oV90 10 °TE.0TT | 1S °L2.66 | 0090-00026 ueer 8Z-LZ a OFFL | .6L | OFFT | GL oL VI iG PZoITL | 18° VH.%S | 0006-0080 UeL LE Vv moneys deoq (on) mm | ime [is (zo61) | (uonses) SJUIOg BIR [ROL uoyoertq | uotjeinqg | uontsog [erjUeD ouLL o1eq ajdures pue (9,) posq waoey.osyT asv1roAy NOLLOGS Bye (cg o8ed uo panuyu0D) SISATVNV YOU Gasn SATdNVS VLVG NIVHO YOLSINUAHL JO NOILVOOT GNV AWIL °¢ AIaAVL 34 OPFT | .0G | OVFT | WT 0666 0°S6L iG “6E.TIT | 19° 67.66 | O€ET-OETO qed VI 9ECT | 0G | 9OCT | ET ol 9G 0°Or i9 TPOTT | 1 °86066 | LE LO-STST Gea VI-éT OVPI | 0G | OVFT | oT i oG60 0°<6I iS “LE.OIT | i. TETS | O€TT-0€ES qe et-21 | 16 °82.01T | iL L€.06 | O€€2-OTTT | gaa at | iV 8S.60T | 18 °8S.0¢6 | OTTT-0000 | dea at | i8 “€S.60T | 14 °OT.66 | OOVE-OTET [ am | i8 “LT.60T | 11° €0.66 | 0080-0566 qe TT-OT iL°€G.80T | 10°9G.06 | 0S6¢-O0S0T oVEG 16 °80.80T | 18 °LE.06 | 6VOT-0000 qe4 OL OGET | .0G | OGET | OST o8 SL iV FO.80T | 1€°SZ.1% | OOVZ-O0ET | eae OFFI | 61 | OFFT vet] eet | 16°00.60T | 1€ 61.6% | 00ET-00TO rey woes | daa | (ony | cw | me | xo | (e961) | (uonses) sjulog e7eq [e10L uonoerIq | uoTeaing UOT}ISOd [e1yUaD owl 21eq ejdures pue (D,) pesg UlteyjOST ISBIOAY NOLLOGS eyed @\elal/el|>leleix/e INS ‘(ponutju0D) Z AIAVL 35 36 Differences of Depth Values (Isotherm Slopes) The first method of presenting isotherm variability is by depth differences from point to point along selected isotherms. The isotherm depths were scaled from the original record at half- minute intervals. SELECTION OF SLOPE INTERVALS From each section shown in table 2 (except J and L), two isotherms were chosen for analysis. One of the selected iso- therms was located in the main thermocline and the other below it. Of two isotherms analyzed in part of section Q (fig. 16), the temperature of the shallower one in the main thermocline was 19°C and in the deeper one below the main thermocline, 12°C. The depth differences from point to point along the isotherms were determined from the formula MS UR i Ape LS eS X, and X;,, are depths (in feet) of a given isotherm at the beginning and end of the 7** distance (or time) interval along the track; Y, is the depth difference (in feet). When the isotherm is falling, the difference is negative. d From ship speed and depth difference, approximate slopes can be calculated. Ata speed of 6 knots, the ship traveled 304 feet in each half-minute interval; therefore dividing the depth differences by 304 feet gave the slope of the isothermal surface in the direction of the ship's motion. The slope could also be ex- pressed by the angle having this slope for a tangent. From 240 to 2040 consecutive observations of isotherm depths were taken from each sample section. The distribution of depth changes and the slopes for each selected isotherm on each 2-17 hour section were diagrammed as a cumulative frequency curve of depth changes and slope angle (Appendix B). SEA SURFACE “ 5 5 yeaa i scares eermnee YN, MN Any i ( ‘ance Ma VE fit! sean rte Hh amy ihm vi 4 St 2 au 1 Mt ae vf mS emf! 4 : > oe ae TA et PO ae a = SK. : : " - SURFACE TEMPERATURE ° : " : ~ a ene mm Ce ae o 7 MAXIMUM DEPTH. nica: eerie ive ff -W—— 720 - - be Orta rg NT RT STAI SERN ia cron 00 yregg MENA) areas wv eMREE ES Ang pei? . vo Figure 16. Original data from which 1/2-minute depth readings of the 19°C and 12°C isotherms were obtained (Section Q, fig. 15). : 37 38 PERCENT OF OBSERVATIONS The graphs show that, in several of the isotherms, half- minute depth changes as large as plus or minus 30 feet were ob- served within 304 feet, which correspond to a slope angle of 5°40'. However, 24.3 percent of the adjacent half-minute readings showed changes of less than one-half foot for the shallower isotherm; 16.6 percent showed changes of less than one-half foot for the deeper isotherm. An example of a single cumulative frequency curve of depth differences (fig. 17) represents data derived from section Q (fig. 16). The change in depth of the 19°C isotherm may be plus or minus with distance. To derive a meaningful value for a large sample of slopes, the 50th and 70th percentiles were chosen. The frequency distribution shows that for the shallower isotherm the CENTRAL 70 PERCENT OF DATA CENTRAL 50 PERCENT OF DATA |CHANGE| LESS THAN 4.75 FEET \ ICHANGE| LESS THAN 2.4 FEET |SLOPE] LESS THAN 0°54 |SLOPE| LESS THAN 0°27 ’ 85TH PERCENTILE +4.8 SECTION Q IPE 7S PERCENTILE 22.5 , CUMULATIVE PERCENTAGE DISTRIBUTION 25TH PERCENTILE -2.3 FREQUENCY DISTRIBUTION OF DIFFERENCES IN DEPTH =F0 ~20 =0 0 10 20 30 DEPTH CHANGE (FEET) Figure 17. Cumulative percentage distribution of differences in depth between half- minute or 304-foot-spaced readings of the 19°C isotherm (Section Q). The 25th and 75th percentiles delineate the central 50 percent of data; the 15th and 85th percentiles delineate the central 70 percent. FREQUENCY DISTRIBUTION (PERCENT) 25th and 75th percentile depth changes are -2.3 and +2.5 feet; thus in 50 percent of the cases the change is less than 2.4 feet (in absolute value) in a horizontal distance of 304 feet. The 15th and 85th percentile changes occur at -4.7 and +4. 8 feet, with 70 per- cent of the data in this range. The corresponding vertical angles are less than 0°27' (in absolute value) for the central 50 percent of the cases and less than 0°54! for the central 70 percent of the data. The example is a nearly typical case because the median of the absolute values of the slope of more than 65,000 data samplings is 0°25', and the 70th percentile of the absolute values of the slope is OMB, As a measure of depth-change variability in the entire area, the values of depth changes per 304 feet, which corresponded to the 25th and 75th percentile, were scaled from each of the cumu- lative percentage distributions (Appendix B). The absolute values were averaged as was done in the single example (fig. 17). The 15th and 85th percentiles were also determined and averaged. This is analogous to the "significant wave'' method whereby the upper 30 percent is "average."' However, these values represent a depth change greater in absolute value than 70 percent of the observations. As an alternate treatment, a cumulative percentage distribu- tion curve could be plotted for the absolute values of depth differ- ences. The new 70th percentile change would agree almost exactly with the average of the absolute values of the 15th and 85th per- centiles. Hence the average will be designated 70th percentile of absolute value of depth change (absolute-value 70th percentile — depth change). Likewise, the 50th percentile in an alternate treat- ment would agree with the average of the absolute values of the 25th and 75th percentiles, and that average will be designated absolute-value 50th percentile — depth change. DISTRIBUTION OF SLOPE The frequency distribution and cumulative frequency of all slope data on isotherms, both shallow and deep, are presented (fig. 18). The cumulative frequency is based on 65, 000 data points and summarizes the isotherm slope in the entire area around the tip of Baja California. The cumulative frequency curve shows that 39 PERCENT OF OBSERVATIONS CENTRAL 50 PERCENT OF DATA CENTRAL 70 PERCENT OF DATA ICHANGE| LESS THAN 2.19 FEET |CHANGE| LESS THAN 4.54 FEET ISLOPE| LESS THAN 0°25’ ISLOPE] LESS THAN 0°51’ aN 100 : ‘ | | | 90 85TH PERCENTILE 4.52. | | | : 80 75TH PERCENTILE 217) | f-'- CUMULATIVE PERCENTAGE DISTRIBUTION 70 | r | 60 l t| 50 (| | | | ~<— FRE QUENCY DISTRIBUTION OF DIFFERENCES IN DEPTH AO | OF SHALLOW ISOTHERM bol 30 25TH PERCENTILE -2.22 FREQUENCY DISTRIBUTION OF DIFFERENCES IN DEPTH 20 OF DEEP ISOTHERM | 15TH PERCENTILE -151/) y, ~30 250 -10 Oo 10 20 30 DEPTH CHANGE (FEET) Figure 18. Frequency distribution of all slopes in foot drop per 304-foot travel for both shallow and deep isotherms separately, and cumulative percentage distribution of both shallow and deep isotherms together (65,132 data points). the isotherm waves are nearly symmetrical, with the absolute- value 50th percentile being the average of absolute values down slope, 2.17 feet, and up slope, 2.22 feet per 304 feet of travel. This corresponds to an absolute-value average median slope of 0°25'. The absolute-value 70th percentile comes from a 4.52-foot down-slope and a 4.57-foot up-slope change over the same dis- tance, and corresponds to an average absolute-value median slope of 0°51'. The Baja California waters thus contain much steeper isotherms than does the open Pacific, where the 50th percentile of absolute values of slope was 0°16' and the 70th absolute-value per- centile, where the value is 0°30'.°? Some difference exists in the frequency distribution curves of depth changes for the shallower and deeper isotherms. The deeper isotherms show a flatter curve with fewer zero values and more high slope values than do the shallow ones, which means FREQUENCY DISTRIBUTION (PERCENT) that the deeper isotherms undergo greater vertical oscillations per unit distance. Since the distribution of values is not skewed, the oscilla- tions can be approximated by a sine curve of the form Z=Z,+ A sin (kx+wt). The second term for the shallower iso- therm is approximately equal to 1/119 sin (kr +wt), whereas the deep isotherm is 1/84 sin (kx+wt). The total of the 65,000 observations (fig. 17) is about 1/100 sin (kr+wt). DIRECTION OF SLOPE If there is a dominant direction to internal-wave propagation in the thermocline, the absolute-value 50th percentile of slope should be greater when (1) the tow is opposite to the direction of propagation, or (2) in the same direction as the waves if the ship speed is much greater than that of the waves. The slope values would be expected to be relatively small when the ship is running parallel with the crests or troughs. Although the data samplings are not distributed equally in all directions of tow, there is considerable spread around the compass and in different areas. The steepness of the thermocline may be related to the direction of tow. To show this relationship, the computed absolute-value 50th percentile of slope for each sec- tion of isotherm depth is plotted with reference to the direction of tow (fig. 19, open points). The individual values are marked A to AA corresponding to the sections shown (fig. 15). A wide fluctua- tion of median slopes is present in all directions of tow. The absolute-value median slopes range from less than 10 minutes (0.9 foot change per 304 feet of travel) to over 52 minutes (4. 7 foot change per 304 feet of travel). The average slope value of all data was 25 minutes, which is higher than the average of 16 minutes measured on a previous cruise between San Diego and Honolulu.? A similar presentation of the absolute-value 70th percentile slope values for the shallow isotherm of each section is also given (fig. 19, solid points). The results show that this percentile angle varies from 0°17' to 1°37'. To smooth the values and demonstrate any dependence on the towing direction, data were averaged by 45-degree increments of direction of tow and the averages were connected by a solid line for 41 SLOPE IN MINUTES S 70TH PERCENTILE ae S0TH PERCENTILE 00 OAA oT 0 45 90 135 180 225 270 315 360 AVERAGE DIRECTION OF TOW (DEGREES) Figure 19. Direction of tow vs average median vertical isotherm angle derived from differences in depth between the half-minute or 304-foot-spaced depth readings. Curve represents isotherm slopes averaged by 45-degree groupings. (A) Upper: 70th percentile of absolute value of isotherm slope in the main thermocline. Sample values in solid points. (B) Lower: 50th percentile of absolute value of isotherm slope in the main thermocline. Sample values in open points. the 50th percentile and for the 70th percentile (fig. 19). Although considerable variability in the changes in the vertical angle was shown in both the 50th and 70th absolute-value percentile slope, the 50th absolute-value percentile values in the shallow isotherm have a higher average when the towing is to the north or southwest. This would imply that the vertical wave crest structures in shal- lower parts of the thermocline were oriented more to the east and west. SLOPE IN MINUTES A similar presentation for the deeper isotherm is given (fig. 20) (absolute-value 50th percentile, open points; absolute-value 70th percentile, closed points). The average curve has two modes. The higher values, implying steeper isotherms, occur when the towing is to the north or south. Also indicated is an east-west orientation in the wave crests on the deeper part of the thermo- cline. The 50th percentile slopes of all shallow and deep iso- therms were combined and averaged by 45-degree increments of @U 70TH PERCENTILE eZ 0 45 90 135 180 225 270 315 AVERAGE DIRECTION OF TOW (DEGREES) Figure 20. Direction of tow vs average median vertical isotherm angle derived from differences in depth between the half-minute or 304-foot-spaced depth readings. Curve represents isotherm slopes averaged by 45-degree groupings. (A) Upper: 70th percentile of absolute value of isotherm slope below the main thermo- cline. Sample values in solid points. (B) Lower: 50th percentile of absolute value of isotherm slope below the main thermo- cline. Sample values in open points. 360 43 SLOPE IN MINUTES 44 towing direction. The resulting slope curve with reference to direction of tow is shown (fig. 21). The similarity of orientation implies that the vertical wave-like structures, or internal waves, are oriented more to the east and west because the slopes are steeper when they are crossed during towing normal to their crests. Since the steeper values occur towing to the south and southwest, it would seem that the propagation of dominant internal waves was northward and into the Gulf of California. 45 90 135 180 225 270 315 AVERAGE DIRECTION OF TOW (DEGREES) Figure 21. Average 50th percentile slope of deep and shallow isotherms; 45—degree grouping vs direction of tow. GEOGRAPHIC DISTRIBUTION To be comparable with other sample sections, and to give a geographic distribution of the measure of isotherm slope, the absolute-value 50th and 70th percentiles of vertical change per 304 feet for the selected isotherms in the main thermocline were spatially plotted (figs. 22A and 22B). These median changes in depth are located at a geographic position corresponding to the center of the line of tow (fig. 15). The distribution of slopes is contoured. When widely spaced values are contoured, an option may exist of where the contour could be drawn. In such event, the contour can be made to cross itself, indicating both options. The areas of steepest isotherms, however, were clearly defined and the choice was not necessary. The contoured values for the 360 24° BAJA CALIFORNIA 23° CAPE SAN LUCAS Ne” ae SLOPE (FEET/304 FEET) N 50TH PERCENTILE Se 8.0 6.0 3.0 CALIFORN]A pe 93° CAPE SAN LUCAS 4.0 Ae ny. | SLOPE (FEET/304 FEET) “4.0 70TH PERCENTILE HE i ZS 111° 110° 109° 108° B MAZATLAN 107° 106° Figure 22. Geographical distribution of difference in depth between the half-minute or 304-foot-spaced depth readings of the shallower isotherms. (A) Upper: 50th percentile of absolute value of isotherm slope in the main thermocline. (B) Lower: 70th percentile of absolute value of isotherm slope in the main thermocline. 45 46 shallower isotherm vary from 1 to 4 feet (per 304 feet of travel) for the 50th percentile and from 2 to 8 feet for the 70th percentile. The relation of vertical change to angle is given in table 3. TABLE 3. CUMULATIVE DISTRIBUTION OF SLOPES OF ISO- THERMS (DEEP AND SHALLOW ISOTHE RMS) Depth Change Angle From Percent of Per 304 Feet Horizontal Observations >5 > 0°56! 11.6 5 0°56! 3.5 4 0°45! 3.5 3 0°34! 4.4 2 6. 1 10.2 0 20.5 2 10.5 -2 6.4 4 -0°45! 3.9 -0°56! | o (Se) on <-5 < -0°56! 11.7 The plots show that the isotherm in the main thermocline has higher values, or a rougher thermocline, in the region ex- tending south and southeast from Baja California. About 100 miles off the point, a wide band of water, running northeast- southwest, showed a smoother thermal structure. Farther off- shore, the roughness increased slightly. A similar presentation was made of the deeper-isotherm slope. The geographic distribution of the absolute-value 50th percentile is shown (fig. 23A) with contours ranging from 2 to 3.5 feet (per 304 feet of travel). The absolute-value 70th percentile values range from 3 to 6.5 feet (fig. 23B). Both contours show 24° CALIFORNIA 930 . Oe CARE SANG? 3.0 22° AP |= N SEORIEN(REEM/304sREEm) SOTH PERCENTILE 20° [ ectigat le ars Sarena reser eign Sle | 23% Deg 5.0 N| SLOPE (FEET /304 FEET) 70TH PERCENTILE 20° | _| HIS? We. wae Wile 110° B 109° 108° 107° 106° Figure 23. Geographical distribution of differences in depth between the half-minute or 304-foot-spaced depth readings of the deeper isotherms. (A) Upper: 50th percentile of absolute value of isotherm slope below the main thermo- cline. (B) Lower: 70th percentile of absolute value of isotherm slope below the main thermo- cline. 47 48 that the higher values form a zone directly off southern Baja California. The low-value contours occurring in the northeast- southwest zone lie in the same position. Of all isotherms con- sidered, those recorded from the region 60 miles to the south- southeast from the extremity of the peninsula are generally steeper and show more variability than those elsewhere in the area. Autocorrelation of Depth Values Another method of measuring subsurface temperature variability is by means of autocorrelation coefficients.!®> By using the same half-minute isotherm depth data, autocorrelations were computed for each selected isotherm and section of Cruise 8. Successive pairs of points at equal but overlapping time intervals were tested for correlation with each other, and the process was repeated for each time interval, increasing by half- minute steps from one-half minute to 72 minutes (144 lags) or 10 percent of the number of data points. Autocorrelation, Ff), was computed for increasing intervals of 2, each interval in- creased by 304 feet (half minute), using the expression: N-2X N-2X N-A (2) Sean) Th D Senn le t= 1 p= il Ig N-A N-A 2)1/2 N- A N-A 2 - ae S way YS x2-| > x, (Wy) Xia-| > Tian fail ja fil wizl where, in general, A=0, 1, 2, . . . 144 lag intervals and = total number of depth recordings ina run. W is usually 1440 and the maximum value of A is 7/10. The computed autocorrelations of the selected isotherms on each sample section were plotted for comparison (Appendix C). One example of the 52 autocorrelations (fig. 24) is from data derived from section Q (fig. 15). Starting with zero lags (zero minutes) the autocorrelation #, is 1.0, but as the lags increase, the correlation becomes less. In some cases the 1/2 120 LAGS (60 MIN) MINUTES Figure 24. Autocorrelation of successive half-minute readings of the depth of the 19°C isotherm (Section Q). The 60-lag (30-minute) and 120-lag (60-minute) values are indicated (A = 60 and 120, respectively). values are negative. In the example, the value of #,after 60 lags is reduced to 0.66; after 120 lags £,, 0.33; and after 144 lags fy, 0.22. There are no dominant peaks in the curve. To summarize the autocorrelation of successive depth changes with time and distance, two points were scaled off the individual plots of autocorrelation, one at 60 lags (30 minutes) and another at 120 lags (60 minutes) (table 4). TABLE 4. AUTOCORRELATION £, OF SUCCESSIVE HALF- MINUTE READINGS OF ISOTHERM DEPTH IN MAIN THERMOCLINE (SHALLOW) AND ISOTHERM BELOW MAIN THERMOCLINE (DEEP) (Continued on page 50) A = 60 Lags A = 120 Lags (30 minutes) (60 minutes) Shallow Shallow Deep 0.70 0.45 0.43 Section 49 50 Section eo) fs) |! [eal | || @ La Wiel Si el |e] Si wl |S] tO] 4 Sle la] So TABLE 4 (Continued) A = 60 Lags (30 minutes) 0.76 0.80 0.61 0.66 0.27 0.49 0.19 A = 120 Lags (60 minutes) 0.28 0.56 0.08 0.44 0.17 Pecan peowse remy amen aa Pee ial ed wen pace | lapel seat es eater om [ea [ a 0.58 0.53 nae 0.24 0.33 0.83 -0.18 GEOGRAPHIC DISTRIBUTION To be comparable with other sample sections, and to give a geographic distribution of autocorrelation values of successive measured isotherm depths, the 60-lag and 120-lag F, values for the shallower isotherm were plotted at a geographic position corresponding to the tow center line (figs. 25A and 25B). These values are contoured with 2, values ranging from 0.3 to 0.7 for 60 lags (30-minute) of the shallower isotherm. The 120 lags (60- minute) of the same isotherm vary from -0.1 to 0.8. Both geographical distributions are similar, but no clearly significant geographic distribution of values exist as in the grouping of slope values. There is, however, a tendency for low values to fall near the southern end of Baja California and extend to the south- east. In the corresponding 2, for deep isotherms, no definite areas of high and low correlation of the 60 and 120 lags (figs. 26A and 26B) are outstanding. The strikingly low correlation area is caused by only one or two values. 51 52 23° Doe i al SS MEXICO CALIFORNIA : x MAZATLAN L \ SHALLOW ISOTHERM Ry (d= 60 LAGS) BAIA MEXICO CALIFORNIA MAZATLAN SHALLOW ISOTHERM Ry (A = 120 LAGS) uee MW WZ 111° 110° 109° 108° 107° 106° Figure 25. Geographic distribution of autocorrelation of successive half-minute readings of isotherm depth in the main thermocline. (A) A= 60 lags (30 minutes). (B) A= 120 lags (60 minutes). CALIFORNIA a CAPE 0.3 SAN LUCAS DEEP ISOTHERM Ry (= 60 LAGS) CALIFORNIA MAZATLAN CAPE SAN LUCAS \ DEEP ISOTHERM Ry (A = 120 LAGS) We? We Wa ie Ox é 109° 108° 107° Figure 26. Geographic distribution of autocorrelation of successive half-minute readings of isotherm depth below the main thermocline. (A) A= 60 lags (30 minutes). (B) X= 120 lags (60 minutes). 106° 53 Power Spectrum of Depth Values The third method of representing variability is by the power spectrum.!® '4 1. 16 The power spectrum U(h) is given by the Fourier transform of the autocorrelation, Io lib 1S the energy (1/2 amplitude squared) per unit bandwidth* and thus emphasizes the bandwidths in which the dominant frequencies occur. The smoothed power spectrum values were obtained as follows: A=n-l 1 ! U(h) =— | R(0) + » R(A) (1 + ease) og wale n n 72 N=1 ‘ where h=0, 1, 2, 3... .m index number of frequency (actual frequencies are given by h /(24t) cycles/min, At= 1/2 min), and NEOs yp Bo Bo oo o 7 1S Wane lag number The power spectra computed from half-minute readings of isotherm depth are given (Appendix D). Each plot is a spectrum of the variations in depth of single isotherms listed (table 2). One example of the computed power spectrum (fig. 27) is based on the depth of the 19°C isotherm of section Q (fig. 15). The importance of the power spectrum lies in the curve peaks that indicate frequencies (or periods) in the original data which may have been obscured by background noise. It is significant that this example of power spectrum has several peaks or peak *The units for U(n)used here are feet”/cycles per min. and Ut) might better be designated as variance. POWER SPECTRUM U(h) (FT2/CPM) 100,000 10,000 1000 20" PEAK ZONE ew Wel 9.1 MIN St PEAK ZONE — oO (oe) BACKGROUND 0 0.05 0.10 0.15 0.20 0.25 0.30 FREQUENCY (CPM) Figure 27. Power spectrum from successive half-minute readings of the depth of the 19°C isotherm (Section Q, fig. 15). The peaks and zones of higher power are indicated. 55 56 zones ranging in frequency* from 0.049 to 0.270 cycle per minute, which is equivalent to a period of 20.4 to 3.7 minutes or a wave- length of 2.04 to 0.37 nautical mile. When the peaks are wide they are considered zones; for example, 0.090 to 0.110 cycle per minute (or 1.11- to 0.91-mile wavelengths) and 0.182 to 0.200 cycle per minute (or 0.55- to 0.50-mile wavelengths) are con- sidered zones or wide bandwidths. The power spectrum curve shows that the greatest power is in the low frequencies without peaks. The number of degrees of freedom is given by v = 2N -4 . When 1440 consecutive depth sample values and 144 lags are used, vy = 19.5. The correspond- ing ratio of computed to true value!’ falls between 0.54 and 1.60 for 90-percent confidence limits. The ratio of background to peak height was determined by constructing a base line and vertical height (fig. 27). For example, the 3.7-minute-period peak of the 19° isotherm depth has a peak-to-background ratio of 82 to 50, or 1.64, whichis significant, whereas the 9.1-minute-period peak in the peak zone (fig. 27) has a ratio of 1.38, which is not significant. DIRECTIONAL POWER SPECTRUM To summarize the power spectrum, the peaks and peak zones were read from the individual power spectrum graphs, and the peak-to-background ratio was computed and listed (fig. 28) for the data sections with the isotherm in the thermocline and (fig. 29) for data sections with the isotherm below the thermocline. *Here the sampling chain is moving through a quasi-stationary field of internal waves and the frequencies discussed are fre- quencies of encounter. The wavelengths are nominal and com- puted from the ship speed of 6 knots, assuming that the internal waves are essentially stationary, i.e. moving much slower than 6 knots. Broad peaks (or peak zones) should be expected as often as narrow peaks if the internal waves are traveling in all direc- tions; e.g. if internal waves of only a very narrow band of frequencies arrived from all directions, the straight track of the ship would intercept apparent wavelengths corresponding to a broad band of frequencies. FREQUENCY (CPM) 0.05 0.00 0 45 90 135 180 225 270 Si5 DIRECTION OF TOW (DEGREES) Figure 28. Summary of direction of tow distributions of power spectrum from successive half-minute readings of isotherm depth in the main thermocline (shallower isotherm). Circled are the more significant ratios. In both graphs, the values were arranged with reference to direction of tow and frequency. The ordinate is frequency (cycles per minute) and the abscissa is direction of tow. If the tow direction creates a Doppler effect, the dominant frequencies would shift with the direction of tow. All the peak-to-background power spectrum values of the shallow isotherm (fig. 28) that were derived from the power spectrum plots are entered. Each peak ratio is numerically identified, and peak zones of high values are con- nected with a dashed line. Some sample sections have nearly the same direction of tow and are thus plotted near each other. The highest values (over 1.6) are circled to emphasize the most important and to more easily relate them to direction and fre- quency. Values greater than 1.6 are considered significant in 360 57 58 FREQUENCY (CPM) 0.35 0.05 0.00 0 45 90 135 180 225 270 315 DIRECTION OF TOW (DEGREES) Figure 29. Summary of direction of tow distributions of power spectrum from successive half-minute readings of isotherm depth below the main thermocline (deeper isotherm). Circled are the more significant ratios. accordance with the 90-percent confidence limits. The important circled points fall at all frequencies and all directions of tow. The values show that the zones of significant frequencies of vertical changes in isotherm depths vary widely from sample to sample. No power spectrum peak ratio to background value exceeds 2.5. The higher values appear to be distributed in patches. A similar presentation of the deeper isotherm power spectrum (fig. 28) shows the circled higher peak values again occurring at all directions of tow. However, slightly more values over 1.6 at the higher frequencies are apparent, especially when towing to the east or south. This contrasts with the omni- directional distribution of the shallow-isotherm power spectrum. FREQUENCY (CPM) GEOGRAPHIC RELATIONSHIP OF POWER SPECTRUM To show a general relation of the power-spectrum peak values over the background to geographic location, the values were plotted with reference to longitude. The purpose was to determine if the internal waves in the Gulf of California (along lower longitudes) had specific frequencies different from those in the open Pacific (along higher longitudes). Peak to background values of 1.6 and greater are circled (fig. 29). For the shallow isotherms (fig. 30), no shift in significant 0.15 Wa? Wve 110° 109° 108° 107° 106° LONGITUDE Figure 30. Summary of longitudinal distribution of power spectrum from successive half-minute readings of isotherm depth in the main thermocline (shallower isotherm). Circled are the more significant ratios. 59 FREQUENCY (CPM) 60 frequency with longitude is apparent. A slightly greater con- centration of high ratios falls between 108°W and 109°W in the area where a water-mass boundary is expected (south-southeast of Cape San Lucas). The power spectrum for the deep isotherm (fig. 31) contains more high ratios in the central part of the area 108°-110°W. There is only a slight relationship of significant power spectrum values to longitude in these data. 0.20 0.10 0.05 WZ? 111° 110° 109° 108° 107° 106° LONGITUDE Figure 31. | Summary of longitudinal distribution of power spectrum from successive half- minute readings of isotherm depth below the main thermocline (deeper isotherm). Circled are the more significant ratios. TOTAL POWER SPECTRUM The relative power in the power spectrum was determined approximately by integrating under the curve of the power spectrum for the frequency band between 0.05 to 0.30 cpm. 0.30 Ua = i U(h) af 0.05 An example of the power in this band at section Q (fig. 15) is shown (fig. 32). The integrated values in the band 0.05 to 0.30 cpm are plotted with reference to their geographic position (figs. 33 and 34) and the values are contoured. In the shallow isotherm the values for the integrated power in the band, Uz , that fall between 0.05 and 0.30 cpm vary from 104.5 to 19.2 ft Z The geographic distribution of Ug (fig. 33) shows the values decreasing with increasing distance. The inverse relationship of UJ, to distance finds the highest values of Up nearest the southern end of Baja California. In the deep isotherm, the values Ug, for the integrated curve are between 136.6 and 16.8 cpm. The higher values also fall near the end of Baja California and to the south. The distribution may be interpreted as a measure of thermal structure roughness similar to that for wave lengths and the slope. 61 62 POWER SPECTRUM U(h) FT2/CPM 10,000 1,000 100 0.00 0.05 0.10 0.15 0.20 0.25 0.30 FREQUENCY (CPM) Figure 32. Total power spectrum in the band between 0.05 to 0.30 cpm. Data are from half-minute readings of depth of 19°C isotherm (Section Q, fig. 15). 0.35 24° 23 MAZATLAN SHALLOW ISOTHERM 0.30 U, -f U(h) df W 112° iis 110° 109° 108° 107° Ws? Figure 33. Geographic distribution of the integrated power spectrum of frequencies between 0.05 and 0.30 cpm from successive half-minute readings of isotherm depth in the main thermocline (shallower isotherms). 106° 63 64 24° eS 23a DEEP ISOTHERM 0.30 U(h)df 0.05 WN? MP Wz Til 110° 109° 108° 107° 106° Figure 34. Geographic distribution of the integrated power spectrum of frequencies between 0.05 and 0.30 cpm from successive half-minute readings of isotherm depth below the main thermocline (deeper isotherm). Turbulence Variation in isotherm depth may be a turbulence phenome- non.'? This supposition is based on evidence that energy is transferred from one spectrum component to another through its transfer from large to small turbulent eddies. In larger eddies, energy is received from an external driving force; in the smallest eddies the same energy is transformed into heat. But a subrange of eddy motion, which participates neither in energy loss nor gain, passes the energy of large eddies to small eddies where it is finally transformed. Within such a subrange, the spectrum function must theoretically have the form:7! B (r) = Be??? where (ik) =the wave number E(k) =the power spectrum function € = the rate of conversion of turbulent energy to heat B =a constant If a constant value of € is assumed to lie in this subrange, the spectrum #(k) plotted as a function of % on a log-log scale must have a slope of -5/3. A curve of this slope (in the appropriate units of fig. 35) has been superimposed on the power spectrum results of the 19° isotherm depths of section Q (fig. 15). This was done by using the following substitution to change the units of the plot from wave number to frequency: k= f/c, where c is the ship's speed. Then the above equation may be rewritten as i = zany 5/3 si = Bs a if And assuming 8, €, and c are constants; the frequency spectrum would have the form BUS mp where / is a constant in the inertial subrange. The Kolmogorov spectrum deals with three dimensions whereas the above data have been measured in only one dimen- sion. The vertical stability of the ocean and reduced horizontal stability indicate anisotropic turbulence. However, if horizontal 65 66 POWER SPECTRUM U(h)(FT?/CPM) 10,000 5,000 LOG U(h) = -5/3 LOG(f) + a \ = SLOPE =1.67 N 2,000 1000 500 200 100 50 20 10 0.01 0.02 0.05 0.10 0.20 0.50 FREQUENCY (CPM) Figure 35. Power spectrum from successive half-minute readings of the depth of 19°C isotherm (Section Q). The slope —5/3 in the log-log plot is indicated as well as the slope (—1.356) estimated from the power spectrum. isostropy is assumed, then the spectral densities in one hori- zontal direction would represent the spectrum in any horizontal direction; thus the numerical value of slope is the same as for the log-log plot of U(h) vs frequency. The slopes were found by visually fitting a straight line through the central part of the log-log points of the power spectrum. The visually fitted curve for section Q data (fig. 35) has a slope of -1.36, which lies close to the -1.67 curve. The data from section Q are approximately average for the area under consideration. The slope values for all the data sections are listed (table 5). To obtain an overall plot of power spectrum, 25 sets of data for the shallower isotherm are averaged together and plotted (fig. 36). A similar average power spectrum for the deeper iso- therm is also included. Since these data are for a wide range of towing directions and cover different areas, they may be con- sidered representative power spectrum curves. The averaged curves show no distinct peaks in the central part of the limited frequency range (0.05-0.30 cpm). Both curves have a slope which approximates the -5/3 reference curve, and this close relationship may be indicative of turbulent motion in accordance with the Kolmogorov theory. There are, however, small peaks in both average power spectra around 0.15 cpm (0.66 mile) and 0.3 cpm (0.33 mile) in the shallower isotherm spectrum, which indicates these to be the dominant frequencies. Individual power spectrum curves have more sig- nificant breaks in this frequency range, but at varying frequencies, which are nearly smoothed out in the average plot (fig. 36). TABLE 5. SLOPE OF LOG-LOG RELATIONSHIP BETWEEN POWER SPECTRUM AND FREQUENCY OF DEPTH OF ISOTHERM IN MAIN THERMOCLINE (SHALLOW) AND ISOTHERM BELOW MAIN THERMOCLINE (DEEP) (Continued on page 68) Shallow Iso- therm Slope M Deep Iso- therm Slope M Section 67 68 Section TABLE 5 (Continued). Shallow Iso- therm Slope -1.67 -1.78 -1.59 = -1.53 Deep Iso- pares Shei -1.83 -2.09 ahs 00 = -1. 82 -1.40 -1.23 -2.06 -1.94 -2.59 -1.51 -1.56 2 i af el ai Se Sil | fp Se] Ol] See [es S| SE ae] el te) | -1.36 -1.53 -1.36 -1.94 Als lbs} -1.49 ile Ol -0.66 -1.67 -1.64 -1.74 ail ey) 2} OY) -1. 83 AVERAGE . SHALLOW ISOTHERM INCREASE IN _ SHALLOW ISOTHERM Nie = o O a kK eS a —< ~ >) = = © | O wu Oo. wn ez Wu = Go o 0.10 FREQUENCY (CPM) Figure 36. Average power spectrum of 25 shallow and 25 deep isotherm depths. The slope of —5/3 in the log-log relationship is indicated. 70 GEOGRAPHIC DISTRIBUTION From the power spectrum slopes of each data sample a geographic distribution of slope values for the shallower isotherm is presented (fig. 37). Values of power spectrum slopes range from -0.66 to -1.94. The lower values are generally near the coast and describe a pattern similar to that of other variables. A similar geographic distribution of the deeper-isotherm slope values (fig. 38) is more irregular than that of the shallower one and has slightly smaller values. CALIFORNIA , & MAZATLAN m 31:7 SAN LUCAS 1.5 SHALLOW ISOTHERM SLOPE, U(h) Ww 112° 111° 110° 109° - 108° 107° 106° Figure 37. Geographic distribution of slope of power spectrum curve from successive half-minute readings of isotherm depth in the main thermocline (shallower isotherm) (frequencies 0.05 to 0.30). 24° MAZATLAN 23° Die 21° N DEEP ISOTHERM SLOPE, U(h) 20° UIs? Wy yz 111° 110° 109° 108° 107° 106° Figure 38. Geographic distribution of slope of power spectrum curve from successive half-minute readings of isotherm depth below the main thermocline (deeper isotherm) (frequencies 0.05 to 0.30). 71 72 RECOMMENDATIONS 1. Continue development of the thermistor chain to improve the quality, accuracy, and reliability of oceanographic data. 2. Investigate the use of additional sensors (in conjunction with temperature) on the thermistor chain for measuring current, turbidity, sound velocity, and salinity. 3. Study, by means of the thermistor chain, the nature of internal waves and the effects on thermoclines of islands, shoals, coastal configurations, tides, known currents, upwelling, water- mass boundaries, storms, and seasons. 4. Determine, by use of the thermistor chain and partially known sea temperature structures, the most persistent oceanic regions of smooth, normal, rough, and irregular thermoclines, and study the effects of such structures on sound transmission. SUMMARY AND CONCLUSIONS The two-dimensional investigation with the thermistor chain of 27 sections of temperature structure off Baja California provides new detailed data on the upper layers of the sea and makes it possible to determine the processes of differential water motion, turbulence, and apparent Doppler effect. The isotherm slope at two levels in the 27 locations re- vealed that the median value generally became steeper when the towing was to the north or south, which implies an east-west orientation of wave-like fluctuations in the thermocline. Similarly, the deeper of the two isotherms, selected where the vertical temperature gradient was weak, had more larger vertical angles than did the shallower one. A wavelength between 1400-2400 feet is common for thermocline oscillations. This corresponds to a frequency of 25-4 minutes, or near the Vaisala frequency. The autocorrelation of successive depth values of given isotherms decreased more rapidly when the towing was to the east or west. The power spectrum of isotherm depth showed peaks at varying frequencies. The higher, more significant peaks appear to be most numerous in the zone marked by an underseas extension of the extremity of Baja California. This corresponds to the water-mass boundary between the Gulf of California Water and two other bodies of water, the California Coastal Current Water and the Tropical Pacific Water. Log-log plots of power spectra averages for each of the shallower and deeper isotherms result in nearly straight lines. A small change in slopes occurs around 0.15 cycle per minute (cpm) for both curves and 0.30 cpm for the shallower curve. The overall slopes appear to be near -5/3, which may mean that the thermal structure is partly a turbulence phenomenon in the frequency range between 0.05 and 0.30 cpm. 73 74 REFERENCES OF LaFond, E. C., ''Two-Dimensional Oceanography, "' Bureau of Ships Journal, v. 10, p. 3-5, December 1961. Navy Electronics Laboratory Report 1130, Measurements of Thermal Structure Off Southern California With the NEL Thermistor Chain, by E. C. LaFond and A. T. Moore, 28 August 1962. Navy Electronics Laboratory Report 1210, Measurements of Thermal Structure Between Southern California and Hawaii With the Thermistor Chain, by E. C. LaFond and A. T. Moore, 7 February 1964. LaFond, E. C., 'Detailed Temperature Structures of the Sea Off Baja California,'' Limnology and Oceanography, v. 8, p. 417-425, October 1963. LaFond, E. C., ''Three-Dimensional Measurements of Sea Temperature Structure," p. 314-320 in Studies on Oceanography Dedicated to Professor Hidaka in Commemo- ration of His Sixtieth Birthday, Tokyo [University of Tokyol, 1964. Roden, G. I. and Groves, G. W., ''Recent Oceanographic Investigations in the Gulf of California," Journal of Marine Research, v. 18, p. 10-35, 1959. Richardson, W. S. and Hubbard, C. J., ''The Contouring Temperature Recorder,'' Deep-Sea Research, v. 6, p. 239-244, 1959-1960. LaFond, E. C., ''Towed Sea Temperature Structure Profiler,"' p. 53-59 in Symposium on Transducers for Oceanic Research, San Diego, California, 1962. Proceedings, Plenum Press, 1963. Griffiths, R. C., "Studies of Ocean Fronts in the Mouth of the Gulf of Lower California, an Area of Tuna Migrations," Experience Paper 34 in World Scientific Meetings on the Biology of Tuna and Related Species, La Jolla, California, 2-14 July 1962. Proceeding, Rome, Italy, Food and Agri- culture Organization of the United Nations, 1962 (SIO Contribution 1392). Eckart, C. H., Hydrodynamics of Oceans and Atmospheres, Pergamon Press, 1960. IIb 12. 13. 14. 15. 16. Wel o 18. il). 20. 21. Vaisala, V., "Uber die Wirkung der Windschwankungen auf die Pilot-Beobachtunger," Societas Scientiarum Fennica. Commentationes Physico-Mathematicae, v. 2, No. 19, Do Bl, 1926. Lee, O. S., "Observations on Internal Waves in Shallow Water, 'Limnology and Oceanography, v. 6, p. 312-321, July 1961. LaFond, E. C., "Factors Affecting Vertical Temperature Gradients in the Upper Layers of the Sea," Scientific Monthly, v. 78, p. 243-253, April 1954. LaFond, E. C., ''Temperature Structure of the Upper Layer of the Sea and Its Variation With Time," p. 751-767 in American Institute of Physics, Temperature, Its Measure- ment and Control in Science and Industry, v. 3, Pt. 1: Basic Concepts, Standards and Methods, Reinhold, 1962. LaFond, E. C. and Moore, A. T., "Short Period Variations in Sea Water Temperature," Indian Journal of Meteorology and Geophysics, v. 11, p. 163-166, April 1960. Navy Electronics Laboratory Report 831, Information Recovery From Finite-Sample Fluctuation Data, by C. A. Potter, 26 February 1958. Navy Electronics Laboratory Technical Memorandum 600, A Review of Power Spectrum and Cross Spectrum Analysis by Digital Methods, by E. E. Gossard, 15 April 1963.* Tukey, J. W., ''The Sampling Theory of Power Spectrum Estimates," p. 47-67 in Woods Hole Oceanographic Institution, Symposium on Applications of Autocorrelation Analysis to Physical Problems, 13-14 June 1949. Panofsky, H. A. and Brier, G. W., Some Applications of Statistics to Meteorology, p. 144-145, Pennsylvania State University, 1958. Mode, E. B., Elements of Statistics, 2d ed., p. 246, 329, Prentice-Hall, 1951. Townsend, A. A., The Structure of Turbulent Shear Flow, p. 32-63, Cambridge University Press, 1956. *NEL technical memoranda are informal documents intended pri- marily for use within the U.S. Navy Electronics Laboratory. REVERSE SIDE BLANK 75 iy a la oe 4 pein * bah APPENDIX A THERMAL STRUCTURES (FIGS. Al-A30) Smooth (long wavelengths) Al to A8 Normal (average wavelengths) A9 to Al4 Rough (short wavelengths) A15 to A20 Displaced (shifted or buckled) A21 to A30 REVERSE SIDE BLANK Sj SEA SURFACE i \ soy, ao lal PN eI EIEN gin yD B Nea Tv en_ pita wm YS K-— 3 MI—+ era SECTION D A-1 SEA SURFACE od ) Orn nen DORON rn aN 20° - iad Ce, ravine ero ESS Nar eae PEP oe Ps ee 13° ao ee RD rnp pr “ A ran ts ee a al Ne ae Een Ba en eee Wo 4 mt , ON ree, An, eee SN 1] 4° EP Oe eR A —™ d DE enti ie len re a SN aged T ; ——SMl——=| S100 Er SECTION F 1 ND Examples of smooth thermal structures. A-4 SEA SURFACE a Ae a! Spee LON = enter Ry nal 3M) ~i0o (a7 SECTION G : Ware EOS Jena CS Ue See Pee , a Oe Nmn oA. 2 Re a foe re 5 Pres ees Se im We ] 4° ” of i. ae yy A) at vena! amp citnc i ree So Ana * ee jm 6 wn a “, shat n . \ t ry J wr” tl P, at 0 Rope ee is PINS rom rel SEA SURFACE b ON -g oA ee Nae OE ae ENG Lake wet ee pratt ee ros Neg a , 6 s , Pere fe a ene oN AlN ~— 20 — ~ ve ns ort OMe is RAR SLE TIS nS an Siva Aue 18 ape ire ee ae SEH arn ea aloe ea ae NS een om, AA oom sang saa 14° a TY BY : rime pas ean a ae meet SoEe Tae ate ‘ SECTION L Ab, SEA SURFACE 22s - 20° 18° vA Deena one Reta ‘e Me oe A A sed reer CONN Ze i, aN Cae Ae SECTION O SEA SURFACE ~~~ - - Co aoe Hite) e} sored pe eNom "y ee 7% 1 24 ee ad SECTION T OOK Ea a Aen As) cea OY te pin Nay ied Ae BT eo ; Vala SEA SURFACE aa SR Ce aaa i ee Mona Peel 24° iNet 0 zy toe Se mots ay wv % a FR oe ae yf am Pea ws and la wa ww SO a R rr v STAN - oes 5 ee Kn AWAY n\ a are ¥, ni 4 r Ys A A oe pat “A eS, e Ve, Va Waves * w a a, : SECTION W ite Xe rd » 12 hes eine oN! ; poy ae Ne SEA SURFACE 20° “. 18° 2 16° 14° os (CE ENIN AB oe Ae (an ae BN get Sa , sate? B ~ of. if rar ie f we Fru 12 ty ce) , S100 ET Lg yj SECTION F at SEA SURFACE 22s 14° of Examples of normal thermal structures. SEA SURFACE Sn Ni ROE Wedtee A me mye 2 AL ae ale Nee Is We wy ac ‘aa f aN Le NM ay » 14° SEA SURFACE ee ee 9 ke we ir 93° Ch fn —3 MI—>| ~ 100 FT SECTIONS V AND W 4 SEA SURFACE An eee en 16° i A a o. Pl Nein TN oo ° naa vane aa y * . “y . ff 5 are xeon mee pai. wi tons tan aS v VA Ar ye as. f & Lor yaa \ =~ SECTION X om les SEA SURFACE SECTION AA A-10 SEA SURFACE ST ————E—EEEEEEEOEEeEeEeEeEe eee ES 20° 18° 16° 14° \ts, Ro Res a es tag \! : v Pee wit ewe an on ‘ s pai’ — sh) S00 ae Tce S SECTION A st SEA SURFACE ne o os on 1? Dicey 5 rp it vy, ibe), % on nA, Pos aX aN SECTION | " dor Pan 2 ‘ afd Nines en tf se Sl hoe Mae, Ne on ver vane Me be "y Se et ~ 100 7 Nas 2 at /-— 3 Mi} © A-16 Examples of rough thermal structures. SEA SURFACE Do Taal Nine Mt, 0 ES Ct S IN Diy rae — eo Pe 2 era aaa ese ()© OSES RRR ar oe s ¥ Ss = ok ~ te n ~ NS : : je? Ie ea ¢ anen Le i” ~~ py: WAY EEE Viner ~ ae o = ae YR et ED Ca — -- Gosia y , “Me r) /. \ ea Ne 5 Pal vm, ~ Os ‘ 14° oy 2) “we pated 2 ome ~ oe - wer nn he wen velit Ss Y aay Te f Ar pu Afi OAD, Q = ~ AN me "Waals Sat ro ~ 100 FT SECTION M /K-— 3 M—=| eae gp Sey FNS RAOUL “ w, f MY fea! ‘ Weis Oe f , jp oA. 4 of ava he te int Tg Phe Jifeiom v a, ve hon el i. os 4 = ~100 FT -— 3 Mi—=| al hy SECTION N Vom a, PAN YY aa \ f fog “A aS La PAY, af NY A-18 A-11 SEA SURFACE ee R . a iM has 12° SEA SURFACE = ~ we SECTION U fs ny ay fe h ny) io ui eh he, Ha Y) mn 0 Sd as ¥ wt 5 lap nad ‘ Nem MN Bip HE A-20 A-12 SEA SURFACE A-21 GR a : ve . , : wo ‘s oh 4 , Nee ans Bano wre | ~ SECTION E leas Ml ae A-22 Examples of displaced thermal structures. A-13 A-14 SEA SURFACE 20° —~ 18° 16° 14° w) ue Z og Se a SECTION === ae ate i ms, yy N ae fr B ° oN ‘ Co) Ray ae LA BX oD s iy ee iad Re ee “pon a A-23 SEA SURFACE de Ar aN ee he : nes : aig fim NTN aL ee, A o 2 Oe en ae eee 2 a ETT aa aes cama wy oes raf me, wl LP dl ee 1A a r NS aye f Wann he 0S NS - ad Cer ; Me SECTION P iad IP A-24 SEA SURFACE cos = 5 et -. Saf aa NW ee NGS i NS, peta eee Vv ee oaoe ng To NTS As AE a 7 ae Fea In pe SONS NAS gh ipo (Al? Ny PN ONTS eet E/ a ee nbn. ee saa eee ae 0 ~~ pe Sl ea ae Fs MI ~ 100 FT oN nee {1 OS GE oR = ra rd Ti OD) de aa Ba Se oe aries me SECTION P si Ry RPE a6 SEA SURFACE pr ih \, F ryan tage Ver Mae Nasa May i AS Van NE L— 3 Mi q 100 FT Legh, Pn, i 12° amt en tet oO sie mo ea, rc ery, : SECTION Q ay | ane A-26 A-15 A-16 SEA SURFACE cae TN apt, rohan piatiaar Mee NAMM i 2 4° bee: Pea ern i om an a, ee om ie cr OL ES 2 eto raw Vee aa 3 ey yt "ad ey a Nn! dc SLI) ‘hb oF Vn, SECTIONS @Q '—3Ml——] ~ [O0,FT au AND R rt Le ? ‘ ee . te se } \ athe a f* A eto Aa ant a a Reid ONY \ vA wae eA ¥ A-27 SEA SURFACE SEA SURFACE Veg mee mp 22° sf ¢3 cea seeder tate PES, 14° . by iain a) D were —~-, so 8 22° a Ee ae Myra (ORD: > bike Go 3 Fe a . A WD Oa Ne — ~ dO ye lt A 0 A aaa Cm Tata Batya iN : NON ane? 2 Fs 1 fae! “ =e CN AR 2 we Be 4 bag ond +} g Ney “ne. aly 14 wey et sre tl : ts ad BEN SECTION Y NEP ewecize A-30 REVERSE SIDE BLANK A-17 v i Dy een ot ery APPENDIX B ISOTHERM DEPTH DIFFERENCES (FIGS. B1-B52) FREQUENCY DISTRIBUTION OF ISOTHERM SLOPES DERIVED FROM DIFFERENCES IN DEPTH OF ISOTHERMS (SLOPES) AT HALF-MINUTE (304-FOOT) INTERVALS REVERSE SIDE BLANK cr Th OSE eee a i ve ae ca) a aa nt mete PERCENT CENTRAL 70 PERCENT OF DATA |CHANGE| LESS THAN 4.85 FEET [SLOPE] LESS THAN 0°55” 100 = 1 an SECTION A | SECTION D | [ DEEP DEEP | 80 ee alll 12° 70 + CENTRAL 50 4 + =— +1.8 4 60 + PERCENT OF | L 4 —a— + 3.6 50b DATA L sa | ICHANGE|LESS | [| | a0 THAN 2.7 FEET 30+ |SLOPEJLESS 7 | 20+ THAN 0°31’ 4 ] 10r Yi B-1 | B-4 0 1. — il i 1 aT cea] T T SEGHIONIB el) ane SECTION E 4 DEEP DEEP 12° "I ° OES) 4 V2 | —— +4.9 4 4 | a il | B=] Beil ait i —)| SECTION = [ F | = | 7 \- | et | L = B=oee + 0 1 EEE 4 =30) —20 -10 0 +10 +20 +30 -30 -20 -10 0 +10 +20 +30 DEPTH CHANGE (FT) PERCENT 100 = SECTION G DEEP Ig? —e——— + 1.8 —w— +3.2 a SECTION K DEEP 1.6 +2.6 Bt SECTION DEEP 12° [a ee! —a—— + 5.8 i BO | fF tL le. -10 O 210 20 =) — =20 SECTION M DEEP 4+2.4 WZ SECTION N DEEP Ow 13° j—ae— +7.2 DEPTH CHANGE (FT) PERCENT 100 SECTION R4 DEEP Se —e—— +-3.9 >I le— +6.2 B-16 4 SECTION P DEER 2 a 42.4 —=— ET AW/, SECTION S DEEP Iss Lr, eS) —«— +6.0 SECTION Q DEEP. Iz j—=@— 43.3 wet— +5.7 B-15 1 {| +10 +20 +30 DEPTH CHANGE (FT) PERCENT 100 i—a=— +29 m—e— +52 SECTION U 4 + DEEP Ie +2.2 ~—e— +3.8 SECTION X DEEP 13° +30 -30 -20 DEPTH CHANGE (FT) ~—a— 42.8 £5), || t SECTION Y SECTION Z 4 DEEP 13° B-23 : | 3 0 +10 PERCENT T S arenl| T SECTION AA 4 r DEEP Zz an —~— +40 —=— SECTION C 4 SHALLOW | 19° WA) 7) 4 5) || SECTION A- SHALLOW ge |—<_—_— +2.4 ae | SECTION B SHALLOW 1 SECTION E4 SHALLOW 4 B-30 4 — -30 -20 -10 0 +10 2710) 0) 8) 0) DEPTH CHANGE (FT) 0 +10 +20 +30 PERCENT 100 T T T Sina | T 90 | SECTION fF J SHALLOW SECTION | ge 7 SHALLOW 4 ——— + ] 6 =| = +4.2 iv | ha | I~ 48.4 =O, 7 B-34 | ere Stl ———— T T 90 F SECTION G 4 SECTION K 80 - SHALLOW | SHALLOW | 70+ =i ig 2 | 19 60 - 4 gL 2, =| ||| ——2 Sl | —=— +1.5 | 40 + 4 4 30 4 0 lis =| 2 B-32 B-35 10 - 4 4 0 l ! 100 90 F SECTION H SECTION M 80 SHALLOW 1 SHALLOW 20° 19° 70 #9) 4 60 50 i—— +4.2 40 4 30 | AD B-33 | 10 4 0 a —30 -20' —10 +10 +20 +30 -30 +10 +20 +30 DEPTH CHANGE (FT) PERCENT T T T SECTION N L SECTION Q 4 SHALLOW L SHALLOW 202 19° | 70+ i +] 4 ONS 4 —— +42 La—— 44.8 B-37 | B=40 me [ 1 —— 100 - T T TT] T T Taal T + SECTION O L SECTION R 4 IL SHALLOW SHALLOW | Zo 20° IF Lt, 7) —— 1.8 >| [ —— 127 EA B= +0.1- 4 fF =f OL e3 IL C-11 OR 4 + —(0).2) 1 N N Nl | Sales) L— 1 —_l 1 ! x] OE T T T T mall T v7 IE T Ti T T T al 40.9- [ +0.87- - SECTION | =. SECTION N O7- * PS +0. [ DEEP " DEEP 40.45 71 [ ONS in al Ir 440),2))- 7 r +0.17 ae 4 Se es ee on 0 LL Tae, C-9 4 - CaI2 =O "| r ~0.2 I ae a aw cee a) 0 10 20 30 40 50 COMO 0 10 20 30 #840 50 ©660 MINUTES R, AUTOCORRELATION SECTION O DEEP 2 LN) T SECTION R DEER WG? DEEP 22 SECTION S DEER Ig? SECTION Q + t DEEP 123 Gas eee ee) SECTION T DEEP Ig 60 70 0 MINUTES 40.8F ~, SECTION U HOW DEEP DEEP 4 13° 4 WOOL SECTION V ROW Sens DEEP +0.6 + Heke 13° R, AUTOCORRELATION SECTION Y DEEP Ise +0.6 + SECTION W 40.5+ DEEP 40.4¢ Ig? SECTION Z DEEP 13° oO ie) Ww (een ics (OT aroma ena C-6 MINUTES R, AUTOCORRELATION iC ay pe T T T T T | IE T T le T Ww T Ta] [ SECTION AA Aly ale j L DEEP a ae j L 12° ‘ieee: | [ eS SECTION C | om SHALLOW L ee a AL 19° j [ exe I) Cxpen| [ | it it it it it i [ it l 1 it i | ‘| [epee cee onltage teal T T T T] iC T T T T I T me] L SECTION A nlp A SECTION D j L SHALLOW Le SHALLOW ] L 19° | L 20° | L e961) L C-29 | L 1 it it JL it it ‘al [ 1 i t it it | 1 | T T T T T al Vol lim T T T T T T | | if in, Wadi L SECTION B L SECTION E J L SHALLOW hs SHALLOW | i 19° 4 - 20° 7 [ emp JL c-30 | [ IL Eine i i J Le it [ i i it ! | it | MINUTES i ae SECTION | | i SHALLOW 4 SECTION F a ee oo 7 1 SHALLOW i Ge | 19° Lek a Ry, AUTOCORRELATION SECTION G as SECTION K m SHALLOW A at SHALLOW | cee _, ae 4 L ms, Ise | SHALLOW ees SECTION H aa oa | I tay 20° stale alia SECTION M ] SHALLOW ee A a 1 ef C3 | MINUTES R, AUTOCORRELATION +0.1 [E T T i T T T 7 L T T T T T T "7 fie SECTION Q | [ SEALLOW. i SHALLOW | | 20° | ok 19° | the B| IL Pe, | r 4 I | [ It d b 4 — L eg |) IL evn || L tt it it 1 1 rl | i 1 1 IL it J it i IC T T T T T iT v7] [E T IF T T T T T] [ SEICUHON| © i, eae SECTIONR [ Sian eels SHALLOW | [ a 1 20° IL G=some| L C-41 ] i 3 i it it 1 1 All ———————_ =f 1 =i J 1 J IE T T T T T Val L aloes T T T T T T7 > a SSS 4 + SECTION S | LE ee siete, eae + L ; SHALLOW 4 L | ; 20° J L SECTION P ees | L SHALLOW i | L 20° ae | L Se Diag Cn 4 [ tL =+ |i —tt ! it i i it 1 i 1 it i 1 0 1 © 20 © 5 G 0 © © mM @ @ co @ 70 MINUTES ry 0 E T T T T T T Tama E T T T T T T T7] HOOP a a ols SECTION W | ee ety ie SHALLOW | eal dts ati: se dea 20 | +0.5+ 4 oF 4 +0.4-L aL J +0.3 fal =| in =] 0.2L SECTION T AIL a, | +0.1b SHALLOW Asal a, | OF 20 ee 4 iE a C-46 | -0.1} spon | (0) L 1 L L 1 L n N | L fe. 1 ! fd 234] 0 Ee T T T We T aps T7] L T T T T Tie T T7] +0.9 ite a =l l= = =z +0.8- o04 SECTION U al ies SECTION X | © 40,7/|- eee SHALLOW | em SHALLOW e AOI by p 70° || IL Soa | ; 70° | =i FORD > ey 7 Iz ina: >| az +O4e Sle dnes| cats RRA AM ra Pe ml npagty te ase 5] x +0.3- 4 ie s) +0.2 ae = u, ] +0.1F |r 5 SL ew) hel €=47) | = 2 0.4 oer 4 fz —0)9) ! ll It 1 ! 1 rt ene L iL 1 1 i! aj 0 = T T Tm ml T va c T T T T eo le T ~ vy +0.9- : 4 in OR Bites ti Ae a +0.8+ SECTION V eg eran ia Mac Pew) nO). 7/|E SHALLOW a L ce 1 0.6 ie etc 20 a +0.5} ——. SECTION Y | ee E eee “| r SHALLOW 71 +U.5-b teen, 4 ye 20° 4 40.24 4 L a 40.1 a QE ye J OL Cxasaale. ae C-48 -0.1- a L = ORD. i ! ! | | (L | i 1 n 1 Nl fe i 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 MINUTES R, AUTOCORRELATION SECTION Z SHALLOW 20 (eo) SECTION L 1 SHALLOW 7 iw SECTION AA SHALLOW 20° C-50 | I~ SECTION J 1 SHALLOW =| 18° zat REVERSE SIDE BLANK ai 70 0 MINUTES APPENDIX D ISOTHERM DEPTH POWER SPECTRA (SEMI-LOG) (FIGS. D1-D52) POWER SPECTRUM JU (h), FROM DIFFERENCES IN DEPTH OF ISOTHERMS AT HALF-MINUTE (304-FOOT) INTERVALS ON SEMI-LOG SCALES REVERSE SIDE BLANK POWER SPECTRUM U(h) FT2CPM 10° 104 ] © C5 WO 01S 220.25 sd) « ir T alr T T T T T T T T T SECTION A [ SECTION C DEEP 4 DEEP 12° { i 13 SECTION B DEEP 22 D-2 [Ei | ES SECTION D 12° D-4 es | 1 ! 35 0 WS 210 15 70) 25) .c10) 65 FREQUENCY (CPM) DEEP T T T T T SECTION E DEEP 12° SECTION F DEER Ie Q 5 10 1S 29 .25 .40 5 POWER SPECTRUM U(h) FT7CPM r= T T ee T T | SECTION G SECTION | SECTION M 104 DEEP 4 DEEP : DEEP 1¢2 122 F 12° ; | [ ] ; aa ; ie : E D-9 E Dean ee 1 N ! Nee ne L i 1 = N i [ees 10° T T T T j E “I T T T T Ed T a] T SECTIONH 4 t SECTION K + + SECTIONN 4 104 DEEP E DEEP E DEEP E 12 E 12° E E 1s E [ i - - Mate 3 OE E D3 3 E D-10 4 ] [ | | | ! | lt | L It | ! | _Il ] = ! ! fue i ® 05 JO 15 20 .25 .20 35 © 05 10 15 .20 25 .s0 .25 © 05 10 15 20 25 20) 25 FREQUENCY (CPM) D-4 POWER SPECTRUM U(h) FT2CPM a La | | SECTION O DEEP 12° : on cart ala Pelion 5 j SECTION P SECTION R DEER DEER Zz F lg? j : F , ; D-16 4 eek ners pee aed | sa a a ee SECTION Q DEER ; We OS IO 15 A 25 80 35 l © 05 .10 15 .20 .25 .20 .35 FREQUENCY (CPM) SECTION S DEEP Ig? L i i IL i fL T T T T T j SECTION T | DEEP 13° bi ininl l 0 05 10 oS .20) 25 .c0 sos POWER SPECTRUM U(h) FT2CPM S SECTION U DEEP iss i it it a it 1 E T T T T T T 4 SECTIONV 1 DEEP Is* na | [ie i en | 0 05 0 tS .20'.25 30 35 T T T T T ln = SECTIONW | DEEP a DEER ss | SECTION X | : j d D-22 ! ! 1 1 1 1 —) © 5 VO IS 20. 25 .80 .35 FREQUENCY (CPM) T VW T T T T SECTION Y DEEP 13° ae oe SECTION Z DEEP 13° 05) IO IS 20) 25) 230 6 POWER SPECTRUM Uh) FT2CPM 10° 104 T T T i: SECTIONA | SHALLOW ome D-26 = = 1 1 1 = © 05.10 .15 20 25 280 535 T as lca legreciegee lege tlior ary ae lan [ SECTION AA J SECTION B DEEP SHALLOW J 2 3 a 19° SECTION C SHALLOW ge bo iitiul : D-28 L It 1 Ss le SECTION D SHALLOW 20° F | SEGTHIONTE SHALLOW 20° wil 4 4 1 Po tt) D-30 E SSS SS —eEE———— @ 205 10 cS .A0 2S 20.65 FREQUENCY (CPM) OSS 20) 25) 80) 265 POWER SPECTRUM U(h) FT°CPM 10° >I T T T E lenge lacie eam T | ananassae cae eas ras SECTION F J L SECTION H [ SECTION K 104 SHALLOW SHALLOW SHALLOW 19° 4 20° 19° Sh i | jes Ras SE (es sea a a me 3 Sa [alae eel SECTION G SECTION | iG SECTION M 104 SHALLOW SHALLOW SHALLOW 20° F We ; 19° * 3 102 3 10 | F D-32 D-34 E q ] eth eS ee i 1 zi (ier er 0 0 1 1 @ 05 10 15 .40 .25 30 65 05 10 315 .20 25 .d0 .d8 05. 15 20 25 .30 .35 FREQUENCY (CPM) POWER SPECTRUM U(h) FT2CPM 10° E I T T T t SECTIONN | 104 SHALLOW 4 103 102 10 1 10° T T r SECTION O 104 SHALLOW 20° 4 102 102 10 J D-38 ] L fe fs fb ms Noe Nl On 510) 115152025. 30-35 T homo aed [ f SECTION P F SHALLOW 3 t 20° fc sa a ee Tianna Renee ar eet SEGTIONION | SHALLOW 19° : D-—40 1 1 1 ——— ate T T T T 4 SECTIONR | SHALLOW 4 20° { SECTION S SHALLOW ——It 1 | ! el @ 05.10 s15 .20) 25.30 35 FREQUENCY (CPM) @ 05.10 .15 .20 .25 60.35 POWER SPECTRUM U(h) FT°CPM SEGIIONNT 2 104 SHALLOW 4 20° | T T Vi T SECTION V 4 SHALLOW 20° i ] pees ! ! i eee ! ! ! ! 10° Tesi naraet eeaoiea| ae SECTION U 104 SHALLOW SHALLOW 20° 20° F D-44 E ] \ 1 af ecalnests Pose Nl 205 10 1S 20.25.60 . 8 ; Vee | TTT i b Qo riiiiul 1 1 = 1 0 05.10 cS .20).25) 30) .o8 FREQUENCY (CPM) SECTION X 4 SHALLOW Tpinseilerr melas SECTION Y SHALLOW | 1 1 ET @ 05 sisi -240) 025.60). POWER SPECTRUM U(h) FT2CPM 10° i SECTION Z 104 SHALLOW = 20° i SECTION AA SHALLOW 20° | D-50 ] 1 1 L 1 1 1 ! | —l | al | 103 aT T T 3 SECTIONL 4 SECTION J 2 SHAL | SHALLOW | 10 a LOW = 18° 1 pou 1 he 1 1 1 D-52 © 0S 10 15 20.25 .30) 25 © OF .1@.1 FREQUENCY (CPM) REVERSE SIDE BLANK L 1 1 5) 20) 28) 80) « by i Security Classification : DOCUMENT CONTROL DATA - R&D ~ (Security classification of title, body of abstract and indexing annotation muat be entered when the overall report ie classified) 1. ORIGINATING ACTIVITY (Corporate author) 2a. REPORT SECURITY CLASSIFICATION Navy Electronics Laboratory UNCLASSIFIED San Diego, California 92152 3. REPORT TITLE VERTICAL AND HORIZONTAL THERMAL STRUCTURES IN THE SEA 4. DESCRIPTIVE NOTES (Type of report and inclusive dates) Research and Development Report 1962 -1966 5. AUTHOR(S) (Laat name, fret name, initial) LaFond, E. C. and LaFond, K. G. 6. REPORT DATE 7a. TOTAL NO. OF PAGES 29 July 1966 138 Ga. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER(S) b. PROJECT NO. SR 104 03 01, Task 0580 1395 (NEL L40461) 9b. QT HERIREEORT NO(S) (Any other numbere that may be aesigned 10. AVAIL ABILITY/LIMITATION NOTICES DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED 11. SUPPL EMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Naval Ship Systems Command Department of the Navy 13. ABSTRACT The sea temperature structure of the upper layers was investigated by the use of a thermistor chain towed off the southern extremity of Baja California, Mexico, which revealed vertical and horizontal motion, large scale turbulence, and possible Doppler effects. The thermoclines were categorized in four types, smooth, normal, rough, and irregular. The power spectrum of vertical oscillation in the thermocline showed small peaks at wavelengths of 0.3 and 0.7 mile. The slopes of isotherms were determined from a study of over 65, 000 data samplings. DD 22. 1473 __ UNCLASSIFIED _ Security Cleesification UNCLASSIFIED Security Classification Sea Water - Temperature Thermoclines UNCLASSIFIED Security Classification CHIEF OF NAVAL MATERIAL MAT 0331 COMMANDER, NAVAL SHIP SYSTEMS COMMAND SHIPS 1610 SHIPS 1620 SHIPS 1631 SHIPS 2021 (2) SHIPS 204113 COMMANDER, NAVAL AIR SYSTEMS COMMAND AIR 032 AIR 0322 AIR 604 AIR 604 (DLI-304) FASS COMMANDER, NAVAL ORDNANCE SYSTEMS COMMAND ORD 5330 ORD 5330 (RUDC-2) ORD 5330 (RUDC-3) ORD 9132 ORD 9132 (DLI-304) COMMANDER, NAVAL ELECTRONIC SYSTEMS COMMAND LIBRARY COMMANDER, NAVAL FACILITIES ENGINEERING COMMAND FAC 42310 COMMANDER, NAVAL SHIP ENGINEERING CENTER CODE 6420 CODE 6440 CODE 64525 CODE 6454 CHIEF OF NAVAL PERSONNEL PERS 118 CHIEF OF NAVAL OPERATIONS OP-312 F OP-O7T OP-701 op-71 OP-03EG OP-09B5 OP-311 OP-322C OP-702C OP 716 OP-922Y4C1 CHIEF OF NAVAL RESEARCH CODE 416 CODE 418 CODE 427 CODE 466 CODE 468 CODE 493 COMMANDER IN CHIEF US PACIFIC FLEET COMMANDER IN CHIEF US ATLANTIC FLEET COMMANDER OPERATIONAL TEST AND EVALUATION FORCE DEPUTY COMMANDER OPERATIONAL TEST + EVALUATION FORCEs PACIFIC COMMANDER SUBMARINE FORCE US PACIFIC FLEET US ATLANTIC FLEET DEPUTY COMMANDER SUBMARINE FORCE» US ATLANTIC FLEET COMMANDER ANTISUBMARINE WARFARE FOR US PACIFIC FLEET COMMANDER FIRST FLEET COMMANDER SECOND FLEET COMMANDER TRAINING COMMAND US ATLANTIC FLEET OCEANOGRAPHIC SYSTEM PACIFIC COMMANDER SUBMARINE DEVELOPMENT GROUP TWO COMMANDER KEY WEST TEST + EVALUATION DETACHMENT DESTROYER DEVELOPMENT GROUP PACIFIC FLEET AIR WINGSs ATLANTIC FLEET SCIENTIFIC ADVISORY TEAM US NAVAL AIR DEVELOPMENT CENTER NADC LIBRARY US NAVAL MISSILE CENTER TECHe LIBRARY PACIFIC MISSILE RANGE /CODE 3250/ JS NAVAL ORDNANCE LABORATORY LIBRARY SYSTEMS ANALYSIS GROUP OF THE ASW R-D PLANNING COUNCIL» CODE RA INITIAL DISTRIBUTION LIST US NAVAL ORDNANCE TEST STATION PASADENA ANNEX LIBRARY CHINA LAKE US NAVAL WEAPONS LABORATORY KXL LIBRARY PEARL HARBOR NAVAL SHIPYARD PORTSMOUTH NAVAL SHIPYARD PUGET SOUND NAVAL SHIPYARD SAN FRANCISCO NAVAL SHIPYARD USN RADIOLOGICAL DEFENSE LABORATORY DAVID TAYLOR MODEL BASIN /LIBRARY/ US NAVY MINE DEFENSE LABORATORY US NAVAL TRAINING DEVICE CENTER CODE 365H» ASW DIVISION USN UNDERWATER SOUND LABORATORY LIBRARY CODE 905 ATLANTIC FLEET ASW TACTICAL SCHOOL USN MARINE ENGINEERING LABORATORY US NAVAL CIVIL ENGINEERING LABe L54 US NAVAL RESEARCH LABORATORY CODE 2027 CODE 5440 US NAVAL ORDNANCE LABORATORY CORONA USN UNDERWATER SOUND REFERENCE LABe US FLEET ASW SCHOOL US FLEET SONAR SCHOOL NAVY UNDERWATER WEAPONS RSCH & ENG STATION OFFICE OF NAVAL RESEARCH PASADENA US NAVAL SHIP MISSILE SYSTEMS ENGINEERING STATION CHIEF OF NAVAL AIR TRAINING USN WEATHER RESEARCH FACILITY US NAVAL OCEANOGRAPHIC OFFICE SUPERVISOR OF SHIPBUILDING US NAVY GROTON US NAVAL POSTGRADUATE SCHOOL LIBRARY(CODE 0384) DEPT.» OF ENVIRONMENTAL SCIENCES OFFICE OF NAVAL RESEARCH BR OFFICE LONDON BOSTON CHICAGO SAN FRANCISCO FLEET NUMERICAL WEATHER FACILITY US NAVAL APPLIED SCIENCE LABORATORY CODE 9200», ELECTRONICS DIVISION CODE 9832 US NAVAL ACADEMY ASSISTANT SECRETARY OF THE NAVY R+D US NAVAL SECURITY GROUP HDQTRS(G43) ONR SCIENTIFIC LIAISON OFFICER WOODS HOLE OCEANOGRAPHIC INSTITUTION INSTITUTE OF NAVAL STUDIES LIBRARY AIR DEVELOPMENT SQUADRON ONE /VX-1/ SUBMARINE FLOTILLA ONE DEFENSE DOCUMENTATION CENTER (20) DOD RESEARCH AND ENGINEERING WEAPONS SYSTEMS EVALUATION GROUP DEFENSE ATOMIC SUPPORT AGENCY NATIONAL OCEANOGRAPHIC DATA CENTER US COAST GUARD OCEANOGRAPHIC UNIT COMMITTEE ON UNDERSEA WARFARE US COAST GUARD HDQTRS(OSR-2) ARCTIC RESEARCH LABORATORY WOODS HOLE OCEANOGRAPHIC INSTITUTION US COAST AND GEODETIC SURVEY WASHINGTON SCIENCE CENTER - 23 FEDERAL COMMUNICATIONS COMMISSION US WEATHER BUREAU DIRECTOR» METEOROLOGICAL RESEARCH LIBRARY NATIONAL SEVERE STORMS LABORATORY NORMAN» OKLAHOMA 73069 NATIONAL BUREAU OF STANDARDS BOULDER LABORATORIES US GEOLOGICAL SURVEY LIBRARY DENVER SECTION “US BUREAU OF COMMERCIAL FISHERIES LA JOLLA WASHINGTON» De Ce 20240 WOODS HOLEs MASSACHUSETTS 02543 HONOLULU» HAWAII 96812 STANFORD» CALIFORNIA 94305 TUNA RESOURCES LAB LA JOLLA ABERDEEN PROVING GROUNDs MDe 21005 REDSTONE SCIENTIFIC INFORMATION CENTER US ARMY ELECTRONICS R-D LABORATORY AMSEL-—RD-MAT COASTAL ENGINEERING RESEARCH CENTER CORPS OF ENGINEERS» US ARMY HEADQUARTERS» US AIR FORCE AFRSTA AIR UNIVERSITY LIBRARY AIR FORCE EASTERN TEST RANGE /AFMTC TECH LIBRARY - MU~135/ AIR: PROVING GROUND CENTER» PGBPS~-12 HQ AIR WEATHER SERVICE WRIGHT-PATTERSON AF BASE SYSTEMS ENGINEERING GROUP (RTD) UNIVERSITY OF MICHIGAN OFFICE OF RESEARCH ADMINISTRATION UNIVERSITY OF MIAMI THE MARINE LABe LIBRARY MICHIGAN STATE UNIVERSITY COLUMBIA UNIVERSITY HUDSON LABORATORIES LAMONT GEOLOGICAL OBSERVATORY DARTMOUTH COLLEGE RADIOPHYSICS LABORATORY CALIFORNIA INSTITUTE OF TECHNOLOGY JET PROPULSION LABORATORY HARVARD COLLEGE OBSERVATORY OREGON STATE UNIVERSITY DEPARTMENT OF OCEANOGRAPHY UNIVERSITY OF WASHINGTON DEPARTMENT OF OCEANOGRAPHY FISHERIES-OCEANOGRAPHY LIBRARY NEW YORK UNIVERSITY DEPT OF METEOROLOGY + OCEANOGRAPHY UNIVERSITY OF MICHIGAN DIRECTORs COOLEY ELECTRONICS LAB DRe JOHN Ce AYERS UNIVERSITY OF WASHINGTON DIRECTOR» APPLIED PHYSICS LABORATORY OHIO STATE UNIVERSITY PROFESSOR Le Ee BOLLINGER UNIVERSITY OF ALASKA GEOPHYSICAL INSTITUTE UNIVERSITY OF RHODE ISLAND NARRAGANSETT MARINE LABORATORY YALE UNIVERSITY BINGHAM OCEANOGRAPHIC LABORATORY FLORIDA STATE UNIVERSITY OCEANOGRAPHIC INSTITUTE UNIVERSITY OF HAWAII HAWAII INSTITUTE OF GEOPHYSICS ELECTRICAL ENGINEERING DEPT HARVARD UNIVERSITY GORDON MCKAY LIBRARY A+M COLLEGE OF TEXAS DEPARTMENT OF OCEANOGRAPHY THE UNIVERSITY OF TEXAS DEFENSE RESEARCH LABORATORY ELECTRICAL ENGINEERING RESEARCH LAB HARVARD UNIVERSITY UNIVERSITY OF CALIFORNIA-SAN DIEGO SCRIPPS INSTITUTION OF OCEANOGRAPHY MARINE PHYSICAL LAB PENNSYLVANIA STATE UNIVERSITY ORDNANCE RESEARCH LABORATORY NAVAL WARFARE RESEARCH CENTER STANFORD RESEARCH INSTITUTE MASSACHUSETTS INST OF TECHNOLOGY ENGINEERING LIBRARY MIT-LINCOLN LABORATORY RADIO PHYSICS DIVISION THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS’ LABORATORY INSTITUTE FOR DEFENSE ANALYSES FLORIDA ATLANTIC UNIVERSITY kD SE ar RA OSES STP e yran 7 hod 5 ro] Le é _— ide Os 40 38 Hebe Mt pte 4 mati TEP PP oe ey Laat are: Weg me. se) Col. ear ana, ee say ea et eg nee HY aby wee ry ek Rey atad ek ert! 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