} A PREDICTIVE HORIZONTAL-TEMPERATURE-GRADIENT -MODEL OF THE UPPER 750 FEET OF THE OCEAN Derived from towed-thermistor-chain data taken in 17 geographical areas of the Eastern North Pacific E.L. Smith Research Report 17 March 1967 NAVY ELECTRONICS LABORATORY, SAN DIEGO, CALIFORNIA 92152 Te. 1255 LUS | we. HS NEL/REPORT 1445 Gpbl 1Y0da¥/14N Se (inti -_ DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED ; PROBLEM In general, investigate oceanographic factors pertinent to the behavior of underwater sound; in particular, study vertical fluctuations in thermocline depth. Specifically, study the thermal structure of the upper 750 feet of the ocean utilizing the towed thermistor chain and thereby gain a predictive understanding of these fluctuations and their distribution in time and space. Finally, incorporate the findings in an improved acoustic model that can be used in critical areas of the ocean. RESULTS 1. Time-dependent vertical-temperature fluctuations in the thermocline were found to exist in all areas of the ocean examined with the NEL Thermistor Chain. 2. Time-dependent horizontal-temperature gradients were com- puted from continuous cross sections of the upper 750 feet of the ocean in 17 geographical areas of the eastern North Pacific. The horizontal-gradient field alternates in sign with a regularity that implies a dominant frequency of internal waves or convection cells. The corresponding wavelength is 0.72 nautical mile with a standard deviation of 0.16 mile. 3. The vertical-temperature gradient in the thermocline is gen- erally of the order 1072 C/ft, but ranges between 1072 and 10-3 °C/ft. The corresponding horizontal-temperature gradient is generally of the order 10°*°C/tt, but ranges between 1073 and 10> Cftt. The slopes of isothermal surfaces are of the order 1072, Thus, the vertical and horizontal gradients normally differ by two orders of magnitude. The horizontal gradient in the thermocline can be predicted within useful limits from the measured vertical-temperature gradient by means of the equation SC LO 301 O04051 4, A predictive model of the horizontal-temperature gradients for a selected area of the sea was constructed on the basis of the above results and a single bathythermograph lowering. RECOMMENDATIONS 1. Continue development of the thermistor chain to improve its accuracy, reliability, and versatility. 2. Further develop the digital temperature-depth recording system. Use the digitized data in conjunction with the UNIVAC 1218 shipboard computer for detailed statistical analyses and real- time computations of the vertical- and horizontal-temperature- gradient fields. 3. Finally, continue the study of the vertical- and horizontal- temperature gradients in the sea and compile an atlas of hori- zontal time-dependent gradients. ADMINISTRATIVE INFORMATION Work was performed under SR 004 03 01, Task 580 (NEL L40461) by members of the Marine Environment Division. This report covers the period July 1962 to July 1965 and was approved for publication 17 March 1967. The author is grateful to O.S. Lee for consultation and assistance throughout this investigation and to D.W. Ternyila for data reduction and analysis. Thanks are also due to E.C. LaFond for the use of previous results and figures, and for comments on the manuscript. Comments on the manuscript by G.H. Curl are acknowledged. CONTENTS INTRODUCTION... page 5 PREVIOUS STUDIES... 5 OBTAINING THE DATA... & GENERAL CHARACTER OF THE DATA... i1 SMOOTHED TEMPERATURE STRUCTURES... 14 GRADIENT FIELDS... 15 GRADIENT-STRENGTH MAGNITUDES... 19 WAVELENGTHS... 23 PREDICTIVE MODEL OF HORIZONTAL-TEMPERATURE GRADIENTS... 29 SUMMARY AND CONCLUSIONS... 33 REFERENCES... 324 APPENDIX A: SMOOTHED TEMPERATURE STRUCTURES... 4-1 APPENDIX B: VERTICAL-TEMPERATURE-GRADIENT FIELDS... 8-1 APPENDIX C: HORIZONTAL-TEMPERATURE-GRADIENT FIELDS... C-1 TABLES Time and Position of each Sample Area... page 9 Temperature-Gradient Magnitudes for Specific Depth Ranges from a Single Bathythermogram... 30 14 15 ILLUSTRATIONS Geographic locations of 17 NEL Thermistor Chain tempera- ture-data sample areas... page 8 Fantail of USS MARYSVILLE and NEL Thermistor Chain and chain hoist... 10 NEL Thermistor Chain data from Sample Area 8, off the southern tip of Baja California... J Examples of low-pass-filtered NEL Thermistor Chain CEM, LS) Example of vertical-temperature-gradient field... 17 Example of horizontal-temperature-gradient field... 16 Track of USS MARYSVILLE showing where temperature data were collected off the southern tip of Baja California during NEL Thermistor Chain Cruise 8... 21 Least-squares fit of a straight line to the logarithms of the vertical- and horizontal-temperature gradients from 17 sample areas and the envelope of the standard error of estimate... 22 Track of USS MARYSVILLE showing locations where tem- perature data were collected between San Diego and Honolulu during NEL Thermistor Chain Cruise 4... 94 Ensemble average spectrum for NEL Thermistor Chain Cruise 4... 20 Ensemble average spectrum for NEL Thermistor Chain Cruise 8... 26 Wavelength histogram for 17 sample areas... 28 Bathythermograph taken 0815, 7 August 1962, during Cruise 14 of the NEL Thermistor Chain. ..50 Predicted horizontal-temperature-gradient field model... 31 Example from Sample Area 1 of the horizontal-temperature- gradient field... 32 INTRODUCTION The performance of any system whereby information is transmitted from one place to another, using radiated energy as a carrier, is limited by the characteristics of the transmitting medium. When measurements are made of the intensity of under- water sound in the ocean, the results are often highly variable. Factors contributing to this variability include divergence or partial convergence caused by refraction, destructive and con- structive interference associated with multipath propagation caused by reflections from the surface and bottom of the sea, and diffraction and scattering caused by inhomogeneities of the water medium. When there are present additional inhomogeneities such as suspended particles, thermal cells, regions of turbulence, or temperature variations caused by internal waves, an additional variation in intensity occurs. Multipath interference arises particularly when a trans- mission path passes through a gradient. Refraction of sound rays by gradients can produce sonar bearing errors and fluctuations in bearing measurements. Although salinity and pressure gradients contribute to this effects,temperature changes normally have the greatest influence on sound velocity and, hence, are the most important source of multipath interference. Therefore, know- ledge of temperature gradients is vitally important in the success- ful use of sonar by the U. S. Navy. This report covers an in- vestigation of a relation existing between the strengths of vertical- and horizontal-temperature gradients and a dominant frequency of oscillation in the thermocline. PREVIOUS STUDIES Information on gross physical features of the ocean including temperature gradients is readily available in oceanographic atlases. These atlases are generally derived in one of two ways: first, from an accumulation of data over many years from in- dependently conducted studies; and, second, from a concentrated study of a specific area ina short time. A good example of re- sults of a concentrated effort is the NORPAC Atlas (1955).! The North Pacific Expedition represented a concerted effort of Japan and the U.S., involving 19 research vessels and 1002 hydrographic stations. Most of the data were taken within one month, showing the intensity of the effort. Coastal stations were about 30 miles apart and oceanic stations were from 50 to 120 miles apart. The distance between hydrographic stations is the determining factor in computing horizontal gradients. Horizontal-temperature gradients derived from such sets of data are termed "'average gradients" and represent the average temperature change per nautical mile for a given depth. Average horizontal-temperature gradients may also be determined from two or more space-separated bathythermograph stations. During underwater acoustic experiments, it is not uncommon to determine the average gradient from the difference of two bathythermograph readings — one taken at the transmitting ship, the other at the receiving ship. Minute physical features, the temperature in particular, have not been investigated as widely as large-scale features even though horizontal thermal microstructure was observed during World War II when Holter (1944) made measurements from a submerged submarine using a thermopile.” He detected 0. 02°F differences over horizontal distances of about 30 feet. Other contributors in this area include Urick (1948) who, near Key West, detected gradients similar to those found by Holter and concluded also that gradient increased with depth within the mixed layers.” From experimental work in deep water, Sheehy (1950) concluded that acoustic intensity fluctuations were caused by inhomogeneities in the water.4 Lieberman (1951) detected inhomogeneities of mean size of about two feet (60 cm) and temperature variations of 0.05° Celsius (G2 Using Lieberman's results, Mintzer (1953 and 1954) made theoretical predictions of intensity fluctuations produced by temperature microstructure in the sea.° Priimak (1961) carried out a statistical analysis during a three-dimensional study of the sea, with investigations of the parameters and statis- tical characteristics of the fluctuations in temperature and 1. Superscript numbers denote references in list at end of this report. pulsations in current. Sagar (1960) found a diurnal cycle of growth and decay of insolation—produced microstructure in the surface layer in the summer months and showed a direct relation- ship between the existence of microstructure and acoustic intensity fluctuations & Helle (1964) measured thermal micro- structure from a submarine using fast-response thermistors.” Murphy (1965) used fast-response thermistors mounted on an unmanned torpedo-like research vehicle and recorded tempera- ture deviations of 0.3 C at 50 meters and 0.02°C at 1500 meters.!° Horizontal gradients measured near the surface were of the order of 0.1°C/nautical mile and 0.001C/nautical mile at 2000 meters. From the above discussion it can be seen miero-horizontal thermal gradients describe temperature changes over distances from a few inches to a few yards, while average horizontal gradients describe temperature changes over distances of several miles or even several hundred miles. Here we shall deal with distances between these extremes, being concerned with tem- perature changes over horizontal distances of about 1 mile. Horizontal-temperature gradients in this intermediate range (1 nautical mile) were first investigated in July 1964 when the NEL Thermistor Chain was used in collaboration with the Marine Physical Laboratory who were making convergence-zone bearing-accuracy measurements. The thermistor chain recorded continuous temperature cross sections parallel and perpendicular to the sound path between the two MPL participating ships. The temperature profiles were resolved into vertical- and horizontal- temperature-gradient fields, which revealed regions of high- intensity gradient. The horizontal-temperature gradient alter- nated in sign at nearly equal intervais and was consistently two orders of magnitude smaller than the corresponding vertical gradient (Smith,1965).'! Fisher etal (1965) reported on bearing fluctuations observed.'” These results, particularly the period- icity of the horizontal-temperature-gradient field, generated interest in gradient fields in other areas already surveyed with the thermistor chain. The speculation followed that, if other areas displayed a similar periodicity in internal temperature structure and if the two-orders-of-magnitude ratio between the vertical and horizontal gradients held, a predictive acoustic model might be constructed. OBTAINING THE DATA Temperature data were selected for analysis from 17 widely separated areas involving several water masses (Sverdrup etal., 1942) !5 The data were taken during eight cruises with the NEL Thermistor Chain and provide the best available representation of the geographic and water-mass variety of temperature struc- tures (fig. 1). The positions of the sample areas, cruise num- bers, and dates are shown in table I. The data were obtained solely from the NEL Thermistor Chain, a massive oceanographic instrument (fig. 2) which has been in operation since 1961. The chain is 900 feet long and capable of measuring and continuously recording the temperature structure to a depth of 830 feet, although the average towing depth is about 750 feet. The chain system consists basically of a hoist, links, storage drum, and electronic temperature recording 180° 160° 140° 120° 100° 5{a¢ 40° Figure 1. Geographic locations of 17 NEL Thermistor Chain temperature-data sample areas. TABLE 1. TIME AND POSITION OF EACH SAMPLE AREA Sample | Time Date Cruise Latitude Longitude 1 | 0800 46°21. 3.N | 126° 23. 0-W 2 | 2000 40° 18. 6.N | 124957. 6W 3 1400 | 27 July 1962 121° 34. S/W 0830 118° 02. 2W 5 0830 32° 04. 2/N 98, 3W 6 1500 | 15 July 1964 120° 56. 7W 21> 34. 6 N LU! BO. SW 212 50: ON NODSA OSs IGW. 16° 04. 2°N 100° 10. OW @ 1300 | 30 Mareh 1965 e 8 1200 18 March 1965 1600 10 June 1965 8N 1502 2A 3 W 11 1300 6 June 1965 = S 145° 07. 5 W 12 1230 | 13 July 1965 56° 39. 176051. TW 1B 1200 | 31 July 1965 39 | 37°54, 135° 07. 3/W 4 0100 42°01. ON |) 154209. 5 W 0100 27 July 1964 28 DSO D5, 4 IN| IBZ? 19), Qaw 16 1730 | 31 July 1964 Ze 26 o YN Hato il, DAW) pt oO V7 2000 | 22 August 1964 29 182 125 aN a7? 47. OW *Cruise conducted specifically for equipment modification or maintenance. equipment. Each link is about a foot iong and is faired for hydro- dynamic stability while the chain is under tow. Thirty-four thermistors are mounted at 25-foot intervals along the chain. An electrical harness passes through the flat, faired links and con- ducts the voltage-temperature analog outputs from the thermistor beads to the ship's laboratory. A special computer built into the data system scans each thermistor output every 12 seconds and interpolates between outputs to fix the depths of all whole-degree- Celsius isotherms within the towing depth of the thermistor chain. Towing depth is maintained by a streamlined, 2300-pound 10 & = VE lect Fim Figure 2. Fantail of USS MARYSVILLE and NEL Thermistor Chain and chain hoist. depressing weight attached to the bottom of the chain. One link below the deepest temperature sensor and two links above the depressing weight is mounted a Bourdon pressure transducer that provides a measurement of the maximum depth of observation. The interpolated whole-degree-isotherm depths for each 12- second scan are printed in analog form on a 19-inch-wide tape. On more recent cruises the temperature data have been simul- taneously punched on paper tape and recorded on magnetic tape in digital form. A single scan of the temperature-depth record- ings of the chain is equivalent to one bathythermograph (BT) every 12 seconds, or every 120 feet for the normal towing speed of 6 knots. DEP Wal, Wlele i GENERAL CHARACTER OF THE DATA Figure 3 is an example of raw chain data taken off the southern tip of Baja California during the USNEL Boundary Ex- pedition. The thermal structure shown is typical of that region of the ocean and is from Sample Area 8. The record is a two- dimensional picture or cross section of the temperature structure in the upper 750 feet of the ocean. The depth scale is not linear because the catenary-like configuration of the chain under tow results in the thermistors being closer together at the top than at the bottom of the chain. In the analog output record the vertical scale is magnified about 100 times (97 times at normal towing depth of 750 feet) over the horizontal. Three points need to be made with respect to the validity of these temperature structure data. First, if the vertical fluctua- tions in isotherm depth are related to internal waves (a periodic phenomenon), a Doppler frequency shift may be introduced into the data measured by moving sensors. The extent of this shift is SURFACE SAMPLE AREA 20°C — ————6 IME S =} Figure 3. NEL Thermistor Chain data from Sample Area 8, off the southern tip of Baja California. Section set off by vertical lines selected for detailed analysis. 11 12 unknown because the direction and velocity of propagation of the internal waves are unknown. However, the shift has no effect on the amplitudes of the vertical variations in isotherm depths. Second, small oscillations of the deep end of the chain are re- flected in the depth changes of the isotherms. However, these chain depth changes are very small compared to the vertical- temperature-structure fluctuations which are retained through a low-pass filtering process (discussed later). Third, the isotherm depths for the entire record are not recorded simultaneously, and some change in the thermal structure occurs in the beginning of the data section by the time the end is being recorded. However, the vertical changes in depth of a particular isotherm will be nearly correct in any case. A broad frequency spectrum exists in the vertical variations of the temperature structure with high frequencies superposed on the lower ones, which is indicative of the complexities of oceanic thermal structure. The sample section selected for analysis is set off by vertical lines in figure 3. To the right of the selected sample area and at a depth of about 200 feet, the 17°C and 14°C isotherms display weak 1°C temperature inversions. Inversions of this nature are not unusual in this area and have been dis- cussed at length in studies of thermal fronts found off the southern end of Baja California (LaFond and LaFond, 1966; Griffiths, 1962) 14.15 Such inversions were purposely omitted from the selected sample section. The effects of temperature inversions on vertical- and horizontal-temperature gradients are shown in a more descriptive example of the summer temperature structure of the deep Bering Sea, Sample Area 12 (see appendices to this report). In the thermistor chain data, the vertical excursions of a particular isoltherm increase with depth as the vertical- temperature gradient decreases. In areas where the vertical- temperature gradient increases sharply, the amplitude of the vertical displacement of the isotherms decreases. This inverse relation of the amplitude of vertical displacement to the slope of the vertical-temperature gradient is probably caused by the dif- erence in the vertical stability between the more stable water in the main pycnocline and the less stable water below it. T. Hesselberg (1918) defined vertical stability by the expression” 1 dp = 28 pimnide (1) where p is density and zis depth. According to this equation, the stability is greatest in the pycnocline where dp dz has the highest value. More energy is required to displace a unit volume of water vertically in an area of high vertical stability than to dis- place it an equal amount in an area of low vertical stability. Ver- tical displacements are therefore smaller in the main pycnocline than at other depths for an equal amount of imparted energy. Normally the thermocline and pycnocline are at the same depth, and this same line of reasoning also applies to vertical variations in the thermocline. The inverse relationship of amplitude of the vertical varia- tions to the vertical-temperature-gradient strength is not unique to this particular sample area but appears to be general through- out the oceans within the penetration depth of the thermistor chain. Most vertical variations of isothermal surfaces (fig. 3) are highly phase-coherent through the entire recorded cross section; this is probably due to single-mode internal waves or a series of convection cells. Other variations are less coherent and probably represent multimode internal waves or turbulence. Periodic, exponential, or random motion may cause these features. The intent here, however, is not to discuss at length the mechanisms by which variations are generated, but to call attention to the magnitudes of the horizontal gradients resulting from them. Re- peated tows over the same track in various areas, and in different directions as well, indicate that vertical motions in the tempera- ture structure are always present and that they change with time. The horizontal-temperature gradients (discussed in a later section) are therefore time-dependent. Close inspection of the record revealed changes of 1 to 4 feet in isotherm depth for each 12-second scan. To eliminate any aliasing of the data by spurious high-frequency components, the data were low-pass-filtered. The section between the heavy ver- tical lines in figure 3 will be used for describing the filtering process and the data reduction methods. 13 14 SMOOTHED TEMPERATURE STRUCTURES The simplification of the data by low-pass filtering assumes that the vertical variations of the higher frequencies have con- siderably lower amplitude than those of lower frequencies, and therefore should have less effect on the refraction of underwater sound. The low-pass filtering was accomplished by running weighted averages of the depth of each isotherm over 2-minute intervals using half-minute increments. The high-frequency cutoff of the filter is 7 radians per minute or 107 radians per nautical mile. The band pass is 0 to 0.5 cycle per minute. The depths of the frequency-smoothed isotherms were replotted on an expanded horizontal scale, and 0. 2°C isotherms were added by linear interpolation between the whole-degree isotherms. Figure 4 displays the smoothed, low-pass-filtered tem- perature structure from Sample Area 8. The horizontal scale is shown as time but may be interpreted as distance with 10 minutes equivalent to 1 nautical mile at the normal towing speed of 6 knots. The vertical scale is 60 times that of the horizontal. These scale factors also hold for the smoothed structures of the other 16 sample areas, shown in Appendix A. Three isotherms, the 15°, 16°, and 17°C, converge to form an area of relatively steep temperature gradients at about 200 feet. This will be designated Area A. The addition of 0.2°C isotherms between 12°C and15°C made the phase coherence of the vertical variations more obvious. The 20°C isotherm comes to the surface at about time 1236, and the temperature structure between 12°C and 15°C diverges about this same time. Even in a simplified form the temperature structure remains complex. Del Wal, PIE I HOURS 1200 210220 1230 1240 1250 1300 1310 1320 1330 ivi Cobh otr dared do dbl htoero org td dod tad tt th dt tf oo oe ee af BRERA Figure 4. Examples of low-pass-filtered NEL Thermistor Chain data; 0.2°C isotherms added by linear interpolation between whole-degree isotherms. GRADIENT FIELDS The following graphic method of differentiation was used to find the vertical- and horizontal-temperature gradient fields. First, the graph of the smoothed temperature structure was over- laid with an exact copy, but the copy was displaced vertically by 15 16 20 (Az) feet. (Several depth intervals were tried but 20 feet yielded the greatest detail for the minimum interval.) This dis- placement of one smoothed temperature chart over the other caused isotherms of one to intersect isotherms of the other. Next, at points of isotherm intersection the temperature values of one chart were subtracted from the values of the other. This yielded the change in temperature (\T) at particular depths and times for Az. Finally, the resulting vertical-temperature- gradient field of computed values of AT’ Az was contoured at selected gradient-strength intervals. Figure 5 shows the contoured vertical-temperature- gradient field obtained by this differentiation process from the smoothed structure of Sample Area 8 (fig. 4). The vertical and horizontal scales for the gradient field correspond in both depth and time to the smoothed structure from which it was derived. The contoured values in figure 5 have been multiplied by 100 for convenience of presentation. The vertical-temperature-gradient field is all negative, because temperature decreases with respect to depth for the entire field. The vertical-temperature-gradient fields for the other 16 sample areas are contained in Appendix B. The same method of differentiation was used to obtain the horizontal-gradient field. Here the horizontal differential incre- ment, Ax, was 1000 feet. (Several values were tried, but 1000 feet provided the greatest detail for the smallest interval.) This provided the change in temperature (AT) for the horizontal distance increment (Ax). The resulting horizontal-temperature-gradient field of computed values of AT/Ax was contoured at selected gradient-strength intervals. The contoured horizontal- temperature-gradient field obtained by differentiation from the smoothed structure of Sample Area 8 is shown in figure 6. The vertical and horizontal scales for the gradient field correspond in both depth and time to the smoothed structure from which it was derived. The contoured gradient strengths in figure 6 have been multiplied by 10°* for convenience of presentation. The actual values of the gradient strengths are in degrees Celsius per foot times 10 4 Assuming wave motion, the zero-horizontal-gradient con- tours that are vertical denote phase multiples of Nz/2 (for \ odd) in a lateral direction. The zero contours that are horizontal de- note the location of nodes in the modal distribution in the vertical DEPTH, FEET HOURS 1200 ~=1210 1220 1230 1240 1250 ~=—- 1300 1310 1320 1330 tt OO ee Geet DP Oy Ge Dee SO sey Tee Meat Fags imate Cree MrT etd Hace Vek Teh i eel ath Alea (det) (Vea) = 1 SA prceese/ AREA A ies : = oy ee) Q Ls ie eh eee ee } : 500 - 0.5 | 0.5 600 - 12°C 700 - Figure 5. Example of vertical-temperature-gradient field in °C/ft x 10~=: Entire field is negative gradient. direction. For this reason, the horizontal portions of zero con- tours are dashed. The horizontal-gradient field alternates in sign. The gradient values in shaded areas are negative and those in the unshaded areas are positive (fig. 6). The gradient sign is affixed on the basis of encounter, as experienced in time and distance through the temperature structure at a given depth. The horizontal-temperature-gradient fields for the other 16 sample areas are contained in Appendix C. 17 18 DEPTH, FEET HOURS 1200 += 1210 1220 1230 1240 1250 1300 1310 1320 8 1330 yp U Lae er Prt hai ath teh it hint ote Pen tent Oe aot ot tp AREA A! Figure 6. Example of horizontal-temperature-gradient field in °C/ft x 10mmes Shaded areas denote negative gradient. GRADIENT-STRENGTH MAGNITUDES The vertical-temperature-gradient field for Sample Area 8 (fig. 5) displays a gradient-strength range of three orders of magnitude in degrees Celsius per foot. The gradient strength for the field, in general, is 10 7°C/ft. In Area A' the vertical gradi- ent increases one order of magnitude to 10 a Cy ita Anea At corresponds to the previously mentioned Area A of figure 4. It was described as an area of converging isotherms and, hence, of relatively-high-intensity vertical-temperature gradient. At depths greater than 410 feet, the vertical gradient decreases one order of magnitude to 10 °°C/ft. The horizontal-temperature-gradient field for Sample Area 8 (fig. 6) also displays a gradient-strength range of several orders of magnitude. The contoured gradient strength for the field, in general, is 10°4°C/ft, and gradient-sign changes occur at zero contours. In area A" the horizontal gradient increases one order of magnitude to 10 °°C/ft, Area A" corresponds to Areas A and A' of figures 4 and 5, respectively. Below 420 feet the horizontal gradient decreases one order of magnitude to 10 °°C/ft. The horizontal-temperature gradient is zero in the region of gradient-sign changes. The horizontal-gradient strengths referred to are the maximum obtained at a specific depth. Comparing the vertical and horizontal gradients shows that they differ in strength by two orders of magnitude. When the vertical and horizontal gradients change orders of magnitude, they appear to do so simultaneously. On the basis of results obtained with the Russian thermistor chain, Lyamin (1965) “ wrote: 'When the temperature fluctuations are compared with the magnitudes of the vertical temperature gradient, they are seen to be proportional to each other. This relationship is noted in all cases without exception and indicates that the temperature fluctuations recorded by horizontally dis- placed transducers are the result of the vertical displacement of the water layers."' The interrelationship of the magnitudes of horizontal- and vertical-temperature-gradient strengths holds throughout all 17 sample areas with but a single exception. In Sample Area 9 it was found that, in regions of very sharp thermocline (high vertical- gradient values) where the vertical variations in the temperature 19 20 structure are small, the magnitude of the horizontal gradient is nearly zero. The smoothed temperature structure of Sample Area 9 exhibits some localized areas essentially free from vertical fluctuations of the isothermal surfaces. Examination of the vertical- and horizontal-gradient fields for Sample Area 9 shows that, when the vertical-temperature gradient is about 2 x 10 !°C/ft, the corresponding horizontal-temperature gradient is of the order 10° °C/ft and decreases to zero. Therefore in regions of strong vertical-temperature gradient (high vertical stability), vertical fluctuations in the temperature structure are small and time-dependent horizontal-temperature gradients nearly disappear. The regularity with which the horizontal-temperature gradient differs from the vertical-temperature gradient suggests that the slope of the isothermal surfaces is the regulating factor. The vertical- and horizontal-gradient interrelationship may be written as the identity dT/dx = (6T/6z) (dz/dx) (2) where 5T/5x is the horizontal-temperature gradient in °C/ft, dT/5z is the vertical-temperature gradient in °C/ft, and dz/dx is the slope of the isothermal surface. The ratio of 6T/6x to 5T/5z taken over the samples shows that the mean value of dz/dx islet pol Olean In an independent investigation (also using thermistor chain data) of the thermal structure around the tip of Baja California (LaFond and LaFond, 1966),!* two isotherms were selected for analysis, one in the main thermocline and one below it. The location of the data sections is shown in figure 7. The depth differences from point to point along the isotherms were deter- mined from the equation Vie eel (3) where 1 RO) (1 + cos = cos TAR n n mw (6) A=1 where h= 0, 1, 2, 3... n,index number of frequency (actual frequencies are given by h/ (2At) eycles/minute, At = 1/2 minute), and i= 0, 1, 2, 3... n,lag number. The individual spectrum for the 32 computations showed no single dominant frequency but, instead, showed many peaks in the spectral curves within the range of 0 to 0.35 cycle per minute. The resolution into narrow frequency bands was prevented by the short duration of the sample sections. The frequency band re- solved was 0.007 cycle per minute for 144 lags. However, POWER SPECTRUM, Ft? CYCLES PER MINUTE dividing each of the 32 spectra into bandwidths (Af) of 0.025 cycle per minute and then averaging the energy per bandwidth does re- veal some dominance in the spectrum. Figure 10 shows the average power spectrum for the two isotherms of the 16 data sections between San Diego and Hawaii. If no frequency band in the spectrum is dominant then the ensemble average would not show any peak. This is not the case, as shown by the two peaks clearly retained in the ensemble average spectrum (fig. 10). One peak is at 0.15 cycle per minute (A = 0.67 mile) and the second at 0.25 cycle per minute (A = 0.4 mile). The thermistor chain data of Cruise 8, from around the tip of Baja California, were also synthesized into spectral ordinates (LaFond and LaFond, 1966) !8 Cross sections of up to 12-hour duration of depths of isotherms were analyzed in the same manner as described for the Cruise 4 data. Figure 7 shows the location FREQUENCY, CYCLES PER MINUTE 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 1,000 Figure 10. Ensemble average spectrum for NEL Thermistor Chain Cruise 4. 25 of the data sections. The smoothed power spectrum values for two isotherms, one in the main thermocline and one below, for each of the 27 data sections A through Z plus & were computed. In this case (as in Cruise 4) no single frequency or frequency bandwidth appeared to be dominant within the range of 0 to 0.35 cycle per minute in the individual spectra. Averaging the energy per bandwidth ( Af = 0.025 cycle per minute) for the 54 computed spectra of Cruise 8 in the same manner as for Cruise 4 again revealed a peak in the emsemble average (fig. 11) at 0.15 cycle per minute (= 0.67 mile). Reexamination of the spectra, individually, shows peaks at many wavelengths but also shows a peak at \ = 0.67 mile for 28 out of 32 cases and 48 out of 54 cases for Cruises 4 and 8, re- spectively. Hence, 88 percent of the spectra thus far computed show a peak at a wavelength of 0.67 mile. FREQUENCY, CYCLES PER MINUTE 0 0.05 0.10 0.15 0.2 0.25 0.3 0.35 10,000 Lu ke =) = > ia Lu eS otal WY Lu =] O > UO tt = ra = 100 O Lu oO WY ~~ lw => (e) oO 10 Figure 11. Ensemble average spectrum for NEL Thermistor Chain Cruise 8. 26 Further analysis of the 17 horizontal-temperature-gradient fields (obtained from the smoothed temperature structures) pro- vides added support for the existence of a dominant frequency of oscillation. More than 600 wavelength measurements at two depths throughout the 17 horizontal gradient fields were made and the mean wavelength was found to be 0.72 mile (f= 0.14 cycle per minute) with a standard deviation of 0.07 mile. The horizon- tal bars in the histogram of figure 12 display the mean wavelength for each of the 17 sample areas, and the vertical lines show the mean wavelength and the standard deviation as derived from the ensemble averages. It should be observed that the mean wave- length (0.72 mile) for all the sample areas is in good agreement with the results of the spectral analysis (0.67 mile) for Cruises 4 and 8. However, the histogram gives no indication of the shorter wavelengths (0.4 and 0.3 mile) as shown in the average spectral curves for Cruises 4 and 8. These results indicate that there is a dominant frequency of oscillation in the thermal structure of the ocean with a wave- length of about 0.7 mile. The frequency spectrum under investi- gation here indicates that this result combined with the relation of the magnitudes of the vertical and horizontal gradients could be utilized as the foundation for a simplified predictive model of the horizontal-temperature gradients of the sea. The consistency of these results over widely separated geographic areas leads to the speculation that they are characteristic of the world ocean. 27 28 SAMPLE AREA A, NAUTICAL MILES 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Obe opt lie depths? Figure 12. Wavelength histogram for 17 sample areas. Horizontal bars are mean wavelength for each sample area. Vertical lines are the mean wavelength, and standard deviation as derived from the ensemble averages. PREDICTIVE MODEL OF HORIZONTAL-TEMPERATURE GRADIENTS A predictive horizontal-temperature-gradient model can be constructed in two steps: first, use half the mean wavelength, 0.35 mile, as the distance for the periodic sign changes of the horizontal-gradient field;* Second, from the results of a single bathythermograph lowering, compute the vertical-gradient strengths in °C/ft for selected depth ranges and assign the horizontal-gradient field with strength two orders of magnitude smaller than that of the vertical field for corresponding depth ranges. As an example of the construction of such a model, consider the bathythermograph of figure 13. The change in the order of magnitude of the vertical-temperature-gradient strength deter- mines the depth range interval as shown in table 2. The horizontal-temperature-gradient strengths for the corresponding depth ranges are also entered in the table. The resulting horizontal-temperature-gradient field model is shown in figure 14. The gradient field changes sign each one- half wavelength as shown by the alternating shaded and unshaded areas. The orders of magnitude of the horizontal-gradient strength in °C/ft are contoured at the depths specified by the matching vertical gradients computed from the bathythermograph. In the construction of such a model, obviously the larger the number of bathythermographs taken, the more reliable the depth ranges will be for establishing the order-of-magnitude con- tours in the model. The bathythermograph used here was made 0815, 7 August 1962, during Cruise 14 with the NEL Thermistor Chain. The simplified model results (fig. 14) may be compared with the more detailed computed horizontal-gradient field for Sample Area 1 in figure 15. The model is in reasonably good agreement with the more detailed horizontal-gradient field for the same time, place, anddepth. There is a slight disagreement * When a single BT is used, the initial gradient sign of the model has to be arbi- trarily assigned. However, when two closely spaced BT’s are used, the actual gradient sign can be determined. 29 30 TEMPERATURE, °C ke WwW WwW Le sc kK oO LU fa) Figure 13. Bathythermograph taken 0815, 7 August 1962, during Cruise 14 of the NEL Thermistor Chain. TABLE 2. TEMPERATURE-GRADIENT MAGNITUDES FOR SPECIFIC DEPTH RANGES FROM A SINGLE BATHYTHERMOGRAM Magnitude of Vertical Gradient dT/dz (°C/ft) Magnitude of Horizontal Gradient dT /dx (°C/ft) Depth Range (ft) 100 - 110 10m 110 - 275 DEPTH, FEET WAVELENGTHS (A = 0.7 MILE) 0) ] 2 3 n-3 n—2 n—1 n 100 200 300 400 500 600 Figure 14. Predicted horizontal-temperature-gradient field model. Horizontal-temperature-gradient contour values are in °C/ft. Horizontal-temperature-gradient contours repeat every A/2 from zero to n wavelengths throughout the model. in the wavelength, probably because of the modal distribution of the internal waves. In general, the simplified model provides a valid description of the horizontal-temperature gradients. Although the simplified model offers only the order of magnitude of the temperature gradients and the wavelength is restricted to a specified frequency spectrum, it must be noted that this is the first presentation of a formulated horizontal model accounting for first-order changes in the temperature structure in the sea. With further refinement in data-gathering-and- reduction processes, this model should reveal more detail and, possibly, a constant numerical relationship between vertical- and horizontal-temperature gradients in the sea. 31 a Nw 0580 | i 04210) | | 108 | 0280 ‘JUoTpeis aATyeSoU aJoUsp seore popeyg *;_OLl * Y/Oo ul pjely JUST peis-oinyeioduis} -[e}UOZTIOY oy} JO | voly ojdueg wor ojdwexq “GT oinsty aN | | | | | 0180 SYNOH ] Roly ofduesg - 005 — 007 - 00€ L Q yO if 1 \ i 002 Z f ew P¥y im - 001 -0 (0/70) 13434 ‘H1d3d 32 SUMMARY AND CONCLUSIONS Time-dependent horizontal-temperature gradients were computed from low-pass-filtered, continuous, temperature cross sections of the upper 750 feet of the ocean in 17 widely separated geographic areas. The selected areas range north to the Bering Sea, south to the coastal waters of the Mexican mainland includ- ing the Gulf of California, and west to the Hawaiian Islands. The horizontal-gradient fields, computed from smoothed temperature structures, alternate in sign with a regularity that implies a dominant frequency of internal waves or convection cells. The wavelength is 0.72 nautical mile with a standard deviation of 0.16 mile. The vertical- and horizontal-temperature-gradient fields contain zones of diverse intensity gradient. The vertical- temperature gradient in the thermocline is generally of the order 10 2°C/ft, but ranges between 107! and 10° °C/ft. The corre- sponding horizontal-temperature gradient is generally of the order 10 *°C/ft, but ranges between 10° and 10° °C/ft. The slopes of isothermal surfaces are of the order 10 2 AN Stemtig= tical analysis of the ratio of the horizontal to the vertical temperature gradient shows that the horizontal gradient in the thermocline can be predicted within useful limits from the meas- ured vertical-temperature gradient by means of the equation dT/dx = 0.0047 (dT/dz) 9.71 The combined interrelationship of the vertical- and horizontal-temperature gradients and the wavelength of the dominant frequency of oscillation of the temperature structure were used as the foundation for a simplified predictive model of the horizontal-temperature gradients of the sea. The consistency of the results over widely separated geographic areas leads to the speculation that they are characteristic of the world ocean. 393 34 REFERENCES 1. Oceanic Observations of the Pacific: 1955, The NORPAC Atlas, University of California Press, 1960 2. U.S. Navy Radio and Sound Laboratory Report S-17, Meas- urements of the Horizontal Thermal Structure of the Ocean, by N.J. Holter, 18 August 1944 3A. Naval Research Laboratory Report S-3392, The Microther- mal Structure of the Ocean Near Key West, Florida, Part I: Description, R.J. Urick and C.W. Searfoss, 1 December 1948 3B. Naval Research Laboratory Report S-3444, The Microther- mal Structure of the Ocean Near Key West, Florida, Part II: Analysis, by R.J. Urick and C.W. Searfoss, 12 April 1949 4. Sheehy, M.J., ''Transmission of 24-ke Underwater Sound From a Deep Source,"' Acoustical Society of America. Journal, v. 22, p.24-28, January 1950 5. Lieberman, L.N., ''The Effect of Temperature Inhomo- geneities in the Ocean on the Propagation of Sound, '' Acoustical Society of America. Journal, v. 23, p. 563-570, September 1951 6A. Mintzer, D., ''Wave Propagation in a Randomly Inhomo- geneous Medium, I.'' Acoustical Society of America. Journal, v. 25, p. 922-927, September 1953 6B. Mintzer, D., 'Wave Propagation in a Randomly nhomo- geneous Medium, II,'' Acoustical Society of America, Journal, v. 25, p. 1107-1111, November 1953 6C. Mintzer, D., ''Wave Propagation in a Randomly Inhomo- geneous Medium, II," Acoustical Society of America. Journal, v. 26, p. 186-190, March 1954 7. Priimak, G.I., ''Certain Results of the Studies of the Statistical Microheterogeneity of a Sea Medium, '' Academy of Sciences, USSR. Bulletin. Geophysics Series, No. 8, p. 805-810, 1961 8, Sagar, F.H., ''Acoustic Intensity Fluctuations and Tempera- ture Microstructure in the Sea, '' Acoustical Society of America. Journal, v. 32, p. 112-121, January 1960 9. Helle, J.R., ''Thermal Microstructure Measurements in the Pacific," p. 249-271 in Naval Oceanographic Office, First U.S. Navy Symposium on Military Oceanography, v.2, CONFIDENTIAL, 17-19 June 1964 10. Murphy, S.R. and Lord, G.E., "Thermal and Sound Velocity Microstructure Data Taken With an Unmanned Research Vehicle," p. 3438-360 in Naval Ordnance Laboratory, Second U.S. Navy Symposium on Military Oceanography, 5-7 May 1965. The Pro- ceedings of the Symposium, v. 1, 7 May 1965 11. Smith, E.L., 'Magnitudes of Time-Dependent Horizontal Temperature Gradients in the Ocean," U.S. Navy Journal of Underwater Acoustics, v. 15, p. 637-640, CONFIDENTIAL, July 1965 12. Fisher, F.H. and others, ''Convergent Zone Bearing Accuracy Measurements,'' U.S. Navy Journal of Underwater Acoustics, v. 15, p. 609-626, CONFIDENTIAL, July 1965 13. Sverdrup, J.U. and others, The Oceans, Prentice-Hall, 1942 14, LaFond, E.C. and LaFond, K.G., "Thermal Structure of Waters Adjacent to the Southern End of Baja California (Abstract), '' American Geophysical Union. Transactions, v. 47, p. 432, June 1966 15. Griffiths, R.C., ''Studies of Oceanic Fronts in the Mouth of the Gulf of California, An Area of Tuna Migrations,'' Experience Paper No. 34 presented at the World Scientific Meeting on the Biology of Tunas and Related Species, La Jolla, California, 2-14 July 1962 36 16. Hesselberg, T., "Uber die Stabilitatsverhaltnisse bei Vertikalen Verschiebungen in der Atmosphare und im Meer," Annalen der Hydrographie und Maritimen Meteorologie, v. 46, p. 118-129, 1918 17. Lyamin, E.A. and others, ''on the Use of a Towed Chain of Thermistors to Investigate the Thermal Structure of the Sea,"' Oceanology, v. 5, No. 3, p. 129-132, 1965 18. Navy Electronics Laboratory Report 1395, Vertical and Horizontal Thermal Structures in the Sea, by E.C. LaFond and K.G. LaFond, 29 July 1966 19. 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 APPENDIX A: SMOOTHED TEMPERATURE STRUCTURES ] Bory o[dureg — 009 Jo8 - 006 — 007 er - 00€ — 002 - 00l =0 1 | ! 1 | I 1 ! ' ! ! ' ! 1 1 ! ! ! 1 1 ! | ' | ! ! ! ' ! 1 | 1 1 1 1 1 1 1 1 0060 0S80 0v80 0€80 0280 0180 0080 0SZ0 (0) 740) 0&Z0 SdNOH 1444 ‘Hld3d A-1 oC i oer ir i Ce it ue r va eC ee a ee TY ee ST fap) i=) oO S oS o) Oo SoS i=) oO (=) (j=) io) Si i=) _— lol (op) —t wy Se) ~ 1444 ‘Hld3d rh tO ot ea ewe de a ea Se eT Sr TT ee LN OT cee] ome Ocoee es Ge ret oe p Rory oydwesg -00Z JoOL -009 - 00S 1 ! | ! ! 0€80 0280 0180 0080 he UES Ue Se Ue wile ai as CS a8 Se SI TMS tte ot oth (i Shee ll 1 ' ! ! 0€60 0260 Ol 60 0060 0580 080 SdNOH 1434 ‘H1ld3d A-4 0810 Homllde one al = es a= ag S co - iS is) << = ® == a LD iS x cI S w ' ' co) =) S >) =) = ‘s) S 3S s) oS S S N o t ra) No} N 1 1444 Hldid © (22h pei rei t Wen Ven ies Sr Saye oh RoC 1344 ‘Hld3d OO we Oo. So foe a= orm s 8On BS SegmmS: we Sn eo a Sona i On eS Sr NS eae aa Sh toe SO RS 1344 ‘H1d3d ' 1 1 (ieee teen ae ree Nem ee eas ees ene LMU ume nN Ce UT Ce MN. tie AVS SHUN CLT FU NE SAS cue TN lth I ae ee SYNOH A-9 OL very ojdues - 009 - 00S - 06h - 00€ 1344 ‘H1d3d Ye je Teme pe eal lcmr (iran Rem Pm) | Jom, a ad) i of} [ee Fee) eee i UD | | OOZL OS9L Ov9l OE9L 0z91 OLOL 0091 Ossl Ors O€Sl Se nn eee... (__(.((5056505858565650565050506068565665806060656080606865856560506560 06060 60 Ee ZL Bealy e[dures - 002 - 009 IoP - 00S 1344 ‘Hld3qd - 008 - 002 - 0 bon Wy Testis el he ole iI ooclL §=Sll id Unit p tio ree i th ho vSZl OSCL Orc! O&cl 0cz1 SYNOH I OlcL A-11 fo} S So fo} So So S = (=) (=) f=) S S (92) SST iva) We) ~ 1434 ‘H1d3d ie 0 ese UP ee TO ee ie eee Di eae mL Cire Uno em rd es (aed ima Lm) i (eevee Tiara ema ee 4 (Oe Om a Co adNOH 20 i=) = = Ss Ss = é S oO 2) i=) i=) oO . Pas t wD Ne} ™~ 14454 Hlddd S S =) =) =) S S =) i=) =) fo) S S = Lome N (oo) = Vo) No) ™~ oO fo) fo) S (2) (2) 5S (=) fo) fe) oS >) fo} oO oO = N o ~—t ive) Ne) ~ 1444 ‘H1dda APPENDIX B: VERTICAL - TEMPERATURE- GRADIENT FIELDS [ eoly e[dureg 1 oO 0} 4210) i oo oO 0€80 ho ao 0280 (i Ula Tl 0180 SUnoH ) 0 0 0080 0 0 0 0520 0 0 0 0vZ0 0 0&Z0 009 00S 00V 00€ 002 ool 1334 ‘Hld4qd B-1 Jol Z vary odureg OL 02 0002 0S6l SUNOH Ovél O61 0261 OLélL 0061 vee 002 009 00S OOr 00& 002 00l 1434 ‘Hld3qd B-2 Orv oer Och Olrl oor OSEL Orel € Paly ofdueg - 00S oor 00€ 002 - 001 Oe 1434 ‘H1d3d B-3 f Bary ojdures — 002 — 009 — 00S — 007 — 00L (tf | ! en Det ! o4 hoo | l | | | 0€80 0280 0180 0080 Uo fl i | | 0Vv80 SdNOH ! 1 I 1 1 i} 0060 0580 1444 ‘H1ld4qd B-4 G voly o[dues — 002 - 009 — 00S — 00r — 00€ — 00¢ ~ ool = 0) Io ! kot | I US eee | ! ! 1 ot ! 1 Im Ie sale Ss SI ! ot | eet} e Et il 8580 0580 0r80 0€80 0280 0180 0080 ¥SZ0 SYNOH B-5 1444 ‘H1diad 9 voy o[dures ~ 009 906 00S i L CF 27 iw) m™ U 4 =e = Es Mm m o — 00¢ [On TT OcSL OLSL O0SL OSyl Orrl O€Fl O2FL SYNOH B-6 OcEL OLEL O0EL OSCl SYNOH Orel O&Zl raga L eoly o[dureg - 009 - 00S - 007 - 00€ - 00¢ - 001 1334 ‘Hld3d IBF SYNOH 0S91 Or9l 09 Oz9L OL9L SYNOH | 009L B-9 OL Bory ofdues - 007 - 008 - 002 1444 ‘Hid3d - 001 -0 OSs ors OES ee a I ee ————————E———————————————————————————— OE ———_ Ee OSEL OvEL O&el OC EL SYNOH OLEl O0€1 0SZl OVvcl IT Bory ojdures O&Zl 00S 007 00€ 002 ool 1344 ‘Hlddad B-10 ZL Bory edures - 009 IOP aes - 00S eS Ye ee + P 4 eer - 007 s0 - 00€ - 002 Na Sa oe = RMN A WP Dts amas Uae Thins 027 OZ oozgl =—~*rSLL ee ee ee ee i] ! i} | 0&1 1434 ‘Hld43ad B-11 €] eoly oydures L 2 Pes rs ees ee ee SS ee = ee £ Co Ss e Gf eee = g 3 8 = = aga : Lot ee SS 01 SS Ga fC ii ol Ol 4 i a 1002 fe fee de Eee te AA? APSR TTS MT TS Tet “Te aivh UTPe Wee SHTTRT Tviny tTFie lm MOV tte Yom TT TRAE ise STi TV Met TRC UTP oe eee TT a OEZl 0221 OLZL olorAlt OSI Ov O€Ll OCLL OLLL ool SYNOH - 007 ro) o ro) 1344 ‘HLddqd ~ 002 - 00L = B-12 po 0 0ZLO p oo OLLO Peat a O0LO [ale a 0700 SYNOH | ! | 0€00 noo a 0200 \ | 0100 Pl voly od ot 0000 weg - 004 ~ 007 - 002 -00l -0 1444 ‘H1ld3ad B-138 G] eory ojdures - 002 = ola — 00¢ - 00l [earth salt titae Nie leet, ei RT tS RSM aI ASI Ts a 4) Uh AM AV ST SEPT 0 a Ea PP Ree 1a (ee PT ea gl ] 0020 0S10 OVO 0€10 OcL0 OLLO 0010 0S00 0v00 000 SYNOH 13444 ‘H1ld3d B-14 008L OSZL | OVvZl | O&Zl OL etal OLZL CSAINDALI OOZL oro 9] voy ofdures 002 — 00€ — 002 — 00l — 0 Oe9l 1544 ‘HLd3ad B-15 OE07 0202 OL07 0002 JoLt Io¥2 0S61L Orel SYNOH O€6l 0261 LI Boly o[dureg — 008 — 002 - 001 1334 ‘Hld3qd B-16 APPENDIX C: HORIZONTAL - TEMPERATURE - GRADIENT FIELDS 7 rN, 0580 | OV 4s{0) — [ Boly o[dures — 00S — 007 — 00€ | | | | | | | | | | | | | | 0€80 0280 0180 0080 0SZ0 | | | | | | | | | | | | | ovZ0 0€40 SUNOH 1444 ‘Hld3d C-1 020¢ ! i 010d 000¢ OSé6lL SYNOH Or6l 0&6 0261 G Roly a[dureg ~ 002 - 009 - 00S 1344 ‘Hld3ad C-2 € Boly o[dureg — 00S - 007 | j=) =) oO 1 S oS N | i ! | i | | | | I OlvL oor OSEL Ovel Ocel SYNOH I 00S OsvL Orr Oerl 0crl cc ee 1444 ‘Hlddd \ 4 = 0160 0060 IDL —7 ~7 “> Jo#l ! 0€80 ! 0280 f Roly oydureg 0180 | 009 - 00 0080 00r 00€ 002 ojo) 0 1444 ‘Hld3ad G Roly o[dueg - 002 - 009 - 00S - 007 - 00€ - 002 dol -00l = (0) 8580 0580 04210) 0£€80 0280 0180 0080 ¥SZ0 SYNOH 1444 ‘Hld4d C-5 9 eoly ofdues — 009 — 00S — 007 NT a eT ae ea aaa OcSl = OLS L OOSL OSPF Ohara Oerl Och SdNOH 1344 ‘Hlddd OfElL 0cEL a N N cay t oN r () A I \ 5 7 I Siena l | ‘ \ { OLEL O0EL Oscl Ovcl L early ofdures - 009 JEL - 00S % -00r -00€ - 002 7N , - 001 O&cl Gal OLZL 1454 ‘HLdda C-7 6 Roly e[dweg - 004 ~ 009 w ~ 00S - 007 w — 00€ ¢ - 002 00 O£10 0210 OLLO 1 i i i i} 1 i} | i ! | ! 00L0 0500 0v00 SdNOH 0200 0100 0000 1434 ‘H1d3a C-8 0c9L SYNOH OLgL OL very ofdures - 004 - 008 - 00L 1334 ‘Hld4qd Cc-9 i OOrL | OSEL | | | Ovel | ! | OE 08 | ! | | ! OZEL SYNOH | | | OLEL | | | O0el TL Bory efdues | | ! Ovel - 00S - 007 -00€ - 00 - 001 -0 | | oral 1444 ‘Hld3d C-10 GL Barly eTdues C-1li — 002 —009 - 005 - 007 ‘HL did dlelelsl — 008 — 002 - 00l vSCl OSZL Orel O&Zl OZ CL OLcL oocl = WSL GI Bory oydures = (ofa — 004 H1d4qd 13354’ — 002 0 il oa OLLI OOLL | ! \ 1 i ! | 1 i i 1 | u 1 ' ! 1 | ' I OE Waal OLL olorat OSL orl Oell C-12 ! vat SYNnoOH 906 PI early efdureg C-13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | O€10 OZ | OLLO 00L0 0S00 0700 0€00 0200 0100 0000 SdMOH Cy Bory eydurg | 0020 no a OSLO | OrLO i 4 OELO i wd 0210 to SYNOH en OLLO | 0010 l 0S00 | 0v00 - 002 - 009 - 007 - 002 - 001 1544 ‘HLddad C-14 ee) 0081 OSZ1 OrZl O&Zl oa Jolt = 4 LP BEY 44 OcZ1 OLZL oT 0021 OS9L ovgl Boly oydureg - 002 - 009 - 00S - 00r - 00€ - 00 - 00 1444 ‘Hld4ad C-15 0€0C 020d ! | | | | | i | | 0102 0002 0S6l SdNOH Orél | | i | i | | | | i | | | | | | | | i O61 026l 1] Boly a[dures — 009 — 00S — 002 — 00L > 0) | | ! | | | | | OL6L 0061 1434 ‘Hld3q C-16 UNCLASSIFIED Security Classification DOCUMENT CONTROL DATA-R&D (Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified) 1, ORIGINATING ACTIVITY (Corporate author) 2a. REPORT SECURITY CLASSIFICATION Navy Electronics Laboratory UNCLASSIFIED et is ik Sa ae 3. REPORT TITLE A PREDICTIVE HORIZONTAL-TEMPERATURE-GRADIENT MODEL OF THE UPPER 750 FEET OF THE OCEAN 4. DESCRIPTIVE NOTES (Type of report and inclusive dates) Research Report July 1962 to July 1965 5. AUTHOR(S) (First name, middle initial, last name) E.L. Smith 17 March 1967 90 19 8a, CONTRACT OR GRANT NO. 9a. ORIGINATOR’S REPORT NUMBER(S) PROSE Nee IR OO O8 Wil 1445 Task 580 9b. OTHER REPORT NO(S) (Any other numbers that may be assigned NEL 140461 this report) 10. DISTRIBUTION STATEMENT Distribution of this document is unlimited. 11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Naval Ship Systems Command Department of the Navy 13. ABSTRACT Time-dependent horizontal-temperature gradients were computed from vertical- temperature cross sections taken with the towed thermistor chain in 17 areas of the eastern North Pacific. The horizontal gradients were found to be generally smaller than the vertical gradients by two orders of magnitude. The horizontal-gradient field alternated regularly in sign, implying a dominant frequency of internal waves or convection cells (with a corresponding wavelength of 0.72 nautical mile). The horizontal gradient in the thermocline can be predicted from the measured vertical gradient by means of the equation: Gp ie \ Oo are 0. 0047 ie On the basis of these results, plus a single bathythermograph lowering, a simplified predictive model of the horizontal-temperature gradients was constructed. DD "1473 (Pace 1) UNCLASSIFIED S/N 0101- 807-6801 Security Classification UNCLASSIFIED Security Classification KEY WORDS Oceans - Temperature - Prediction DD Wn'..1473 (ack) UNCLASSIFIED (PAGE 2) Security Classification GAldISSVIONN S$! 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BA0eD mall 3 *Pa}9NJ}SUOD SEM SjUalpesb aunyesadwiay =|P}UOZI0Y au} Jo japowW antjoipaid paljijdwis e ‘bulsamo| -YdesHowsayyAujeg ajbuis e snjd ’s}jnseu asau} Jo siseq au} UD 2p xp See t= —— 1p LEOO'O Ip *pajon4}suO0d Sem SjUaIpesb aiunjesadway -|P}UOZIJOY 34} Jo |apOW aANdIpaud palsijdwis e “bulsamo| YdesbowsayyAyjeg ajbuis e snjd ’s}jnsed asay} jo siseq ay} UD zp EXD swe IDB 26000 - 1p *paj9n4jsuod Sem SjUalpesb asnjyesadwa} -|P}UOZIJOY 94} Jo JapoW aAijdipaid parjijdwis e “‘bulsamo| YdesbowsayyAuyjeg ajbuis e snjd “s}jnsad asauy jo siseq ay} UD =p P e xp 2-0\ LP SAE LP CHIEF OF NAVAL MATERTAL MAT 0331 COMMANDER, NAVAL SHIP SYSTEMS COMMAND SHIPS 1610 SHIPS 1631 SHIPS 2021 (2) SHIPS 204113 COMMANDER, NAVAL AIR SYSTEMS COMMAND AIR 5330 AIR 5401 AIR 604 COMMANDER, NAVAL ORDNANCE SYSTEMS COMMAND ORD 03C ORD 0322 ORD 9132 COMMANDER, NAVAL FACILITIES ENGINEERING COMMAND FAC 42310 COMMANDER, NAVAL ELECTRONIC SYSTEMS COMMANC TECHNICAL LIBRARY COMMANDER, NAVAL SHIP ENGINEERING CENTER CODE 6120 CODE 61798 CODE 6179C03 CODE 6360 CHIEF OF NAVAL PERSONNEL PERS 118 CHIEF OF NAVAL OPERATIONS OP-03EG op-311 OP-312F OP-322C OP-07T op-702C op-71 op-716 OP-09B5 op-922Y4C1 CHIEF OF NAVAL RESEARCH CODE 416 CODE 418 CODE 427 CODE 466 CODE 468 COMMANDER IN CHIEF US PACIFIC FLEET CODE 93 US ATLANTIC FLEET COMMANDER OPERATIONAL TEST AND EVALUATION FORCE KEY WEST TEST AND EVALUATION DETACHMENT DEPUTY COMMANDER OPERATIONAL TEST AND EVALUATION FORCE, PACIFIC COMMANDER SUBMARINE FORCE US PACIFIC FLEET CODE 21 US ATLANTIC FLEET COMMANDER ANTISUBMARINE WARFARE FORCE US PACIFIC FLEET COMMANDER FIRST FLEET COMMANDER SECOND FLEET COMMANDER TRAINING COMMAND US ATLANTIC FLEET OFFICE OF THE OCEANOGRAPHER OF THE NAVY COMMANDER OCEANOGRAPHIC SYSTEM PACIFIC COMMANDER SUBMARINE DEVELOPMENT GROUP TWO COMMANDER, DESTROYER DEVELOPMENT GROUP, PACIFIC COMMANDER FLEET AIR WINGS, ATLANTIC FLEET NAVAL AIR DEVELOPMENT CENTER LIBRARY NAVAL MISSILE CENTER TECHNICAL LIBRARY PACIFIC MISSILE RANGE CODE 3250 NAVAL ORDNANCE TEST STATION CHINA LAKE CODE 753 PASADENA ANNEX LIBRARY NAVAL WEAPONS LABORATORY KXL LIBRARY PEARL HARBOR NAVAL SHIPYARD CODE 246P PORTSMOUTH NAVAL SHIPYARD CODE 242L PUGET SOUND NAVAL SHIPYARD CODE 246 SAN FRANCISCO NAVAL SHIPYARD HUNTERS POINT DIVISION NAVAL RADIOLOGICAL DEFENSE LABORATORY CODE 222A OCEANOGRAPHIC OFFICE PACIFIC SUPPORT GROUP, SAN DIEGO NAVAL SHIP RESEARCH & DEVELOPMENT CENTER CARDEROCK DIVISION LIBRARY ANAPOLIS DIVISION CODE 257 INITIAL DISTRIBUTION LIST NAVY MINE DEFENSE LABORATORY CODE 716 NAVAL TRAINING DEVICE CENTER TECHNICAL LIBRARY NAVY UNDERWATER SOUND LABORATORY LIBRARY CODE 905 ATLANTIC FLEET ASW TACTICAL SCHOOL LIBRARY NAVAL CIVIL ENGINEERING LABORATORY u54 NAVAL RESEARCH LABORATORY CODE 2027 CODE 4320 CODE 5440 NAVAL ORDNANCE LABORATORY CORONA TECHNICAL LIBRARY SILVER SPRING, MD. DIVISION 221 DIVISION 730 NAVY UNDERWATER SOUND REFERENCE LABRATORY LIBRARY FLEET ASW SCHOOL TACTICAL LIBRARY FLEET SONAR SCHOOL NAVAL UNDERWATER WEAPONS RESEARCH AND ENGINEERING STATION LIBRARY OFFICE OF NAVAL RESEARCH BRANCH OFFICE PASADENA CHIEF SCIENTIST BOSTON CHICAGO SAN FRANCISCO LONDON NAVAL SHIP MISSILE SYSTEMS ENGINEERING STATION CODE 903 CHIEF OF NAVAL AIR TRAINING TRAINING RESEARCH DEPARTMENT NAVY WEATHER RESEARCH FACILITY NAVAL OCEANOGRAPHIC OFFICE CODE 1640 SUPERVISOR OF SHIPBUILDING, US NAVY GROTON, CONN. CODE 249 NAVAL POSTGRADUATE SCHOOL DEPT. OF ENVIRONMENTAL SCIENCES LIBRARY FLEET NUMERICAL WEATHER FACILITY NAVAL APPLIED SCIENCE LABORATORY CODE 9200 CODE 9832 NAVAL ACADEMY ASSISTANT SECRETARY OF THE NAVY CRESEARCH AND DEVELOPMENT) NAVAL SECURITY GROUP G43 AIR DEVELOPMENT SQUADRON ONE VxX=1 SUBMARINE FLOTILLA ONE, US PACIFIC FLEET DEFENSE DOCUMENTATION CENTER (20) DEPARTMENT OF DEFENSE RESEARCH AND ENGINEERING WEAPONS SYSTEMS EVALUATION GROUP DEFENSE ATOMIC SUPPORT AGENCY DOCUMENT LIBRARY SECTION NATIONAL OCEANOGRAPHIC DATA CENTER CODE 2400 COAST GUARD OCEANOGRAPHIC UNIT NATIONAL ACADEMY OF SCIENCES/ NATIONAL RESEARCH COUNCIL COMMITTEE ON UNDERSEA WARFARE COAST GUARD HEADQUARTERS OSR-2 ARCTIC RESEARCH LABORATORY WOODS HOLE OCEANOGRAPHIC INSTITUTION DOCUMENT LIBRARY LO-206 ENVIRONMENTAL SCIENCE SERVICE ADM. COAST AND GEODETIC SURVEY ROCKVILLE, MD. WASHINGTON SCIENCE CENTER — 23 WASHINGTON, D. C. US WEATHER BUREAU DIRECTOR, METEOROLOGICAL RESEARCH LIBRARY GEOLOGICAL SURVEY LIBRARY DENVER SECTION ESSA/INSTITUTE FOR TELECOMMUNICATION SCIENCES AND AERONOMY BOULDER, COLO. FEDERAL COMMUNICATIONS COMMISSION RESEARCH DIVISION NATIONAL SEVERE STORMS LABORATORY CENTRAL INTELLIGENCY AGENCY OCR/DD-STANDARD DISTRIBUTION NATIONAL BUREAU OF STANDARDS BOULDER, COLO. BUREAU OF COMMERCIAL FISHERIES LA JOLLA, CALIF. TUNA RESOURCES LABORATORY LA JOLLA WASHINGTON, D. C. BRANCH OF MARINE FISHERIES WOODS HOLE, MASS. BIOLOGICAL LABORATORY LIBRARY HONOLULU, HAWAII FISH AND WILDLIFE SERVICE LIBRARY STANFORD, CALIF. is BIOLOGICAL LABORATORY ABERDEEN PROVING GROUND | TECHNICAL LIBRARY ‘ ARMY MISSILE CENTER REDSTONE SCIENTIFIC INFORMATION CENTER DOCUMENT SECTION ARMY ELECTRONICS RESEARCH AND DEVELOPMENT LABORATORY ARMY ELECTRONICS COMMAND « MANAGEMENT & ADMINISTRATIVE SERVICES DEPT AMSEL-RD-MAT COASTAL ENGINEERING RESEARCH CENTER. ARMY CORPS OF ENGINEERS | |, AIR FORCE HEADQUARTERS ae: DIRECTOR OF SCFENCE AND TECHNOLOGY AFRSTA *” AIR UNIVERSITY “LIBRARY. AUL3T-5028 AIR FORCE EASTERN TEST RANGE AFMTC TECHNICAL LIBRARY - MU-135 AIR PROVING GROUND CENTER PGBPS-12 HEADQUARTERS AIR WEATHER SERVICE AWSSS/SIPD WRIGHT-PATTERSON AIR FORCE BASE (1) SYSTEMS ENGINEERING GROUP (RTD) SEPIR UNIVERSITY OF MICHIGAN OFFICE OF RESEARCH ADMINISTRATION NORTH CAMPUS COOLEY ELECTRONICS LABORATORY UNIVERSITY OF CALIFORNIA-SAN DIEGO MARINE PHYSICAL LABORATORY SCRIPPS INSTITUTION OF OCEANOGRAPHY LIBRARY UNIVERSITY OF MIAMI THE MARINE LABORATORY LIBRARY MICHIGAN STATE UNIVERSITY LIBRARY-DOCUMENTS DEPARTMENT COLUMBIA UNIVERSITY LAMONT GEOLOGICAL OBSERVATORY DARTMOUTH COLLEGE RADIOPHYSICS LABORATORY CALIFORNIA INSTITUTE OF TECHNOLOGY JET PROPULSION LABORATORY HARVARD COLLEGE OBSERVATORY HARVARD UNIVERSITY GORDON MCKAY LIBRARY LYMAN LABORATORY OREGON STATE UNIVERSITY DEPARTMENT OF OCEANOGRAPHY UNIVERSITY OF WASHINGTON DEPARTMENT OF OCEANOGRAPHY FISHERIES-OCEANOGRAPHY LIBRARY APPLIED PHYSICS LABORATORY NEW YORK UNIVERSITY DEPARTMENT OF METEOROLOGY AND OCEANOGRAPHY UNIVERSITY OF ALASKA GEOPHYSICAL INSTITUTE UNIVERSITY OF RHODE ISLAND NARRAGANSETT MARINE LABORATORY LIBRARY YALE UNIVERSITY BINGHAM OCEANOGRAPHIC LABORATORY FLORIDA STATE UNIVERSITY OCEANOGRAPHIC INSTITUTE UNIVERSITY OF HAWAII HAWAII INSTITUTE OF GEOPHYSICS ELECTRICAL ENGINEERING DEPARTMENT A&M COLLEGE OF TEXAS DEPARTMENT OF OCEANOGRAPHY THE UNIVERSITY OF TEXAS DEFENSE RESEARCH LABORATORY ELECTRICAL ENGINEERING RESEARCH LABORATORY PENNSYLVANIA STATE UNIVERSITY ORDNANCE RESEARCH LABORATORY STANFORD RESEARCH INSTITUTE NAVAL WARFARE RESEARCH CENTER MASSACHUSETTS INSTITUTE OF TECHNOLOGY ENGINEERING LIBRARY LINCOLN LABORATORY RADIO PHYSICS DIVISION FLORIDA ATLANTIC UNIVERSITY DEPARTMENT OF OCEAN ENGINEERING THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY DOCUMENT LIBRARY INSTITUTE FOR DEFENSE ANALYSES DOCUMENT LIBRARY