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Horizontal coherence of oceanic temperature structure
Deep-Sea Research, 1975, Vol. 22, pp. 767 to 776. Pergamon Press. Printed in Great Britain.
Horizontal coherence of oceanic temperature structure A. E. GARGETT* (Received 16 July 1974; in revised form 27 March 1975; accepted I April 1975) A b s t r a e t h T h e horizontal correlation of temperature structures with vertical scales of meters is examined, using data from the cycling mode of a towed body system operating within the thermod i n e in the North Pacific. Results show significant loss of correlation for temperature features with vertical scales of less than 5 m, over horizontal distances of the order of 100 to 200 m, and often as little as 20 m. Examination of temperature and salinity along isopycnal surfaces serves to differentiate between true low horizontal correlation and apparent low correlation due to internal wave motions in a fluid having purely vertical stratification of all properties. This analysis indicates that some complex interleaving and/or frontal process must be present instead of, or in addition to, internal waves, in at least 50% of the observations.
INTRODUCTION To date, information on the horizontal extent IN RECENTyears, much effort has been devoted to of the features in mean temperatureprofileswhich investigation of the vertical fine structure of have been called by various investigators 'layers', various oceanic properties. Standard salinity- 'sheets', 'laminae', or merely 'irregularities' has temperature-depth recording systems yield resolu- been fragmentary, the difficulty inherent in the tion of a few metres, while more sophisticated vertical character of the measuring instruments. free-fall instruments (GREGG and Cox, 1971) In the South Pacific off Mindanao, STOMMELand resolve temperature and conductivity to a few FEDOROV (1967) carded out a series of STD millimetres. A growing body of measurements stations separated by ~ 1.7 km, and were able to made with such instruments attests to the com- identify laminae of 5- to 10-m thickness from plexity of the vertical distribution of oceanic station to station, over a total horizontal range of properties, a complexity which appears to increase ~ 20km. Variation in depth of individual as the scale decreases. In a few special locations, laminae, by as much as 50 m, was attributed to organized step-like structure of temperature and internal wave motions. Similar work by ELLIOrr, salinity has been observed (Howe and TAIT, HOWE and TAIT (1974) in the layered region of the 1970; NEAL, NESHWA and DE~ER, 1969); more Mediterranean outflow showed continuity of generally, the vertical structure is less organized, individuallayers over ~ 50 km, but discontinuities taking the form of irregularities about a mean in the system as a whole. OSBORNand Cox (1972) gradient. The smallest significant scale of irregu- attempted a qualitative estimate of the coherence larity seems to depend only on the diffusive among records obtained by dropping 3 free-fall coefficients of the property being measured, temperature probes in the California Current, yielding scales of the order of centimetres for with horizontal spacing varying from 50 to 750 m; temperature, millimetres for salinity. Variations they estimated significant coherence of high on the scale of a few centimetres or less are gradient regions over that horizontal range. usually termed 'microstructure'; this paper con- Recently, POCHAPSKY and MALONE (1972) cerns temperature variations on a somewhat larger of Ocean Sciences, Patricia Bay, Environscale, of the order of metres, which we shall call ment*Institute Canada, 512-1230 Government St., Victoria, British fine structure. Columbia, Canada. 767
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reported quantitative results showing no significant coherence between temperature records obtained over a depth range of ~ 1000 m at a slowly rising and sinking free float, even though only a few hours passed between successive sampling at a fixed location. The purpose of this paper is to present some further information about the horizontal correlation of temperature fine structure, using thermistor data obtained from towed body measurements in the northeast Pacific. MEASUREMENTS
The observations described here were taken from February 12 to 15, 1972, on a line in the northwest Pacific from Cobb Seamount ( ~ 46°45 'N, 130°50'W) to the continental shelf off Washington. The towed body system used to obtain the measurements is the present version of a system originally developed by H. L. Grant of the Defence Research Establishment Pacific, and most recently used by NASMYTH(1970). Designed primarily to measure high frequency velocity and temperature, the towed body also carries a variety of supplementary instruments. Figure 1 shows the body in its cradle, preparatory to launching, and indicates the position of the following sensors: three thermistors, mounted 0-6 m apart, the central one located inside the throat of a through-flow conductivity meter (NASM~'TH, 1970), and a platinum film velocity probe (GRANT, STEWART and MOILLIETT, 1962) mounted on a vibration isolation mount slightly forward of the thermistors. A depth gauge is mounted within the body housing, approximately 2 m behind the middle thermistor. The analysis described in this paper used the temperature information from the central thermistor, which has a cut-off frequency around 8 Hz. The thermistor response is the limiting factor for the resolution of salinity and density, as calculated from the measured values of temperature, depth and conductivity. The conductivity head is a refinement of a design by Mr. R. W. Chappell of the Defence Research Establishment, Pacific; the original was used by NASMYTn (1970). The head
is made of pyrex, with a 1-cm diameter intake hole, and two outlet ports symmetrically located about 5 cm to the rear. The thermistor is located where the flow branches to these outlet ports. Flow visualization experiments in a water tunnel show direct flow through the head for representative towing speeds. A uniform field is produced in the throat of this instrument by a constant amplitude 5 kHz driver. Between the field electrodes, a third pair of electrodes sense the changing voltage associated with varying seawater resistivity, with a system of electronics quite similar to that used by GREGG and Cox (1971). The body is towed behind a surface ship on armoured multi-conductor cable, under the control of a specially designed servo-controlled winch capable of maintaining the body depth constant to within ~: 0.3 m in reasonable sea state. The depth range over which the body can be towed is limited by mechanical constraints to approximately 100 to 300 m. The maximum depth is determined by the length of cable which can be put on the winch, while the minimum is set by a length of heavy rubber fairing placed on the cable directly above the towed body to reduce vibration; in normal operation, this fairing must be well below the main towing sheave at all times. For all measurements described in the paper, the winch was operated in cycling mode, first used by NASMYTH (1970). While under servo-control to remove surface wave effects, the winch is programmed to haul in and out at a constant rate while the ship steams slowly ahead, so the body follows a 'sawtooth' path through the water. Signals from all sensors in the body pass up the cable to the ship, where they a re converted to digital signals, multiplexed, and stored on magnetic tape under the control of a small computer system. One tape holds data from approximately 21 min of operation, corresponding to total horizontal distance in the range 1.2 to 2.0 km tbr typical towing speeds of 3.5 to 5.5 km h -1. Two tape units allow continuous recording for any desired length of time. The winch is usually set to cycle ~ 15 m about the mean depth, which is set at successive 30-m intervals between 90 m and 300 m. Figure 2 shows typical recorded
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The cycling mode of operation produces a rather peculiar hybrid between the usual vertical and horizontal sections: however, if the cycle pattern is fairly uniform it is possible to extract information about a strictly horizontal coherence. Figure 3 shows the idealized path of one thermistor, with D ----cycle length in the horizontal and half-cycles numbered consecutively. In order to examine 'fine structure', the temperature signal Twill be considered to be the residual fluctuations about a least squares mean gradient, computed
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for each half-cycle. Each pair of points, at equal depths but on different half-cycles, produces an estimate of the temperature covariance CA~(h) = TATB as a function of horizontal distance in the range of 0 to nC, where n = maximum number of cycles in some unit record. Some form of averaging is necessary, both to increase the statistical significance of the covariance estimate and to provide the variances, Vi and ~ , needed for calculation of the correlation coefficient, R(h) = C'ij ( Vi~) -~. Two averaging methods have been used: the first involves horizontal distances less than a single cycle length D, while the second is a computationally efficient means of covering the range D to nD. For the short-scale, covariances and variances were originally averaged over intervals of Az ---- 1.5 m in the vertical (approximately 4 m in the horizontal): the corresponding horizontal separation h is taken as the separation of the midpoints of the averaging interval on consecutive half-cycles, as shown in Fig. 3. When it was found that these estimates still had a large scatter, the estimates themselves were averaged over 20-m bins in the horizontal. Thus, each short-scale average uses roughly 600 to 900 covariance estimates, where the range depends upon the
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speed of vertical travel during cycling. The second, long-scale method averages the signals over the whole depth range AZ common to a pair of odd or even half-cycles. For example, since points along section 1 of the path shown in Fig. 3 have a constant separation D from points at the same depth along section 3, an estimate of the correlation coefficient at separation D is given by R(D) = r l T .
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The overbar indicates an average along the path, which involves roughly 2000 to 5000 points, again depending upon the vertical speed during any individual tow. Each cycle yields two estimates of R(D), since thermistor records over sections 2 and 4 have the same property of constant separation D of corresponding points. By correlating all possible odd-odd and even-even half-cycle pairs, the correlation distance is increased in steps of D, up to nD where n = maximum number of full cycles in a unit record. The number of estimates possible for R obviously decreases with increasing separation, with only 2 estimates possible at maximum separation. Use of real data invariably introduces a few complications, although the basic technique remains as described above. Since the winch is unable to remove surface wave effects completely, the body path varies slightly about an ideal straight line path, as seen in Fig. 2. Because of this depth variation, the straightforward correlation of time-based temperature signals is not sufficient and the time series of temperature and depth are combined to give a temperature versus depth signal, from which appropriate correlation of temperature at corresponding depths (and hence equal horizontal separation) along the halfcycle paths can be formed. The depth increment of ,,, 1 cm is determined by the maximum frequency response of the thermistor and the maximum vertical velocity experienced by the body under normal towing conditions. Signals from portions of the path close to a trough or a peak are not used, since they may be contaminated by the motion of the body as it swings between an upward and downward orientation along the
path; thus the minimum separation which can be obtained is not 0 but approximately 5 to 10 m. Finally, it was considered unnecessary to correct the temperature signal for the effect of the thermistor time constant because scales which significantly affect the horizontal correlation coefficient are quite large (the order of metres) and well resolved. For the purpose of analysis, one digital tape of data has been chosen as the unit sample, yielding horizontal correlations over a range of 0 to 2 km. The depth signal is scanned to determine the maximum vertical range common to all cycles, and to locate maxima and minima, defining cycles within the sample. An average velocity for each half-cycle is computed from the signal of the platinum velocity probe, after suitable lowpass filtering. This then defines an average towing angle (from the horizontal) having sin 0 = AZ/VAt, where AZ = total vertical excursion, V --~ average velocity along the towing path, and At = time for the half-cycle. This angle may vary considerably between samples, due to variation in ship speed and/or the speed at which the winch hauls in and out, but variation among the halfcycles of a single sample is generally small, of the order of 1 to 2°. The actual angle is used in calculation of h, the horizontal separation corresponding to the short-scale estimates. The slight changes in mean angle also produce variation in the actual separation of values averaged by the second method, but this is unimportant since there is no reason to suspect that the correlation function will have any sharp peaks away from the origin. Finally, the various averaged estimates are calculated for the signal minus a least squares linear gradient (giving the correlation of fluctuations about the mean temperature gradient calculated for each half-cycle). At this point it should be noted that no attempt has been made to calculate the horizontal covariances as a function of vertical wave number: the limited vertical extent of the cycle path makes this approach unprofitable.
Horizontal coherence of oceanic temperature structure RESULTS AND DISCUSSION A total of 29 samples were available for analysis. For most of these samples, it is clear from simple visual inspection of the profiles that the temperature variance about a mean linear gradient is due mainly to features with vertical scales of less than ~ 5 m; all such samples exhibit significant loss of correlation over a horizontal distance of the order of 200 m, as shown for two samples (1373 and 1361) in Fig. 4(a) and (b). In fact, from the results of the shortscale averaging, it appears that the greater part of this loss in correlation occurs over ~ 20 m in the horizontal. The exceptions to this behaviour are the 5 samples for which the major contribution to the variance comes from temperature features with a vertical scale greater than ~ 10 m: such samples have a much slower decrease of correlation with horizontal distance, as shown 10=~
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by Sample 1393 in Fig. 4(c). This indicates the type of results which will be obtained when appropriate data become available for investigating the horizontal correlation as a function of vertical wave number. At the moment, it is interesting to examine the possible processes which may act to produce the low horizontal correlations (as obtained by this technique) of temperature features with vertical scales less than ~ 5 m: present conjecture offers three such processes. The first and most popular is the apparently ubiquitous internal wave. Horizontal internal modes result in vertical shifts and stretch/compression deformations of structure, while a judicious combination of modes propagating off the vertical can produce any other desired anomaly. A second possibility is the existence of meso-scale 'frontal' regions within the pycnocline: that is, regions of rather abrupt
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change separating two masses of water with distinctly different physical properties. The final proposal involves gravitational collapse of large mixed region, which spread into the surrounding fluid along appropriate in situ density levels. Any of these processes could produce low horizontal correlation of the temperature field, the first through space/time changes produced by internal waves, the second by passage through a 'frontal' zone, the third by interleaving of collapsing mixed regions. Measurements of the temperature field alone cannot distinguish among these possibilities, but addition of a conductivity probe, hence salinity and density information, allows at least a preliminary investigation. The technique used is that of following changes in T and S along surfaces of constant at (almost exactly surfaces of constant % for the slight pressure changes involved). This procedure can at least determine whether or not the low horizontal correlation of the
temperature structure has been produced by nondissipative internal waves in a medium with vertical stratification of all properties. If we suppose that, in the mean, the ocean is stably stratified in the vertical and uniform horizontally (allowing for a 'sheets and layers' structure in the vertical, if so desired), then a given density surface, no matter how distorted by internal waves, must correspond to fixed T and S, that is, to a single point in the T-S plane. Changes in T and S along isopycnals will be produced by either of the other two processes, or by internal waves in frontal regions, that is, in regions with horizontal gradients of temperature and salinity. Thus, the method of analysis is to select a set of ~, levels within the range of at common to all halfcycles of one sample; each level is located within each half-cycle, and the values of T and S plotted as a point along the curve of constant at in the T/S plane. There is no ambiguity in location of ~, surfaces because all of the measurements show 7,20"
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gravitationally stable density profiles for vertical scales greater than about 1 m. Very infrequently, a profile will contain a region where the density gradient appears to be very slightly unstable, but such regions are less than a metre in the vertical and are not observed on successive profiles, which sets an upper bound of roughly 100 m in horizontal extent. Because of the limited vertical and horizontal extent of such regions, it is easy to avoid them when choosing a set of at levels. The resulting plots are then examined rather carefully, in order to reject the occasional point which is influenced by such things as the usual spikes in the salinity record in regions of high vertical temperature gradient, or the small uncertainty in location of a a t surface in regions of high a t gradient. Although the results of such an analysis are not all clear-cut, the extremes are fairly readily identified, as shown in Fig. 5. Figure 5(a) is a composite of two successive samples, 1373 and 1374: since the set of a t levels common to all half-cycles of a given sample is not the same for all samples, the levels from 1373 and 1374 are marked by different symbols. The 'noise' level about a constant T (hence S) along a surface of constant at is less than about 0-05°C: these samples are taken as typical of those in which internal waves may alone produce the observed loss of correlation with horizontal distance [shown for 1373 in Fig. 4(a)]. The other extreme is shown in Fig. 5(b), where three consecutive samples, 1361-1362-1363, are plotted: surfaces of at generally descend during this run, so that the group of at levels included within the 30-m vertical sampling range shifts to lower values with each sample. The progression towards higher values of T and S is very marked, the changes along most at surfaces being 2 to 5 times the 'noise' of ~ 0.05°C which is taken as typical of the technique in situations of no motion or those in which only internal waves are present. Although the rest of the samples are often much more complicated than the two described above, it is possible to sort them into rough categories by the degree of scatter of T along surfaces of constant ~rt. Of the 29 samples, only 9
show a scatter less than ~ 0.05°C, while 14 show changes of more than 0-10°C along some (though not necessarily all) at surfaces. Of those samples showing significant changes of T and S along at surfaces, the example shown in Fig. 5(b) is much more clear-cut than most. More typically, temperatures may change in opposite directions on different % surfaces and/or variation of T along a given isopycnal may not be uni-directional throughout a sample. It is tempting to identify the situation shown in Fig. 5 as a frontal region, and the other more complicated examples as regions of interleaving: however, the reality seems more like a mixture of both. Even the samples shown in Fig. 5(b) are, on closer examination, extremely complex, as evidenced by the distinct non-uniformity of property gradients along any isopycnal. The complexity of the region can perhaps be better appreciated by looking at the original quasi-vertical temperature profiles. A portion of the records from 1362 and 1363 is shown in Fig. 6(a): Fig. 6(b) shows the isotherm field, contoured at 0.04°C intervals and plotted with correct horizontal scale. The contours are meaningful only if we accept the evidence of Fig. 5(b) that the changes in profiles are n o t due to internal waves: even having accepted this, there remain the usual ambiguities in the contouring process, particularly for a limited range in depth. Nevertheless, some features must be considered real. First is the distinct difference in character between the beginning and end portions of the record. The former is characterized by temperature extrema which change with distance in such a way as constantly to require contours which turn back on themselves; the latter has almost horizontal, parallel isotherms. The second feature is the extremely well-defined 'tongue' of warmer water, marked A in Fig. 6(b). This tongue is approximately parallel to the isopycnal surfaces and involves axial gradients of 0.4°C km -1. With present information, it is not possible to determine whether the tongue is relict or maintained, although the large vertical temperature gradients associated with its edges, and the associated high level of temperature microstructure (as measured by a hot film thermometer with high frequency
Horizontal coherence of oceanic temperature structure response) strongly suggest the latter. This region, though certainly the strongest and best defined that has been measured, is not unique. All of the samples which show significant changes of T and S along ~t surfaces require such regions of folded contours. The measurements described above have shown the existence of many areas within the main oceanic thermocline where irregularities about a smooth temperature profile change extremely rapidly with horizontal distance in a manner which cannot be produced by internal waves in a horizontally uniform, vertically stratified fluid. In such areas, contouring of the temperature field shows the existence of disparate water types along the same isopycnal, and suggests the existence of quasi-horizontal spreading (quasihorizontal since the density surfaces along which spreading occurs may well be distorted by internal waves). Fairly convincing evidence of horizontal spreading has been produced by PINGREE (1972) from STD records in the region of the Mediterranean outflow; however, the existence of regions of small-scale (of the order of 200 m to 1 km) horizontal inhomogeneities within the main thermocline of a 'quiet' oceanic area fairly remote from boundaries of any large-scale water mass is more of a surprise and gives rise to some speculation as to the origin of such inhomogeneity. A fairly complicated picture can be created if, like WOODS (1972), we postulate the existence of an oceanic 'front' (akin to the atmospheric), fuither allow it to be distorted along its horizontal extent, then traverse the result at some arbitrary angle. Indeed, samples like those shown in Fig. 5 do suggest the passage through some complex frontal zone and into a fairly uniform mass of water. Such measurements may be equally well staged by postulating random occurrences of such large-scale internal wave instabilities as those proposed by GARRETTand MUNK (1972) or ORLANSKI and BRYAN (1969), creating well-mixed regions which subsequently collapse and spread horizontally along the appropriate isopycnal. Finally, even the internal wave re-enters the picture, if the assumption of horizontal homogeneity of all fluid properties is relaxed to that of
775
horizontal homogeneity of density, allowing density-compensating horizontal gradients of temperature and salinity. An inertial wave in such a fluid could produce the type of features observed in the temperature profiles. It should be remarked, however, that on the basis of the mean large-scale horizontal temperature gradients observed in the North Pacific region of the measurements, the particle excursions necessary to produce the observed temperature fluctuations would be of the order o f hundreds of kilometres. This figure, coupled with the observed vertical scale of less than 5 to 10 m, seems a bit unreasonable, and suggests that the wave mechanism is a possible explanation of the observations only if operating in a region of locally intensified horizontal property gradients, that is, in the neighbourhood of some frontal structure. The present measurements, severely restricted in vertical range and limited to one horizontal dimension, are, unfortunately, incapable o f differentiating among the above mechanisms. Further investigations seem advisable, in view of the apparently widespread occurrence of regions of small-scale horizontal inhomogeneity, and the possibly large influence of such regions on vertical mixing in the upper ocean.
Acknowledgements--The towed body measurements would not have been possible without the considerable support provided by the Defence Research Establishment, Pacific, for which I would like to express my gratitude. Thanks are also due to Dr. P. NASMYTH,G. CHASE,R. TEICHROB,L. BEAUCHEMINand to the officers and crew of the CFAV Endeavour, for their help in gathering and reducing the data. I should also like to thank Dr. R. W. STEWARTand Dr. J. F. GARRETTfor helpful discussions during the data analysis. REFERENCES ELLIOTT A. J., M. R. HOWE and R. I. TAIT (1974) The lateral coherence of a system of thermohaline layers in the deep ocean. Deep-Sea Research, 21, 95-107. GARRETT C. J. R. and W. MONK (1972) Oceanic mixing by breaking internal waves. Deep-Sea Research, 19, 823-832. GRANTH. L., R. W. STEWARTand A. MOILLmT(1962) Turbulence spectra from a tidal channel. Journal of Fluid Mechanics, 12, 241-268. GnJEC,o M. C. and C. S. Cox (1971) Measurements of
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the oceanic microstructure of temperature and electrical conductivity. Deep-Sea Research, 18, 925-934. HOWE M. R. and R. I. TArt (1970) Further observations of thermo-haline stratification in the deep ocean. Deep-Sea Research, 17, 963-972. NASMYTn P. W. (1970) Ocean turbulence. Ph.D. thesis, University of British Columbia. NEAL V. T., S. NESHYBA and W. DENNER (1969) Thermal stratification in the Arctic Ocean. Science, 166, 373-374. ORLANSKII. and K. BRYAN (1969) Formation of the thermocline step structure by large-amplitude internal gravity waves. Journal of Geophysical
Research, 74, 6975-6983. OSBORN T. R. and S. Cox (1972) Oceanic fine structure. Geophysical Fluid Dynamics, 3, 321-345. PrNGREE R. D. (1972) Mixing in the deep stratified ocean. Deep-Sea Research, 19, 549-561. POCHAPSKYT. E. and F. D. MALONE(1972). Spectra of deep vertical temperature profiles. Journal of Physical Oceanography, 2, 470--475. STOMM~L H. and K. N. FEOOROV (1967) Small-scale structure in temperature and salinity near Timor and Mindanao. Tellus, 19, 306--325. WooDs J. D. (1972) The structure of fronts in the seasonal thermocline. Proceedings of Conference 'Strait of Sicily', Saclancent, La Spezia, Italy.
Horizontal coherence of oceanic temperature structure A. E. GARGETT* (Received 16 July 1974; in revised form 27 March 1975; accepted I April 1975) A b s t r a e t h T h e horizontal correlation of temperature structures with vertical scales of meters is examined, using data from the cycling mode of a towed body system operating within the thermod i n e in the North Pacific. Results show significant loss of correlation for temperature features with vertical scales of less than 5 m, over horizontal distances of the order of 100 to 200 m, and often as little as 20 m. Examination of temperature and salinity along isopycnal surfaces serves to differentiate between true low horizontal correlation and apparent low correlation due to internal wave motions in a fluid having purely vertical stratification of all properties. This analysis indicates that some complex interleaving and/or frontal process must be present instead of, or in addition to, internal waves, in at least 50% of the observations.
INTRODUCTION To date, information on the horizontal extent IN RECENTyears, much effort has been devoted to of the features in mean temperatureprofileswhich investigation of the vertical fine structure of have been called by various investigators 'layers', various oceanic properties. Standard salinity- 'sheets', 'laminae', or merely 'irregularities' has temperature-depth recording systems yield resolu- been fragmentary, the difficulty inherent in the tion of a few metres, while more sophisticated vertical character of the measuring instruments. free-fall instruments (GREGG and Cox, 1971) In the South Pacific off Mindanao, STOMMELand resolve temperature and conductivity to a few FEDOROV (1967) carded out a series of STD millimetres. A growing body of measurements stations separated by ~ 1.7 km, and were able to made with such instruments attests to the com- identify laminae of 5- to 10-m thickness from plexity of the vertical distribution of oceanic station to station, over a total horizontal range of properties, a complexity which appears to increase ~ 20km. Variation in depth of individual as the scale decreases. In a few special locations, laminae, by as much as 50 m, was attributed to organized step-like structure of temperature and internal wave motions. Similar work by ELLIOrr, salinity has been observed (Howe and TAIT, HOWE and TAIT (1974) in the layered region of the 1970; NEAL, NESHWA and DE~ER, 1969); more Mediterranean outflow showed continuity of generally, the vertical structure is less organized, individuallayers over ~ 50 km, but discontinuities taking the form of irregularities about a mean in the system as a whole. OSBORNand Cox (1972) gradient. The smallest significant scale of irregu- attempted a qualitative estimate of the coherence larity seems to depend only on the diffusive among records obtained by dropping 3 free-fall coefficients of the property being measured, temperature probes in the California Current, yielding scales of the order of centimetres for with horizontal spacing varying from 50 to 750 m; temperature, millimetres for salinity. Variations they estimated significant coherence of high on the scale of a few centimetres or less are gradient regions over that horizontal range. usually termed 'microstructure'; this paper con- Recently, POCHAPSKY and MALONE (1972) cerns temperature variations on a somewhat larger of Ocean Sciences, Patricia Bay, Environscale, of the order of metres, which we shall call ment*Institute Canada, 512-1230 Government St., Victoria, British fine structure. Columbia, Canada. 767
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reported quantitative results showing no significant coherence between temperature records obtained over a depth range of ~ 1000 m at a slowly rising and sinking free float, even though only a few hours passed between successive sampling at a fixed location. The purpose of this paper is to present some further information about the horizontal correlation of temperature fine structure, using thermistor data obtained from towed body measurements in the northeast Pacific. MEASUREMENTS
The observations described here were taken from February 12 to 15, 1972, on a line in the northwest Pacific from Cobb Seamount ( ~ 46°45 'N, 130°50'W) to the continental shelf off Washington. The towed body system used to obtain the measurements is the present version of a system originally developed by H. L. Grant of the Defence Research Establishment Pacific, and most recently used by NASMYTH(1970). Designed primarily to measure high frequency velocity and temperature, the towed body also carries a variety of supplementary instruments. Figure 1 shows the body in its cradle, preparatory to launching, and indicates the position of the following sensors: three thermistors, mounted 0-6 m apart, the central one located inside the throat of a through-flow conductivity meter (NASM~'TH, 1970), and a platinum film velocity probe (GRANT, STEWART and MOILLIETT, 1962) mounted on a vibration isolation mount slightly forward of the thermistors. A depth gauge is mounted within the body housing, approximately 2 m behind the middle thermistor. The analysis described in this paper used the temperature information from the central thermistor, which has a cut-off frequency around 8 Hz. The thermistor response is the limiting factor for the resolution of salinity and density, as calculated from the measured values of temperature, depth and conductivity. The conductivity head is a refinement of a design by Mr. R. W. Chappell of the Defence Research Establishment, Pacific; the original was used by NASMYTn (1970). The head
is made of pyrex, with a 1-cm diameter intake hole, and two outlet ports symmetrically located about 5 cm to the rear. The thermistor is located where the flow branches to these outlet ports. Flow visualization experiments in a water tunnel show direct flow through the head for representative towing speeds. A uniform field is produced in the throat of this instrument by a constant amplitude 5 kHz driver. Between the field electrodes, a third pair of electrodes sense the changing voltage associated with varying seawater resistivity, with a system of electronics quite similar to that used by GREGG and Cox (1971). The body is towed behind a surface ship on armoured multi-conductor cable, under the control of a specially designed servo-controlled winch capable of maintaining the body depth constant to within ~: 0.3 m in reasonable sea state. The depth range over which the body can be towed is limited by mechanical constraints to approximately 100 to 300 m. The maximum depth is determined by the length of cable which can be put on the winch, while the minimum is set by a length of heavy rubber fairing placed on the cable directly above the towed body to reduce vibration; in normal operation, this fairing must be well below the main towing sheave at all times. For all measurements described in the paper, the winch was operated in cycling mode, first used by NASMYTH (1970). While under servo-control to remove surface wave effects, the winch is programmed to haul in and out at a constant rate while the ship steams slowly ahead, so the body follows a 'sawtooth' path through the water. Signals from all sensors in the body pass up the cable to the ship, where they a re converted to digital signals, multiplexed, and stored on magnetic tape under the control of a small computer system. One tape holds data from approximately 21 min of operation, corresponding to total horizontal distance in the range 1.2 to 2.0 km tbr typical towing speeds of 3.5 to 5.5 km h -1. Two tape units allow continuous recording for any desired length of time. The winch is usually set to cycle ~ 15 m about the mean depth, which is set at successive 30-m intervals between 90 m and 300 m. Figure 2 shows typical recorded
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The cycling mode of operation produces a rather peculiar hybrid between the usual vertical and horizontal sections: however, if the cycle pattern is fairly uniform it is possible to extract information about a strictly horizontal coherence. Figure 3 shows the idealized path of one thermistor, with D ----cycle length in the horizontal and half-cycles numbered consecutively. In order to examine 'fine structure', the temperature signal Twill be considered to be the residual fluctuations about a least squares mean gradient, computed
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for each half-cycle. Each pair of points, at equal depths but on different half-cycles, produces an estimate of the temperature covariance CA~(h) = TATB as a function of horizontal distance in the range of 0 to nC, where n = maximum number of cycles in some unit record. Some form of averaging is necessary, both to increase the statistical significance of the covariance estimate and to provide the variances, Vi and ~ , needed for calculation of the correlation coefficient, R(h) = C'ij ( Vi~) -~. Two averaging methods have been used: the first involves horizontal distances less than a single cycle length D, while the second is a computationally efficient means of covering the range D to nD. For the short-scale, covariances and variances were originally averaged over intervals of Az ---- 1.5 m in the vertical (approximately 4 m in the horizontal): the corresponding horizontal separation h is taken as the separation of the midpoints of the averaging interval on consecutive half-cycles, as shown in Fig. 3. When it was found that these estimates still had a large scatter, the estimates themselves were averaged over 20-m bins in the horizontal. Thus, each short-scale average uses roughly 600 to 900 covariance estimates, where the range depends upon the
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speed of vertical travel during cycling. The second, long-scale method averages the signals over the whole depth range AZ common to a pair of odd or even half-cycles. For example, since points along section 1 of the path shown in Fig. 3 have a constant separation D from points at the same depth along section 3, an estimate of the correlation coefficient at separation D is given by R(D) = r l T .
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The overbar indicates an average along the path, which involves roughly 2000 to 5000 points, again depending upon the vertical speed during any individual tow. Each cycle yields two estimates of R(D), since thermistor records over sections 2 and 4 have the same property of constant separation D of corresponding points. By correlating all possible odd-odd and even-even half-cycle pairs, the correlation distance is increased in steps of D, up to nD where n = maximum number of full cycles in a unit record. The number of estimates possible for R obviously decreases with increasing separation, with only 2 estimates possible at maximum separation. Use of real data invariably introduces a few complications, although the basic technique remains as described above. Since the winch is unable to remove surface wave effects completely, the body path varies slightly about an ideal straight line path, as seen in Fig. 2. Because of this depth variation, the straightforward correlation of time-based temperature signals is not sufficient and the time series of temperature and depth are combined to give a temperature versus depth signal, from which appropriate correlation of temperature at corresponding depths (and hence equal horizontal separation) along the halfcycle paths can be formed. The depth increment of ,,, 1 cm is determined by the maximum frequency response of the thermistor and the maximum vertical velocity experienced by the body under normal towing conditions. Signals from portions of the path close to a trough or a peak are not used, since they may be contaminated by the motion of the body as it swings between an upward and downward orientation along the
path; thus the minimum separation which can be obtained is not 0 but approximately 5 to 10 m. Finally, it was considered unnecessary to correct the temperature signal for the effect of the thermistor time constant because scales which significantly affect the horizontal correlation coefficient are quite large (the order of metres) and well resolved. For the purpose of analysis, one digital tape of data has been chosen as the unit sample, yielding horizontal correlations over a range of 0 to 2 km. The depth signal is scanned to determine the maximum vertical range common to all cycles, and to locate maxima and minima, defining cycles within the sample. An average velocity for each half-cycle is computed from the signal of the platinum velocity probe, after suitable lowpass filtering. This then defines an average towing angle (from the horizontal) having sin 0 = AZ/VAt, where AZ = total vertical excursion, V --~ average velocity along the towing path, and At = time for the half-cycle. This angle may vary considerably between samples, due to variation in ship speed and/or the speed at which the winch hauls in and out, but variation among the halfcycles of a single sample is generally small, of the order of 1 to 2°. The actual angle is used in calculation of h, the horizontal separation corresponding to the short-scale estimates. The slight changes in mean angle also produce variation in the actual separation of values averaged by the second method, but this is unimportant since there is no reason to suspect that the correlation function will have any sharp peaks away from the origin. Finally, the various averaged estimates are calculated for the signal minus a least squares linear gradient (giving the correlation of fluctuations about the mean temperature gradient calculated for each half-cycle). At this point it should be noted that no attempt has been made to calculate the horizontal covariances as a function of vertical wave number: the limited vertical extent of the cycle path makes this approach unprofitable.
Horizontal coherence of oceanic temperature structure RESULTS AND DISCUSSION A total of 29 samples were available for analysis. For most of these samples, it is clear from simple visual inspection of the profiles that the temperature variance about a mean linear gradient is due mainly to features with vertical scales of less than ~ 5 m; all such samples exhibit significant loss of correlation over a horizontal distance of the order of 200 m, as shown for two samples (1373 and 1361) in Fig. 4(a) and (b). In fact, from the results of the shortscale averaging, it appears that the greater part of this loss in correlation occurs over ~ 20 m in the horizontal. The exceptions to this behaviour are the 5 samples for which the major contribution to the variance comes from temperature features with a vertical scale greater than ~ 10 m: such samples have a much slower decrease of correlation with horizontal distance, as shown 10=~
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change separating two masses of water with distinctly different physical properties. The final proposal involves gravitational collapse of large mixed region, which spread into the surrounding fluid along appropriate in situ density levels. Any of these processes could produce low horizontal correlation of the temperature field, the first through space/time changes produced by internal waves, the second by passage through a 'frontal' zone, the third by interleaving of collapsing mixed regions. Measurements of the temperature field alone cannot distinguish among these possibilities, but addition of a conductivity probe, hence salinity and density information, allows at least a preliminary investigation. The technique used is that of following changes in T and S along surfaces of constant at (almost exactly surfaces of constant % for the slight pressure changes involved). This procedure can at least determine whether or not the low horizontal correlation of the
temperature structure has been produced by nondissipative internal waves in a medium with vertical stratification of all properties. If we suppose that, in the mean, the ocean is stably stratified in the vertical and uniform horizontally (allowing for a 'sheets and layers' structure in the vertical, if so desired), then a given density surface, no matter how distorted by internal waves, must correspond to fixed T and S, that is, to a single point in the T-S plane. Changes in T and S along isopycnals will be produced by either of the other two processes, or by internal waves in frontal regions, that is, in regions with horizontal gradients of temperature and salinity. Thus, the method of analysis is to select a set of ~, levels within the range of at common to all halfcycles of one sample; each level is located within each half-cycle, and the values of T and S plotted as a point along the curve of constant at in the T/S plane. There is no ambiguity in location of ~, surfaces because all of the measurements show 7,20"
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gravitationally stable density profiles for vertical scales greater than about 1 m. Very infrequently, a profile will contain a region where the density gradient appears to be very slightly unstable, but such regions are less than a metre in the vertical and are not observed on successive profiles, which sets an upper bound of roughly 100 m in horizontal extent. Because of the limited vertical and horizontal extent of such regions, it is easy to avoid them when choosing a set of at levels. The resulting plots are then examined rather carefully, in order to reject the occasional point which is influenced by such things as the usual spikes in the salinity record in regions of high vertical temperature gradient, or the small uncertainty in location of a a t surface in regions of high a t gradient. Although the results of such an analysis are not all clear-cut, the extremes are fairly readily identified, as shown in Fig. 5. Figure 5(a) is a composite of two successive samples, 1373 and 1374: since the set of a t levels common to all half-cycles of a given sample is not the same for all samples, the levels from 1373 and 1374 are marked by different symbols. The 'noise' level about a constant T (hence S) along a surface of constant at is less than about 0-05°C: these samples are taken as typical of those in which internal waves may alone produce the observed loss of correlation with horizontal distance [shown for 1373 in Fig. 4(a)]. The other extreme is shown in Fig. 5(b), where three consecutive samples, 1361-1362-1363, are plotted: surfaces of at generally descend during this run, so that the group of at levels included within the 30-m vertical sampling range shifts to lower values with each sample. The progression towards higher values of T and S is very marked, the changes along most at surfaces being 2 to 5 times the 'noise' of ~ 0.05°C which is taken as typical of the technique in situations of no motion or those in which only internal waves are present. Although the rest of the samples are often much more complicated than the two described above, it is possible to sort them into rough categories by the degree of scatter of T along surfaces of constant ~rt. Of the 29 samples, only 9
show a scatter less than ~ 0.05°C, while 14 show changes of more than 0-10°C along some (though not necessarily all) at surfaces. Of those samples showing significant changes of T and S along at surfaces, the example shown in Fig. 5(b) is much more clear-cut than most. More typically, temperatures may change in opposite directions on different % surfaces and/or variation of T along a given isopycnal may not be uni-directional throughout a sample. It is tempting to identify the situation shown in Fig. 5 as a frontal region, and the other more complicated examples as regions of interleaving: however, the reality seems more like a mixture of both. Even the samples shown in Fig. 5(b) are, on closer examination, extremely complex, as evidenced by the distinct non-uniformity of property gradients along any isopycnal. The complexity of the region can perhaps be better appreciated by looking at the original quasi-vertical temperature profiles. A portion of the records from 1362 and 1363 is shown in Fig. 6(a): Fig. 6(b) shows the isotherm field, contoured at 0.04°C intervals and plotted with correct horizontal scale. The contours are meaningful only if we accept the evidence of Fig. 5(b) that the changes in profiles are n o t due to internal waves: even having accepted this, there remain the usual ambiguities in the contouring process, particularly for a limited range in depth. Nevertheless, some features must be considered real. First is the distinct difference in character between the beginning and end portions of the record. The former is characterized by temperature extrema which change with distance in such a way as constantly to require contours which turn back on themselves; the latter has almost horizontal, parallel isotherms. The second feature is the extremely well-defined 'tongue' of warmer water, marked A in Fig. 6(b). This tongue is approximately parallel to the isopycnal surfaces and involves axial gradients of 0.4°C km -1. With present information, it is not possible to determine whether the tongue is relict or maintained, although the large vertical temperature gradients associated with its edges, and the associated high level of temperature microstructure (as measured by a hot film thermometer with high frequency
Horizontal coherence of oceanic temperature structure response) strongly suggest the latter. This region, though certainly the strongest and best defined that has been measured, is not unique. All of the samples which show significant changes of T and S along ~t surfaces require such regions of folded contours. The measurements described above have shown the existence of many areas within the main oceanic thermocline where irregularities about a smooth temperature profile change extremely rapidly with horizontal distance in a manner which cannot be produced by internal waves in a horizontally uniform, vertically stratified fluid. In such areas, contouring of the temperature field shows the existence of disparate water types along the same isopycnal, and suggests the existence of quasi-horizontal spreading (quasihorizontal since the density surfaces along which spreading occurs may well be distorted by internal waves). Fairly convincing evidence of horizontal spreading has been produced by PINGREE (1972) from STD records in the region of the Mediterranean outflow; however, the existence of regions of small-scale (of the order of 200 m to 1 km) horizontal inhomogeneities within the main thermocline of a 'quiet' oceanic area fairly remote from boundaries of any large-scale water mass is more of a surprise and gives rise to some speculation as to the origin of such inhomogeneity. A fairly complicated picture can be created if, like WOODS (1972), we postulate the existence of an oceanic 'front' (akin to the atmospheric), fuither allow it to be distorted along its horizontal extent, then traverse the result at some arbitrary angle. Indeed, samples like those shown in Fig. 5 do suggest the passage through some complex frontal zone and into a fairly uniform mass of water. Such measurements may be equally well staged by postulating random occurrences of such large-scale internal wave instabilities as those proposed by GARRETTand MUNK (1972) or ORLANSKI and BRYAN (1969), creating well-mixed regions which subsequently collapse and spread horizontally along the appropriate isopycnal. Finally, even the internal wave re-enters the picture, if the assumption of horizontal homogeneity of all fluid properties is relaxed to that of
775
horizontal homogeneity of density, allowing density-compensating horizontal gradients of temperature and salinity. An inertial wave in such a fluid could produce the type of features observed in the temperature profiles. It should be remarked, however, that on the basis of the mean large-scale horizontal temperature gradients observed in the North Pacific region of the measurements, the particle excursions necessary to produce the observed temperature fluctuations would be of the order o f hundreds of kilometres. This figure, coupled with the observed vertical scale of less than 5 to 10 m, seems a bit unreasonable, and suggests that the wave mechanism is a possible explanation of the observations only if operating in a region of locally intensified horizontal property gradients, that is, in the neighbourhood of some frontal structure. The present measurements, severely restricted in vertical range and limited to one horizontal dimension, are, unfortunately, incapable o f differentiating among the above mechanisms. Further investigations seem advisable, in view of the apparently widespread occurrence of regions of small-scale horizontal inhomogeneity, and the possibly large influence of such regions on vertical mixing in the upper ocean.
Acknowledgements--The towed body measurements would not have been possible without the considerable support provided by the Defence Research Establishment, Pacific, for which I would like to express my gratitude. Thanks are also due to Dr. P. NASMYTH,G. CHASE,R. TEICHROB,L. BEAUCHEMINand to the officers and crew of the CFAV Endeavour, for their help in gathering and reducing the data. I should also like to thank Dr. R. W. STEWARTand Dr. J. F. GARRETTfor helpful discussions during the data analysis. REFERENCES ELLIOTT A. J., M. R. HOWE and R. I. TAIT (1974) The lateral coherence of a system of thermohaline layers in the deep ocean. Deep-Sea Research, 21, 95-107. GARRETT C. J. R. and W. MONK (1972) Oceanic mixing by breaking internal waves. Deep-Sea Research, 19, 823-832. GRANTH. L., R. W. STEWARTand A. MOILLmT(1962) Turbulence spectra from a tidal channel. Journal of Fluid Mechanics, 12, 241-268. GnJEC,o M. C. and C. S. Cox (1971) Measurements of
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the oceanic microstructure of temperature and electrical conductivity. Deep-Sea Research, 18, 925-934. HOWE M. R. and R. I. TArt (1970) Further observations of thermo-haline stratification in the deep ocean. Deep-Sea Research, 17, 963-972. NASMYTn P. W. (1970) Ocean turbulence. Ph.D. thesis, University of British Columbia. NEAL V. T., S. NESHYBA and W. DENNER (1969) Thermal stratification in the Arctic Ocean. Science, 166, 373-374. ORLANSKII. and K. BRYAN (1969) Formation of the thermocline step structure by large-amplitude internal gravity waves. Journal of Geophysical
Research, 74, 6975-6983. OSBORN T. R. and S. Cox (1972) Oceanic fine structure. Geophysical Fluid Dynamics, 3, 321-345. PrNGREE R. D. (1972) Mixing in the deep stratified ocean. Deep-Sea Research, 19, 549-561. POCHAPSKYT. E. and F. D. MALONE(1972). Spectra of deep vertical temperature profiles. Journal of Physical Oceanography, 2, 470--475. STOMM~L H. and K. N. FEOOROV (1967) Small-scale structure in temperature and salinity near Timor and Mindanao. Tellus, 19, 306--325. WooDs J. D. (1972) The structure of fronts in the seasonal thermocline. Proceedings of Conference 'Strait of Sicily', Saclancent, La Spezia, Italy.