INVESTIGATION OF TTE1 INFLUENCES ON THE MIJCEDHUXSR DEPTH DURING THE COOLING SEASON # a # k # * Donald H. Edgren and John J. MacPherson -> . • . . . 1 . - INVESTIGATION OF TIE INFLUENCES ON THE MIXED-LAIER DEPTH DURING TIE COOLING SEASON by Donald H, Edgren Lieutenant, United States Navy and John J. MacPherson Lieutenant Commander, United States Navy Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN METEOROLOGY United States Naval Postgraduate School Monterey, California 1962 \° \ U.S. NAVAL P( INVESTIGATION OF THE INFLUENCES ON TIE MIXED-LAYER DEPTH DURING THE COOLING SEASON by Donald H. Edgren and John J. MacPhorson This work is accepted as fulfilling the thesis requirements for the degree of MASTER OF SCIENCE III METEOROLOGY from the United States Naval Postgraduate School . jtragt An analysis of batiivthermograph data re ord d it C »t bion Papa (latiti 5021, longitude 145W) hir: - " • cooling ~son (l r through December) indicates that the annual deepening and subsequent decay of thr>. seasonal thermocline is accompanied by many random fluctuations. Th« physical processes causing the decay and the fluctuations in the mixed-r layer depth are examined and qualitatively evaluated. The Tukey spectrum analysis programmed for the GDC 1604. electronic digital computer was used in analysis of oscillations at the bottom of the mixed layer to determine the distribution of wave energy for series of data taken at hourly intervals. An energy peak centered near 12 hours was observed to predominate, and this energy is equivalent to that of a 12-hour internal wave with height of 27.0 feet. The computer v:as also used to select the significant meteorological and oceanographic parameters which could be used to predict a change in the mixed -layer depth by use of the BIMD 07 multiple regression program. The most significant parameter was sea surface temperature. The best correlation coefficient for this parameter occurred for lags of r.oro to 12 hours. ^he results of the analysis support the theory that convection is the physical process vhich causes the seasonal decay of the thermo- cline during the cooling season and that short-term fluctuations of the mixed-layer depth are due primarily to internal waves. The authors wish to express their appreciation for the assistance and encouragement given them by Associate Professors G. II. Jung and J. D. Wickham, and by Professor D. A. Williams and the staff of the com- puter center at the U. S. Naval Postgraduate School in this investigation. The authors also wish to thank the Pacific Oceanographic Group of Canada for making the oceanographic data available, ii TABLE OF CONTENTS Section Title Page 1 . Introduction 1 2 . Background 3 3. Description of Ocean Station Papa 4- U* Review of Temperature and Salinity Structure during the Cooling Season 5. a. Object 6 b. Method of Investigation 6 6. Analysis of Internal Waves 11 7. Conclusions and Roc ornnendat ions 16 8. Bibliography 36 Appendix Heat Transport in the Sea and Exchange across the Air-Sea Interface 38 in LIST OF ILLUSTRATIONS Figure Page 1 . Location of Ocean Station Papa 18 2. Position- Indicating Grid for Ocean Weather Station Papa, with a Hercator Projection of a Latitude and Longitude Grid Superimposed 19 3. Decay of the Themocline (1956) 20 4-. Salinity Structure in Eastern Subarctic Pacific Ocean 20 5. a. Cross-Spectrum - 1XD and Sea-Surface Tem- perature Time Series (November, 1958) 21 b. Cross-Spectrum - MLD and Sen-Surface Tem- perature Time Series (October, 1956) 22 6. Mean MLD and Sea-Surface Temperature (October through Do comber, 1957 and 1958) 23 7. Average Daily MLD (October through December, 1956) 24- 8. Hourly Tine Series of MLT) (November, 1958) 25 9. Hourly Time Series of MLD (December, 1956) 25 10. Hourly Tine Series of Thermocline Thickness (November, 1958) 26 11. Correlogram for One- Hourly Time Series (October, 1957 and November. 1958) 27 12. Energy-Density Spectrum (November, 1958) 28 13. Energy-Density Spectrum (October, 1957) 29 IV LIST OF TABLES Table Pago I Bathythermograph Soundings Available 30 II Simple Linear Correlation Coefficients between the 13 Primary Parameters and the 1XD 31 III Sinple Linear Conola^ion Coefficients for Sea-Surface Temperatures and the MLD 32 IV Regression Results for One Independent Variable 33 V Multiple-Regression Results for 18 Inde- pendent Variables 34- VI Three- Year Averages of Regression Results 35 TABLE OF SYMBOLS ilffi .4B3H:iT/IATI0NS [h{h)j ' energy density (spectrum analysis) BT bathythermograph Jc(h)j ' energy density (cross- spectrum analysis) f frequency F low cloud cover (eights) FF wind speed FFe wind speed with 5-hour lag GPMc 500-mb height in geopotential meters Hw, significant- wave height h 2mf4t (II = 0, 1, 2 m) (^l/3)«J5 significant-wave height with 5- hour lag k number of lags (k = 0, 1, 2.....m) m maximum lags and number of spectral values MLD mixed-layer depth MLD mean mixed-layer depth N number of observations P pressure change P e pressure change with 5-hour lag R1 multiple-correlation coefficient RH relative humidity RH_xi relative humidity with 11-hour lag Rile 500-mb relative humidity RR range of residuals S standard deviation SE standard error of the estimate T period (hours) vi Ta air temperature Ta_2 air temperature vith 2-hour lag a u air-sea temperature difference (Ta-rv)_2 air-sea temperature difference with 2-hour lag T^p dev-point temperature Ty sea- surface tomperature Tw_2 sea-siunface temperature vith 2-hour lag Twk wet-bulb temperature T5 50C~mb temperature ^t sampling interval via. 1 . Introduction The vortical temperature structure of the near-surface layor in the open ocean is a complicated phenomenon which varies in space and time. Certain aspects of the temperature structure are of great significance in determining sonar effectiveness. Thus, both the military and the com- mercial fishing industries are interested in prediction of the thermal structure. Various processes continually modify the thermal structure to produce an essentially homogeneous (mixed) surface layer, underlain by a thin layer of rapidly increasing density, which varies in thickness through- out the year. The aixed»layer depth (referred to as the 1ILD) is the depth below the water surface to which mixing has established isothermal condi- tions. The lower boundary of the MLD is the top of tho thermocline, a thin layor of large, negative vortical temperature gradient, usually associa- ted with the layer of increasing density. A complex interaction of meteoro- logical, oceanographic, and (indirectly) astronomical factors provide the driving forces for changes in the ocean thermal structure. Random and periodic fluctuations of the MLD have been examined by many investigators. It is known, as a result, that the MLD may vary from a fev; inches in the heating season to several hundred feet in the cooling season. At times it may fluctuate tens of feet in a matter of minutes. The objective of this research is to identify more clearly significant processes which affect the MLD during the cooling season and to relate tho MLD to meteorological and oceanographic parameters. The processes capable of affecting the vertical temperature distribution are discussed. in the appendix. Certain of those processes will be considered in this paper: (l) thermohaline convection, (2) dynamic convection due to wind and wave action, and (3) unidentified processes which generate internal waves. Up to now, only rjualit tivo descriptions of the mixed-layer behavior during the cooling season arc found in the literature. Those usually state that increased wind stirring and surface cooling act together during the cooling season to drive the seasonal thermocline down to its maximum annual depth. Our findings will shov that, at Station Papa, thcrnohaline convection is the most important factor and that wind nixing (dynamic con- vection) is actually insignificant during the cooling season. Meteorological and occanographic parameters contributing significantly to the change in the KLD during the cooling season are determined, and from these the physical processes of importance are inferred. The investiga- tion was carried out with the aid of statistical correlation and wave- analysis programs, the BUD 07 [lG\ and the Tukey spectrum analysis [15], utilizing the GDC I6O4. digital computer. Regression equations and correla- tion coefficients are obtained by the BUD 07 program. One part of the Tukey spectrum analysis was used to determine cross spectra of the 1ILD fluctuations and the sea-surface temperatures. This program was also used in the analysis of internal waves. The investigation is based on occanographic and weather data obtained by the Fisheries Research Board of Canada, Pacific Oceanographic Group, for the months of October, November, and December during the years 1956, 1957 and 1958 J6. 7] . 2. Background The attempt to identify the factors which bring about the hourly fluctuations in the IILD van based on the authors' earlier endeavor to derive an empirical method to predict the average TTT.D on a daily basis during the cooling season. It became apparent then that the hourly fluc- tuations of the 11D could bo of equal or larger magnitude than the average deepening of the KLD during one or more days; thus, to use one or an average of tv/o or more observed IILD values per day as representative of the depth for any particular hour of that day is misleading ff.J . The probable cuasc of these fluctuations is internal v/aves. Students at the U. S. Naval Postgraduate School during 1961 and 1962 derived empirical methods to predict the MTJD at Ocean Station Papa during each of the 12 months of the year. In addition, the onset of the seasonal thormocline at Ocean Station Papa, which takes place in April or Kay, \:as studied by Clark in 1961 [z}» Clark successfully related the thermocline onset to upper-air parameters. During the heating season, \;hen the sea- sonal thormocline gradually increases in magnitude, vdnd mixing processes have been clearly established as the dominant factor in determining the MLD, by Tabata Q >] rind Geary jiq] in 1961. The cooling season remains to be studied. We have made this attempt. 3, Description of Ocean Station Papa The geographic location of Ocean Station Papa is 50N, 145W (figure 1). It is approximately /+.00 miles north of the boundary between the eastern subarctic \vrator mass and the sub tropic water mass £S'J . The water depth at Papa's loco.tion is 2000 fathoms; therefore, the thermal structure is in no way influenced by bottom topography. Also, its location is approxi- mately in the center of the Alaskan Current Gyral p"\ 9j (figure 1). Because of this location, the effects of advection arc minimized and will not be considered. The weather ship normally maintains an on-station position within a ten-mile square centered on 50N, 145W. In order to avoid rough weather, the ship nay steam anywhere within the 210-mile square grid (figure 2). Each bathythermograph (3T) sounding is identified by a two-letter code. If the ship is on-station, the letter group OS indicates the position. The ship position for the greater part of the period of our concern was within a 30-mile square centered at OS. Any data outside of this 30-mile square were not considered in this study. 4., Review of Ten] 2r : . and Salinity Structure during t!'.o Cooling Season Figure 3 repr< icnl the decay of the thermocline during the year 1956. In Augur. t, the surface layers have been heated to a maximum, approxi- mately 57F. Due primarily to wind nixing, there is a shallow mixed layer approximately 100 feet In depth with a sharp underlying thermocline . With- in the thermocline, the water temperature drops to 4-0F at a depth of 200 feet. Progressing into the fall and winter, the MLD continually increases and the magnitude of the thermocline decreases. By the one} of December, the UjD is nearly 330 foot in depth; and the sea-surface temperature has decreased to approximately 4-2F. Due to the presence of an intense halo- cline, the MLD reaches a limiting depth of 330 feet in January and iso- thermal conditions' prevail down to this depth for the remainder of the winter. The basic salinity structure for the eastern subarctic Pacific water mass is shown in figure 4-. Three zones are indicated. The upper zone extends from the sea surface to a depth of 330 feet, and is characterized by relatively low-salinity water (32.7/^ [2l] ► In the fall, the upper zone is isohaline and is marked by the presence of the season '.1 thermo- cline. Because of the isohaline conditions in the upper 330 feet, we assume that significant variation in density is governed by changes in temperature only. The haloclinc represents a transition zone between the upper and lover zones. Here, the salinity increases markedly \:ith depth (as much as one part per thousand within .an interval of 330 feet). The halocline represents a limiting depth for the seasonal thermocline. It is similar to having an ocean bottom at this depth as far as convective nixing is concerned. The density increase is so great through this layer that mixing cannot take place through it [20] . Within the lower zone (> 650 feet) the salinitv gradually increases with depth to the ocean bottom. 5 ; . . Cbj 3ct Tho purpose of this statistical study of tho MLD is three-fold. An attempt is made: 0) to determine the relative importance of therno- haline convoctivc mixing and wind-induced mixing on the deepening of the thermoclino during the cooling season; (2/ to determine the lag between a significant meteorological or oceanographic event and a subsequent change in the MLD; and (3) to examine the importance of the seemingly random short-term fluctuations of the MLD and to provide a description of those internal waves present. First, the parameter or parameters are identified which have the largest linear correlation with the deepening of the MLD. Next, a further investigation has been undertaken of these significant parameters to deter- mine tho lag in the mixing process, that is, the time between the onset of a change in the parameter and a subsequent deepening of the MLD. Finally, the observed variations in the MLD which cannot be accounted for by either mixing process are investigated, 5.b. Method of Investigation The parameters to be investigated are sub-divided into three groups. Those related to convoctivc stirring are; (l) temperature of the sea, at tho time of the sounding and with a 2-hour lag; (2) air temperature, at tho time of the sounding and with a 2-hour lag; (3) dew-noint tempera- ture and wet-bulb temperature, at the time of the sounding; (4.) relative humidity, at 2-hour and 5-hour lags; and (5) low-cloud cover, with a 2- hour lag. Parameters chosen to represent wind and wave mixing are: (1) wind speed, at 2-hour and 5-hour lags; and (2) height of significant waves, at 2-hour and 5-hour lags. 6 Parameters cho con which were shown to have a correlation with the thermal structure by others in previous studies, but did not conveniently fall into the above categories, are: (l) 500-mb height, in geopotential meters; (2) 500-mb temperature and 500-mb relative humidity, at a 2-hour lag; and (3) surface- pressure change, with a 2-hour and 5-hour lag. These data were obtained from synoptic 3-hour ly reports, twice-daily constant-pressure records, and the BT traces. The available BT's for the period of investigation were tabulated in two groups, 02002 and 1700S, for each year to eliminate any possible yearly anomalies or diurnal trends. An investigation by Scripps Institution of Oceanography of the annual KLD fluctuation in the northeastern Pacific Ocean shows that the MLD most fre- quently observed in a given month often varies considerably from year to year [}8j. The available literature on diurnal trends during the cooling season is not so clear. A preliminary investigation of the data showed no marked diurnal trend. This indication was supported by Dr. Tully of the Pacific Oceanographic Group, in a conversation with the authors, in which he stated that during the cooling season the MLD is too deep to have a clearly defined diurnal fluctuation. With the aid of a multiple-rogression and correlation analysis, the BIMD 07 programmed for the GDC 1604. high-speed computer, the linear- correlation coefficients were obtained for the prc-selected group of me- teorological and oceanographic parameters with the MLD. The BIMD 07 pro- gram was used because it can select different sub-samples of data that are obtained from the same population. Thus, the program would perform linear-correlation analysis and linear multiple regression on the data for 02002 and 17003, separately and in combination. In this way, a close examination of possible diurnal trends could be made for each of the three years studied, 1956 through 1958. The analysis provided regression equations for nine different data groups for the periods shown in Table I. The BUD 07 program yields best results when the number of indepen- dent variables is not greater than one-half t'.e nunber of values of the dependent variable. Since the smallest number of values for the depen- dent variable is 36 (at 02002, 1958) , only IB independent variables were investigated. A set of 18 secondary parameters was tabulated in the event that the analysis of the 18 primary parameters proved inconclusive. There was no attempt by the authors to eliminate possible duplication of parameters that arc indicative of the same process. For example, dew- point temperature, wet-bulb temperature, relative humidity, and low-cloud cover are all related to evaporation; but it was left to the BI1ID 07 program to discern which ones, if any, were significant in contributing to the prediction of the deepening of the liLD. The BIKD 07 is unable to produce a multiple linear-regression equation if any independent variable is a linear combination of two or more inde- pendent variables. Therefore, temperature of the air minus temperature of the sea, x^hich is often used as an indicator of thermohaline convection, could not be investigated in conjunction with the air temperature and sea temperature. Consequently, three additional problems were computed using the air-minus-se? temperature parameter in olace of sea-temperature para- meters. See Table II for the tabulated results of the 12 problems. Tn analysis of all the data, certain facts and tendencies are evident; these are discussed in the following two paragraphs. The only parameters that show a consistently high linear correlation with the 1-H.D in every sample or sub-sample are the sea-surface tempera- tures, at the time of e sounding and with a 2-hour lag. They also accounted 1(This small nunber results because BT data for October, 195§ are miss- ing; only a small number of observations was available in 1957 as well, since December, 1957, observations were not taken.) for almost all of the variance explained by the regression equation using all 18 parameters. Figure J+ shows the close relationship between the sea- surface temperature and the I'M) from October through December, 1958. Likewise, Zettcl [25] suggested that sea- surface tcmoerature might be a good "indicator" for the 1LD. Wind speed and height of the significant waves, the parameters chosen as indicators of wind stirring, have either very low negative or low posi- tive correlation coefficients. In order to determine the time required for an increase in cenvoctive activity due to a reduction of sea-surface temperature to effect a sub- sequent deepening of the MLD, the MLD's for 17002, 195^ w ere tabulated with the sea temperature at lags of zero, two, five, eight, eleven, four- teen, seventeen, twenty-one, and twenty-three hours as the independent variables. A simple linear-correlation program was used to determine that the lag yielding the best correlation was two hours (Table III). Also, two one-hourly series of MLD for 79 hours in October, 1957, and for 51 hours in November, 1953, were tabulated with their corresponding sea- surface temperatures. The energy-density spectrum and the cross- spec- trum of both the 11LD and the sea-surface-temperature time series was ob- tained from the Tukey analysis. Maximum lags of 39 hours and 2/+ hours were used for the 79-hour and 51-hour scries respectively. The two co- spectra for the 79-hour and the 51-hour series show large values for h's around 3 hours and 4- hours respectively (figure 5)» From the results of the simple linear correlation and the Tukey analysis,-^- it is seen that all lags from two to six hours show high correlation. Be- yond 12 hours the correlation rapidly decreases, A. linear-regression equation was derived for 17003, 1956, using sea temperature with a 2-hour lag as the single independent variable (Table IV ). 1 on cross-correlation, not shown 9 The fact that the results of this equation as measured by the standard error conuare favorably with the multiple- regression equation derived from 13 independent variables for the same year supports the initial analysis of the problem. If a regression equation were to be used to forecast MLD, one using only the sea- surface temperature taken with a lag of up to 12 hours would be much more reliable than an equation with more parameters. This is true simply because it would have a larger number of degrees of freedom. Note that all of the regression equations have a standard orror of from 15 to 30 feet, with an average for all problems of 22.15 feet (Table V, Table VI). There are several possible explanations for this standard error of more than 20 feet: (l) it is possible that not enough parameters were used, and that by substituting for primary parameters which showed a very poor correlation, some of the secondary parameters or primary parameters with different lags, the standard error of the new regression equation would bo roduccdj or (2) there is a strong possibility that a non-linear relationship between a parameter and the MLD could account for a large part of the standard error (however, the BIMD 07 program cannot detect this); or (3) the error may be due to internal waves. Of these possi- bilities, (3) seems the most likely reason to explain the observed stan- dard error. 10 ' 6. Analysis of Internal Waves The base of the mixed layer in the ocean is subject to many vortical oscillations. Figure 7 shows a series of daily MLD's for the period Octo- ber through December, 1956. Each plotted point on the curve is an average daily value of the MLD. Two individual soundings are normally used; how- ever, uo to 24- soundings were available on several days. It is observed that the MLD undergoes a seasonal downward trend. During the October through December period, the seasonal trend of the MLD finds it increas- ing from approximately 130 feet to 330 feet. This is an average deepen- ing of 2.17 feet oer day. Also, large vertical fluctuations are super- imposed on this downward trend, which become larger in magnitude as the mixed -layer thickness increases. Note in figure 7 that the vertical fluc- tuations of the MLD can be ten times greater than the average daily deepen- ing. In addition, it is seen (figure 8) that hourly fluctuations can be of equal or greater magnitude than the average daily deepening during the fall. Figure 8 represents a one-hourly time scries for 51 consecutive hours during November, 1958 (scries 1). A second one-hourly time series rep- resents 79 consecutive observations taken during October, 1957 (series 2). The magnitude of the MLD fluctuations is about the same, whether it is computed from hourly, twice-daily, or daily observations. The average fluctuation per hour of the MLD for series 1 is 18 feet. The average fluctuation between the consecutive 02002 and 17002 soundings for the month of November, 1958,, is 21 feet. Also, the averaged daily fluctuations during November is 25 feet. The numbers for series 2 arc similar. A December, 1956, one-hourly time series (figure 9) Was available but was too short for detailed analysis. However, it illustrates the extreme fluctuation of the MLD which takes place over a short time interval. Over a 3-hour 11 period, MLD increased fro;.. 270 foot to 370 foot, and thon decreased again to 235 foot. Since nixing processes can account for only an increase in the IXD, and since observed fluctuations are in both directions (up and down) , and arc a consistent feature of the data, these observed fluctuations are considered to be due to internal waves. Internal waves may occur within stratified water and in water in which the density increases with depth. The largest vertical displace- ments of the water particles are to be found within the boundary between layers of different density. The displacement amplitude diminishes above and below this boundary, approaching zero at the sea surface and the ocean bottom. The density difference between the waters above and below the seasonal thermocline is, of course, much less than the density difference between the air and the water at the sea surface. Therefore, a boundary within the ocean can be much more easily displaced than the surface of the sea [l7j Ufford \2U\ states that surface waves require 30,000 times more energy to start and maintain than is required for internal waves of the same amplitude. Energy for internal waves could come from surface disturbances or from currents within the ocean. Besides rapid vertical oscillations in the MLD, it was observed that the thickness (or vertical extent) of the thermocline layer below the MLD may vary markedly with time. Figure 10 shown the thermocline thick- ness for scries 1. Variations in the thermocline thickness indicate that internal-wave characteristics of phase and .amplitude vary with depth. Also, the temperature gradient in the thermocline varies markedly because of changes in its thickness. The actual tern] srature differenc through the thermocline is a relatively stable feature and is therefore predict table [llj . 12 T bn Q22] ! itcd from tl: ; bhat in. rn ] waves with as low a period ivo 2 inutcs could for] a i propagate during the summer at the level of b : sasonal thcrnocline at Ocean Station Papa. With one-hourly observations available for analysis, the minimum ^-rind that could bo inv sti ;ated Is two hours. The Tukey spectrum analysis, programmed for the GDC I604. computer, was need, to analyze each tine series. The main object was to find any predominant periods and associated amplitudes present in the MLD oscil- lations. The Tukey analysis estimates the energy-density as a function of period in a given series. Thin is done by computing th aiito-correla- bion function for a nu ifoer of given lags in the series; then a smoothed spectral estimate ir> 1 t incd from the Fourier cosine transform, of the auto-correlation function. Initially, a correlogra was plotted for both time series (figure 11). The correlogram is a plot of the non— normalized auto-correlation coeffi- cients as a function of the lag (k} . Inspection of this correlogram appears to indicate that the spectrum of series 1 has a relatively large energy- density maximum near the 12-hour \ oriod and a secondary maximum with a pea!: near six hoars; and that the spectrum of series 2 has only one maximum near 12 hours. Next, the energy-density spectrum of both tine series was obtained from the Tukey analysis. Figure 12 is a plot of the energy-density spectrum for series 1. A maximum lag (n) of 24- hours was used, which allowed the spectrum to include a range of periods from two hours through 4-S hours. The spectrum helps confirm the indications of the correlogram. A maximum of energy of the variance of the MT,D is shown to be produced by fluctua- tions with periods on the order of 12 hours. Also, a large energy-density is indicated for periods around six hours. There is an energy gap Tor the 13 periods around eight hours, and the energy for periods loss than five hours drops off rapidly to an insignificant amount. The total energy is a known quantity, equal to twice the variance. By measuring total area under the spectrur. curve and the area under each frequency peak between half-energy points, equivalent amplitudes for waves with periods near 12 hours and six hours wore computed. These computed amplitudes arc IS feet and 12 feet for the 12-hour and the 6-hour periods, respectively. The energy-density spectrum for scries 2 is shown in figure 13# A maximum lag (m) of 30 hours was used, which allowed inspection of periods ranging from two hours through 60 hours. A relatively large energy maxi- mum is again indicated for periods around 12 hours. The curve then falls off rapidly, but shows a slight maximum n«ar the 6-hour range of periods. A single sine wave with energy equivalent to that under the 12-hour peak would have an amplitude of nine feet. This analysis reveals three features of the thermal structure at Ocean Station Papa during the time interval investigated, (1) Vertical oscillations of the MLD are present at the thermocline during the cooling season, Tne magnitudes of these oscillations are similar in all data, whether they be from hourly, twice-daily, or daily observations, (2) A L though the time series available was much too short on which to base strong conclusions, the analysis did reveal that the major energy peaks occurred with a period of approximately 12 hours with an average amplitude of 13.5 feet. (3) The value of the standard error of estimate resulting from the 313 D 07 regression equations is very close to the height of the postulated 12-hour wave (that is, 27 feet). Therefore, it is concluded that there u is a direct relation between this error and the presence of internal waves during the period of investigation. 15 7, Conclusions and Recommendations As a result of this study of the influences on the KLD during the cooling season, the following conclusions can bo reachea. (1) Thermohalinc convection is tho important process for the deepen- ing of the I-XD in the autumn season. (2) Du ring the period of study, the MLD is too deep to be affected by wave stirring or diurnal trends. (3) Th3 tine lag between surface cooling and deepening of tho I ID by the convcctivc process is small; this suggests that once the cooling season begins, convective circulation is essentially continuous. This circulation nay be maintained during periods of near-zero heat flux across the air-sea interface by wind energy, as suggested by LaFond [l3J J how- ever, until an injection of potential energy in the form of rapid surface cooling, the MLD will remain relatively static. If the increased surface density caused by surf/ace cooling is sufficient, the convective circula- tion intensifies and drives the MLD deeper. (4.) A major portion of the MLD variability appears to be associated with internal waves. The analysis of internal waves revealed that the major energy peaks occurred with a period of approximately 12 hours with an average amplitude of 13.5 feet. "Early in 1953, at a Navy-sponsored thernocline conference attended by 20 of this country's most prominent oceanographors and meteorologists, the following question was asked his colleagues by Dr. T. F. KaloneJ "How accurate a prediction of the iXD and its hourly fluctuations is required by tho military?" [19J This remains a vital question. Tf the military is willing to accent forecasts of the MLD within ranges of 20 or 30 feet, then existing methods of prediction will suffice. Any increase in accuracy over existing schemes for predicting the MLD at 16 a particular hour on a particular day can bo accomplished in areas where internal waves are important only after prediction of the internal wave pattern is possible. This is a complicated oroblem. If a sufficiently long, detailed time series of BT's could be made available, internal waves could be filtered out by use of a technique such as proposed by Linnettc jl/U , This would leave a tine series of the 1ILD that is due entirely to convoctive nixing or other causes, thus enabling a much better quantitative analysis of the convectivc process. This is suggested as the next logical extension of the research reported in this paper. 17 UKE I 18 I47°00' l4Ge00' 145°00' 5I°30' — B 5I°00' - £ 50°30' - H 50°00' 49°30'-M 49°00' — Q 48°30' — U B -fil"30'N j\Z|--49°30' __ _} 1 Q— 49e00' (J — 48°30' 147 °00' I46°00' I45°00' I44°00' I43°00' Figure 2. Position- Indicating Grid for Ocean Weather Station Papa, with . Mercator Projection cf a Latitude and Longitude Grid Superimposed 19 40 • 0 10 (U) ..' ■ J-.'.-l. .±i.r- .' .; ii . 3 ^ - v. '.iOv. -Ji '. ' ! ■ ' i-' I^UU^MOt.igi I L l_i L_j L j o t:, 14 Figure 3* CAUNITY 0 (%.» „„%S _ 33.9 3-1.0 i i £#>p#f Zone 50 ■t . 100 i tfto Na toe tin* •> « l_ •- «> -J 1 1 1 r / ^V 33.8%. «uo \ Upward .C o. 8 Lower Zoi.fi \ 77ff/»* far 250 ; goo - SOt) J 10 II *v tf Figure ^. Salinity Structure in East . Jabarctic Pacific Oc 20 ure 5,-u Cross-Spec trun - MLD and Sea- Surf ace - Temperature Tine Series (November, 1958) 2™ r **s n^t, M h = 2mf ^t N = 51, m = 24-, At = 1 .025 -T-- in l)h , .020- ,0/5 " t .oio- ,b, Crosr;-5p Surface-Tenperature Tine SerieG (October, lf,"'6) h = 2mf.At N = 79, b = 39, ^t = 1 T^7 HPS. t XC°c) /3 - I OCT OB l UOVFMBEh' ! DECEMBER MLD 6 L Figure 6. Mea LD and Sea-Surface - ire (C a tir ;] D >er, 1957 . ' " ■ »] M/.D r/v; i 23 C UJ o Q m u 1 o 0) Q toO >-. O r-l M Cfl 4J Q 0) 0) bO J3 cO O U 4-1 ^ ° toO •r4 A cm * (±33 J) cniw o CM oo 24- ^0° -a- 5 3: u 60 •W fa \1 A J 7 (113J) C77W <*-, -io CM O 3: — o CM h CO 00 3 toO fa C 1*1 a^^) - • Thermocline Thickness (November, 1958) 26 cu •r-l U CO 00 LO (U CTn •r-l H " u >, & B > o -d c S-i O i o; c o u o M-l lO CTn 6 r-' H » bO M O <1> r-l JO 0) O S-l 4-1 o o r-l fa ^£> u ■D B tu > o 3 o CO a CO w C QJ a i tu c w 3 M •H fa -l_, o 2 I! Co a- T.n»i.-i r va-.1 r— 1 * u CD o o *J (J ■ u e •H W »» C ON 0) r-~. Q l II >, bO as u 0) c W U W) •r-l o CM ^ 00 CM 3- o ^1 NO •CO 1S ^ o - 29 Table I 1256 1957 1953 02003 £3 /J, 36 17002 61 46 43 109 90 79 (02003 is 160C local mean tine) (17003 is 0700 local noan tine) Bathythermograph Soundings Available 30 C e II 02002 17003 020CS and 17003 Parameter 1956 -,905 1957 -.903 3 -.649 mk.. 1957 _1958 1956 1217 1958 ?y -.350 -.767 -.814 -.371 -.329 -.734 Ta -.635 -.533 -.354 -.410 -.386 -.331 -.502 -.489 -.333 Ta-Tv .369 .372 .369 Tdp - . 344 -.146 .104 -.162 -.020 .017 -.242 -.050 .062 Twb -.519 055/ -.008 .153 -.189 -.115 .092 -.211 .063 RH .167 .266 .272 .121 .290 .202 .HI .263 .238 (rh;-h .028 .266 .333 .069 .400 -.015 .049 .327 .14.3 F .180 .107 .212 .351 -093 .249 .276 .004 .231 FF -.0^6 .339 .012 .110 . 307 -.131 .047 .360 -.062 Hl/3 -.200 .636 -.089 -.077 .487 -.053 -.127 .581 -.060 (Tw)-2 -.925 -.379 -.793 -.oo4 -.649 -.343 -.399 -.726 -.019 (Ta)-2 -.63/, -.646 -.228 -.382 -.440 -.314 -.505 -.502 -.277 (Ta-Tw)-2 .3H .44<-> .383 (FF)-5 .019 .302 -.073 -.262 .352 0.172 -.143 .311 -.115 (Hl/3)-5 -.200 .633 -.037 -.223 .525 -.339 -.192 .583 -.245 P -.311 -.134 .125 .039 .170 -.34^ -.107 -.027 -.090 (P)_5 -.060 -.004 -.101 .041 .327 -.215 .047 .125 -.158 GPM5 .113 -.463 -.043 .215 -.419 .143 .169 -.437 -.050 T5 .113 -.439 .091 .166 .623 .080 .U5 .181 .080 RH5 -.136 .235 .150 .137 .045 .136 .028 .166 .154 Simple Liinoor-Corrclation Coefficients betveen the 18 Primary Paranoters and the I1»D 31 Table III Sea-Surf ace-Temperature Correlation Coefficients Lag in Hours '..'ith the /MLD o -.04975 2 - ,30409 5 -.87828 8 -.,77576 11 -.87173 H -.86/+79 17 -.86829 20 -.86125 23 -.85139 Scrapie Linear-Correlation Coefficients for S'ea-iSuri .. Te iperatures and the IXD 32 Table IV Linear-correlation coefficient (for Ts_2) -.884 Standard error of the estimate 30.33 Range of residuals 121.2. Regression equation: ^VQst. ~ 1152.94 - 20.24 (Tc_2.) Regression Results for One Independent Variable (17002, 1956) 33 Table V 02003 17003 02002 and 17008 1956 1957 1953 1956 1957 1958 1956 1957 1958 (Tw and Tv;_2 included, Ta_Tw and (Ta-Tw)_2 omitted) R' .950 .9a .364 .915 .831 .915 .909 .374 .863 SE 26.5 H.4 26.7 31.4- 13.0 19.4- 29.9 15.3 21.0 RR 8O.4. 45.4 29.9 104.8 49.6 59.8 118.8 57.1 102.5 MLD 210.1 179.4 273.3 212.7 170.5 279.6 211.6 174.8 276,3 S 67.3 32.4 37.0 64.9 25.0 36.27 65.7 29.0 36.5 (Ta-Tw and (Ta-Tw)_2 included, Tw and Tw_2 onitted) R1 .950 .917 .910 SE 26.5 30.9 29.8 RR 80.4 104.4 121.8 MLD 210.1 212.7 211.6 S 67.3 64.9 65.7 Ihltiple-Regrossion Recults for 18 Independent Variables 34 • Table VI I'iultiplci-correlation coefficient (for IS independent variables) .896 Linear-correlation coefficient (for Ts and Ts_2) -.8L4 Standard error of the estimate 22.15 Ran^e of residuals 72,0 Standard deviation A3. 8 Three- Year Averages for Regression Result: 35 3I3LI00RAPHY 1. Ball. F. K., Control of Inversion Height by Heating, C&iarterly J. R. Met. Soc, Vol. 86, Mo. 370, op. 433-494, I960. 2. Clark, Marion J., The Influence of Winds and Relative Humidity on the Seasonal Thernocline at Ocean Station "P", MS Thesis, U. S. Naval Postgraduate School, 1961. 3. Cromwell, T. , Pycnoclines Created by Mixing in an Aquarium Tank, Journal of Marine Research, Vol. IS, No. 2., pp. 78-82, I960. 4. Defant, A,, Physical Oceanography, Vol. I., Pergarion Press, 1961. 5. Edgren, D. H. , An Objective Forecast Technique of the Mixed-Layer Deoth during the Month of November at Ocean Station Papa, U. S. Naval Postgraduate School, unpublished manuscript, 1962. 6. , Fisheries Research Board of Canada, Pacific Oceanographic Group, Data Record, 1956 0c>-""»n Weather station PAPA. Man".<"",T»ipt Report. Joint Committee on Oceanography, Nanaimo, B. C., 1957. 7. , f Fisheries Research Board of ounada, Pacific Oceanographic Group, Data Record, Ocean Weather Station PAPA Manuscript Report Series. Nanaimo, 3. C,, No, 14, May 1958; No. 44, April 1959*. 8. . — , Annual Report of the Pacific Oceanographic Group, Fisheries Research Board of Canada, Pacific Oceanographic Group. Nainamo, B. C. 1961. 9. Fleming, R. H., Notes concerning the Ilaloclino in the Northeastern Pacific Ocean, Journal of Marine Research, Vol. 17, pp. 158-173, 1958. 10. Geary, J. E. , The Effect of Wi'nd upon the Mixed-Layer Depth, MS Thesis. U. 3. Naval Postgraduate School, 1961, 11, Giovando, L. F. , The "Ocean" System for Assessment of Bathythermograms, Fisheries Research Board of Canada, Pacific Oceanographic Group, Nanaimo, B. C, 1962. IP. Laevastu, T. , Factors Affecting the Temperature of the wSurfaco Layer of the Sea, Societas Scientiarum Fennica, Commentationes Physico- Mathematicae XXVI, I960. 13. LaFond, E. G., Factors Affecting Vertical Temperature Gradients in the Upper Layers of the Sea, The Scientific Monthly, Vol. LXXVIII, No. 4, pp. 24.3-253, April 1954. 14. Linnette, H. M., Statistical Filters for Smoothing and Filtering Equally Spaced Data, U. S. Navy Electronics Laboratory, Report 1049, 19 61. 15. Miller, 0., Tukey Spectrum, Cross-Spectra and Power Spectra, Fortran, CO-OP Manual, ID-G6UCSD TUKEY, 1961. 36 16. - — . f Multiple Regression and Correlation Analysis Ho. 2, BJMD 07, Division of Biostatistics, Department of Preventive Medicine and Public Health, School of Medicine, University of California, August, I960. 17. f National Defense Research Committee, Office of Scientific Research and Development, The Application of Oceanography to Subsurface Warfare, Technical Report of Division 6, Vol. 6A, 194.6. 18. Pattullo, J., Mixed-Layer Depth Determined from Critical Gradient Fre- quency, Scripps Institution of Oceanography, SIO Reference 52-25, Report No. 2%, May, 1952. 19. Pollak, M. J., Notes from the Conference on the Thernocline of 25-27 May, 1952, The Chesapeake Bay Institute of the Johns Hopkins University. 20. Tabata, S., A Study of the Main Factors Influencing the Temperature Structure and its Forecasting during the Heating Season, Fisheries Research Board of Canada, Pacific Oceanographic Croup, Hanaimo, B. C., 1962. 21. Tabata, S., Temporal Changes of Salinity. Temperature and Dissolved Oxygen Content of the Water at Station "P" in the Northern Pacific Ocean, and Some of their Determining Factors, Fisheries Research Board of Canada, Pacific Oceanographic Group, Hanaimo, 3. C., 1961. 22. Tabata, S., The Relation between Wind Speed and Summer Isothermal Surface Layer of Water at Ocean Station "P" in Eastern Subarctic Pacific Ocean, Fisheries Research 3oard of Canada, Pacific Oceanographic Group, Hanaimo, 3. C, 1962. 23. Tully, J. P., M. Pirart and R. K. Lane, Airborne Radiation Thermometer Mark I Feasibility Tests, Manuscript Report Series No. 61, Fisheries Research Board of Canada, Pacific Oceanograohic Group, Nanaimo, B. C, I960. 24.. Ufford, C. W., Internal Waves in the Ocean, American Geophysical Union Transactions, Vol. 28, Ho. 1, February, 1947. 25. Zettel, R. A., Meteorological Factors Affecting Mixed Layer Depth Fluctuations, MS Thesis, U. S. Naval Postgraduate School, 1961. 37 APPENDIX Heat Transport in the Sea and Exchange across the Air-Sea Interface A. Thernohaline convection. The vertical displacement of snail par- cels of water occurs when a snail part of a water mass is heavier than the \;atcr underneath it. To restore this unstable condition to equilibrium, the heavier water tends to sink while the lighter water rises. Associated with those forced vertical movements of snail parcels there is also a trans- port of the characteristic properties of sea water in a vertical direction which leads to an equalization of any vertical differences in these proper- ties which may be present. It is believed that convective nixing is as important an agent of heat transfer in the ocean as wind stirring during the cooling season [*2, 12, 20J r An initial increase in the density of small ^articles at the surface accompanies an increase in salinity (duo to evaporation, or to the forma- tion of ice) or a decrease in temperature. One or more of these in combi- nation may be involved in thernohaline convection. In lower latitudes, v/here there are only small variations in the temperature, the heat loss is outweighed by the effect of evaporation; in polar regions, in addition to radiation and evaporation the increase in salinity due to formation of ice is also effective. Tn temperate latitudes the heat loss by radiation is the decisive factor. Convective sensible heat exchange (conduction) between air and sea surface has been studied by Kuhbrodt [4j for the North Atlantic. He has shown the convectional heat flux to be approximately 20 gm cal/cm^ per day during the period of the year when the air is cooler than the sea surface. This value, even as a rough estimate, is too large to be neglected in the heat budget of the ocean. If the surface of the sea is warmer than the atmosphere, the air is heated at the interface and the vertical stratifi- 38 cation of the air becomes unstable; the air becoraes turbulent with a con- stant replacement by cool air at the sea surface and the vertical heat transport becomes large. Values given by Def ant [4J for the heat loss in units of grr sal/cm^ per day for 50H latitude are 116 units due to effective back radiation, 78 units due to evaporation, and 20 units due to convection of sensible heat (conduction) as a yearly average. Certainly, during the cooling season heat loss due to conduction would be even more significant. These values are derived, assuming that the heat exchange through the ocean sur- face occurs independently for each separate latitude belt. Therefore, no meridional heat exchange (by ocean currents and by horizontal mixing) was considered. B. Dynamic convection (forced vertical mixing due to wind and wave action). This process has been, well studied and considered to be the dominant process of vertical nixing in the heating season. Laevasta L12J has proposed an empirical formula for determining the IILD by significant wave height alone. C. Dynamic convection due to forced vertical mixinr: of ocean currents can result in convective mixing, and influences the MLE„ This process vas not considered because of the difficulty of measurement; how- ever, since the Station is located in the center of the Alaskan G.yral, ocean— current effects are probably small. D. Thermal conductivity can take place when a vertical temperature gradient exists in the ocea' . Heat is transferred by molecular heat con- duction processes. Def ant [4J concludes that this process is insignificant in oceanogra-nhic investigations due to the extremely long period involved in the conduction process . Therefore, this process will not be considered in this study. 39 3. Sntrainment due to turbulence at the pycnocline . During the cooling season in the open ocean, a well-defined isothermal surface layer exists which extends downward to an interface of rapidly decreasing tem- perature, investigations of the subarctic water indicate an isohaline condition to a depth of 33") feet, so the effect of salinity on density can be ignored \?i\ % and thus we nay consider the thermocline as a pyeno- cline. Because less dense warmer water overlies dense cold water, we have a stable condition much like a surface inversion in the atmosphere. When surface cooling takes place, thereby creating an unstable condition, free convection can occur. Cromwell £3/ has demonstrated that this free convec- tion in a model causes a turbulent exchange across the thernocline which is one-way. The fluid particles which move upward from the region below the thernocline are rapidly deformed and mixed throughout the upper layers; fluid particles which move downward toward the quiet layer below the IAD are buoyed upward intact. Thus, the upper layer increases in thickness, but decreases in temperature it the expense of the lower layer. This same phenomenon is observed when the turbulence is induced by wave action or in- ternal wave action £l] . UO thesE235 Investigation of the influences on the m I II I IMI llll I III II ml ii lull 3 2768 001 90326 3 DUDLEY KNOX LIBRARY