ON le USE ONLY TR-146 i. oO TECHNICAL REPORT ASWEPS REPORT NO. 8 STATISTICAL ANALYSIS OF THE THERMAL STRUCTURE AT OCEAN WEATHER STATION ECHO JOHN B. HAZELWORTH Formulation Branch Oceanographic Prediction Division JULY 1964 U.S. NAVAL OCEANOGRAPHIC OFFICE 74/3 WASHINGTON, D. C. 20390 /16/K-|4y | FOR OFFICIAL USE ONLY FOREWORD Knowledge of the space-time variation of thermal structure parameters is prerequisite to development of prediction techniques for use in the Antisubmarine Warfare Environmental Prediction System (ASWEPS) . Since this knowledge can be gained only through analysis of long series of data, historical bathythermograph (BT) observations from U.S. Coast Guard Ocean Station Vessels have been utilized. These observations, supple- mented by high density time series data collected by Naval Oceanographic Office personnel aboard these vessels, form the basis of this report. The Oceanographic Office has assembled these data into the Sonar Experi- mental Research Card (SERC) deck, which is available to the scientific community for research purposes. The statistical techniques of this report involve reduction of BI data to punchcard format suitable for thermal structure research. This report describes the environment at Ocean Weather Station ECHO (35N,48w) and is the first in a series. Subsequent reports will describe the Rear Agwfiral, U.S. Navy Commander U.S. Naval Oceanographic Office INA in Mel L/w il O 0301 ON iii ote nS CONTENTS FOREWORD e e es e e e e e e e e e e e e@ TENERODUCTION Memento halite Meilofioltelielleliteiis SERC CODING AND THE DATATRON PROGRAM . ANALYSIS OF STATTON ECHO DATA .. e «@ Analysis of the Historical Data . Analysis of the Experimental Data RESULTS OF ANALYSIS QUALITY OF THE DATA AND STATISTICAL ANALYSTS CONCLUSIONS ACKNOWLEDGEMENT OF eer Vere) eer OY (© in@so 1@)! (ee je) ee REFERENCES e e e e e e e e e e e e e e e e es APPENDIXES Appendix A. Appendix B. Appendix C. e e e se e e e e e e e e Description of the Datatron 205 Program Statistical Analysis of Parameters . « . Annual Statistics for Various Thermal e e eo e e e Sheblennbhes) Jetshgeieeepas| 46 56 0 59 6 O00 0 O ILLUSTRATIONS Figure 1. Figure 2. Sonar Experimental Research Card . « « o e Schematic Diagram of Thermal Structure Parameters e« e © © © © © © © © e © © e oe eo e e e e e tnt Rae 2 MATRON ae ih , i i et pa INTRODUCTION Major problems in developing oceanographic forecasting techniques include: (1) formulation of a quantitative description of thermal struc- ture variables in various areas; (2) determination of the size of an area that is covered by a point temperature structure forecast within statistical limits; (3) determination of the temporal extent of a point forecast within statistical limits; (4) whether assumed predictors can be isolated and ranked statistically; and (5) if so, whether the para- meters of the predictors can be determined. For examination of these and other thermal structure problems, the Sonar Experimental Research Card (SERC) deck of punchcards was created. The deck, as described below, includes bathythermographs (BT) and associ- ated weather data from four experimental cruises, each of which was about three weeks in duration. These surveys covered each season between Novem- ber 1958 and September 1959 at ocean weather station (ows) ECHO located at 35N,48W. ECHO was chosen for this study, because its location in the Sargasso Sea was thought to assure minimum advection and typical seasonal thermal structure cycles in the surface layers. The experimental survey data from ECHO are composed of half-hourly BI's covering the entire cruise, some observations taken at 10-minute intervals for short periods of time, and several sets of simultaneous BT's. These data are supplemented by about 12 years of historical weather ship data (BI's and meteorological observations) from stations ECHO, BRAVO (56N,51W), CHARLIE (52N,35W), DELTA (44N,41W), and HOTEL (36N,70W). About 8,000 observations from CHARLIE, 5,000 from DELTA, 7,500 from ECHO, and 7,700 from HOTEL have been tabulated and punched on IBM cards. An additional 15,000 to 20,000 observations remain to be tab- ulated and punched on cards. A large majority of the observations were taken with a 450-foot mechanical BI. Some 200-foot observations were included. The ECHO experimental cruises used the 900-foot mechanical BI. SERC CODING AND THE DATATRON PROGRAM After coding, BI and weather data from each observation are punched on a master and three detail IBM cards (figure 1). ‘The first 17 columns of each card are reserved for latitude, longitude, date, and time. Columns 18 through 54 of the master card contain meteorological and additional identifying data. Detail card no. 1 contains the water temperature (°F) at 20-foot increments from the surface to 360 feet and at 40-foot incre- ments from 360 through 440 feet. Detail card no. 2 contains the temper- ature at 40-foot increments to the end of the trace. Space remains on the card for temperature data from the 1,300-foot electronic BT. Columns GYV9 HOYV3ASSY IVLNAWIYSdxX3 YVNOS | 3YNdIS oS amu so|¢9 ca|za|ta gc 9c|cs EI EE spl Zt 3¢|sy|ro]er zelty or 6e|ae|eloe| a. ce ts. 92|sz|z ez i, ztfor|st]tfetlet tafor| ee] zc] 9 Bu 1 3 z alls ae: = | 2) = : = awe elzs|e Saal |e ell os Selloamalm aoe ia aise | odeg [23/22/22] 22 | 2ef| 28 ]2 2] 22/22] 23 gaaalseas| 5234 /ss2e1 2525 [es alle 3222 | 3823 |Re]S2) a2] o & | 3223] 3228 ]82]/22]a7] 5 8 SrSzleamr| SREP SRA ml eR AE 3 5 | 30nui9n07 | aaniiiva ino || 2 T)ema | fRo } Se /sg|ss] 2% | saa | enb | 22) s8153] oF CBlalmz5 | mz 5 |mezoimzez 15 = = 3 sa |e 3 reyes z 3 Bala A) = e3 x g g| FS Fy B26 Ee a = c 3 o ° AN3IGvH9 ISHi4 IN3IOVu9 NVIW lg : ! NOI LISOd|]3WIiL] 31iva €°ON 11VL30 os|6z]az cloz|sc|ve ezlzz tdloc[es]es|z9 99} 89] r9[e9|29] t9] 09 | 9s|zs[9s] ss]vs|ea|zs] 15] 05] 6r| ar] zeor} se| ro]ee] zx] t¥] ov|6e]ee|ze]9e| se|ve eafee{ relocated 2e|92|se|ve ez|ez|tz[oz|er teen orfer[zr|trlor| 6 EZE [efefels| J ose | ove | oo@ | 092 | ,oz2 | 089 | ,ov9 | 009 | ,o9s | jozs | ,oBm | aanonon | sans iG | 2 [nl dle} ee) GG Se \ s 3 yonitiwvwe4uya3adw3atl NOI|ILISOd/3WIiL}] 31Va ¢'ON 1IVL3G a~ 4 aN US Tt AT™ ACN LES as ans 4 AS NS i seen SaGHORRUOPSIGRSGGFTERGTORAONREEREGEET EGE E SETI GETORRSEaRcHERGHEL AGES || BEE | | EPERBEEEEESS Bub BEE | BE eee edlec}1z eee 99] s9|r9[e9| z9| 19/09] 6s [esfes zs|ts os|ey[ae] ce 9¢|sp|pvlev|zv|tv|or]ee| ae ce|se|se[velee|ze|te[oe|ez|sz|z2| 9z|az velee|ze|te|oz[6r]er|ct|at|sx|rr|er|zr|rrlor| |e [z[olsl[ eel 3 2 2 z mele} ,082 092 Oz ,002 ,O8! 091 OF! ,O2! oo! 080 ,090 ,0%O ,020 ,000 30NLI9NO7 3anLitvy ino = H Qa 1 Vv Ss a Y n Jt Vv t=} E] d W a 1 NO} 11SOd/3WI1L} 31va 1ON Tivl3ad Ae cu nOEeH a voxazaam |B] [7 rE a A 0z|6s|89|2s]99]s9]+9| SESE 95|ss] rs] [zz] t2[oe|er/er|zt]or ewzr|ttjor[e|e|zfol|s|r . = ° BS Bee con ° ae |e = . = ial eee |e z m | o393|s533]23 Bei as || .% 8a5/2 a|sa]2 a) sa] ila arslajs joe <|>o 2. S31 .o z 3 |sainmn sainmin| 92349 3 | 3 |§| = a 3 | taz2|isze]as BSI SF 33 1235/8 5/29]8 2/8 o]s/8 mlesissig >| eo 5 S| ae 2 [2aio 5 2/25/25 |)! We = Be aa ia? ° vye >z}e o9}/>=z]7 =rime| Si UP Se: < (eGl tes St a = = sme ome} s +3 z mo a so Sj/So0 a 5 g}o >/ 2 x aha ms| 2mlog z ss] 573/38 $3 3 | 8 ee s ¢ = S23 8) 92) 2 Fl sonowor [son | a i a HOT |s1oqIN} MOT | m Z rT) z Thy re ANZIGVHS WNWIXVW 3ams vas S @ i © Wd ) SUNLVYSdW3L Hi = GNIM WOUSY SOC erija|| 2 Ye (Y31SVW) O6£02 ‘9’ ‘NOLONIHSYM 391440 DIHdDVYSONV3IO IWAVN ‘S'N 18 through 36 of detail card no. 3 are reserved for solar radiation datae Radiation data collected on the experimental cruises have not been tabulated and punched on the cards owing to shortage of manpower. Various thermal structure parameters of importance in forecasting underwater sound can be defined in such a way that a computer can deter= mine them by use of the temperature-depth data on the SERC cards. These parameters, shown in figure 2 and defined in appendix A, include surface effect, layer depth, surface temperature, maximum gradient (thermocline), mean gradient, and first gradient. For purposes of this study, the gra- dient is considered to be the rate of change (°F/100! ) as temperature decreases with increasing depth. A program written for the Datatron 205 (appendix A) computed each of the above thermal structure parameters plus various numerical descrip- tions of the parameters. The results were then punched in columns 57 through 80 of the master card and in columns 46 through 75 of detail card noe 3e The numerical descriptions included the means of the gradients (°F/100'), depths of the upper and lower bounds of the gradients, temper- atures of the upper and lower bounds of the gradients, and thickness of the gradients. Subsequent to preparation of this report (1961), the Datatron 205 was replaced by an IBM 7070, necessitating rewriting of the programs. A more extensive data error check was added, and an additional parameter, the ascendant (increasing temperature with increasing depth), is computed. The data relating to the ascendant is located in subsequent studies on detail card no. 3 in columns 40 through 45 and 76 through 80. SURFACE WATER ___ TEMPERATURE SURFACE EFFECT SP > - LW? CER WSS SS S55 ES = MAXIMUM GRADIENT MEAN GRADIENT (THERMOCLINE) FIGURE 2 SCHEMATIC DIAGRAM OF THERMAL STRUCTURE PARAMETERS Computation and storage of all these descriptive terms on the SERC deck were not necessary. However, it was envisioned that many statisti- cal analyses using the SERC deck would be carried out on a computer with relatively slow input and output rates and a small memory. Thus consider- able computer time and memory would be saved if the descriptive terms were stored on the punchcards. Harvey (1) states that temperatures recorded at standard depths on the National Oceanographic Data Center geographical BT file do not repro- duce a BI trace completely. As the SERC deck was originally intended for special research projects requiring a high degree of accuracy, it contains a finer gradation of the BT data. Although small depth-temperature inter- vals reproduce a BT trace more accurately, decrease of the intervals con- sumes more space on a punchcard. Intervals of 20 feet between the surface and 360 feet and intervals of 40 feet at depths below 360 feet were used as a compromise between the two extremes. Computation errors introduced by this choice of intervals as opposed to either a 5- or a 10-foot interval are a subject for a separate report. ANALYSIS OF STATION ECHO DATA Analysis of the Historical Data In order to obtain a quantitive description of temporal and spatial variations in the thermal structure parameters, the ECHO historical deck was sorted into l-degree quadrangles by months and years. The following parameters were chosen to adequately describe the thermal structure: (1) surface temperature (2) layer depth (3) maximum gradient (a) average gradient ; (b) temperature of the upper bound (c) depth of the upper bound (d) thickness (4) mean gradient (a) average gradient (5) first gradient (a) average gradient (b) depth of the upper bound (c) thickness A Royal-McBee LGP-30 computer was programmed to compute the mean, standard error of the mean, variance, and standard deviation. These statistics were computed for the above-mentioned parameters for each l-degree quadrangle by months for all years. Computations were not made for groups of less than 10 BY observations. Locations of observations were assumed to be accurate. Observations taken at 35°N,48°wW are arbi-. trarily assigned to the l-degree quadrangle to the northwest. Statistics of the chosen parameters are given in tables 1 through 10 (appendix B) which indicate maximum variations of the temporal means (over a period of years) and spatial means (from a given l-degree quad- rangle to the next). The period of time covered by the data is too short to determine any possible cycle or trend. Assuming normal distribution, confidence limits of the observations about the mean can be computed from eae 28, =95% confidence limits where Sy is the standard deviation. Like- wise the confidence limits of the mean can be computed from X + teSE, where t is the t distribution and SE is the standard error. The ranges are indicative of year-to-year variation of the thermal structure during any given month. Unfortunately, a correlation exists between the magnitude of the ranges and the number of years of observa- tions. For example, the mean of the ranges of all groups of 6 or more years of surface temperature observations is 4.4°F, and the mean of the ranges of all groups of 2 to 5 years of observations is 2.5°F. Standard deviations and standard errors are more variable and are larger than expected in some cases, probably because of slide processing, reference temperature, instrumental, key punch, and coding errors. AIl1L data were carefully screened to minimize key punch and coding errors. The remainder of the standard deviation value after elimination of errors ean be ascribed to variation in time and space. In mathematical terms if Ss denotes the standard deviation of the observations, its components can be subdivided as follows: Aas 2 2 2 2 2 2 Of Hay tae + og roe + a, top, + of; (1) where the subscripts denote components due to field operator, instru- mental, key punch, coding, slide processing, and reference temperature errors, and space and time variations, respectively. Population means and standard deviations of the various parameters for the area were computed by the LGP=-30 by sorting “the SERC deck by months and years for the 20-minute quadrangle centered at 35°N, 48Ow. The statistics from this analysis are shown for the various thermal structure parameters in appendix B. Instead of computing and then examining the data for significant spatial or temporal differences between the means of a given thermal structure parameter, a more powerful tool known as the 2=way analysis of variance (unequal numbers in subclasses) was employed. ‘The technique, as outlined in Kendall (2), was programmed for the LGP=30. The 2-way analysis of variance was considered to be only a gross tech- nique, for example, checking computations for significant difference between 1-degree quadrangles over a number of years for a given month for a given thermal structure parameter (historical data). When no significant differ- ence existed between means, a probability of 100 percent was assigned to it. Computations frequently indicated significant differences between time periods and/or areas. If shorter time periods or fewer areas had been analyzed, it is probable that no significant differences might be found. In these cases the t test was used as a detail test to compare all possible combinations of pairs of means, based on the hypothesis that the two means were from the same population. The results of the analysis of variance and of t tests were converted into probabilities and are presented in tables 11 through 20 (appendix B). In these tables the column headed "X" refers to the overall mean of pa, where p is the number of time periods, and q indicates the number of areas having data. The reliability of the probabilities increases as pq increases. The column "monthly mean in adjacent 1-degree quadrangles" contains the comparison of means of all data recorded during the indi- cated month within adjacent l-degree quadrangles for the particular param- eter of the thermal structure. The column "monthly mean in 1-degree quadrangle, year to year" refers to the comparison of means of particular parameters recorded over several years for the indicated month in the same l-degree quadrangle. Therefore, table 11 may be interpreted as follows: mean temperature in January, based on 9 monthly means used in the analysis of variance, was 66.69°F. The probability that mean surface temperatures for the month of January in adjacent 1l-degree areas are not significantly different is 60 percent, while the probability that January mean surface temperatures in the same l-degree quadrangle are not signifi- cantly different from year to year is zero. In other words, there is continuity between areas but not between years. For the remainder of the table, the conclusion can be drawn that mean surface temperatures are coherent or consistent spacewise in most months of the year but that they are rarely coherent from year to year, except in April. During April maximum convective activity may be expect- ed, and, since OWS ECHO is in the area of 18=degree water discussed by Worthington (3), temperatures are consistent because of the annual water mass formation process? Analysis of the Experimental Data At the various ocean weather stations, two to four BT's were taken each day. The requirement of a minimum of 10 observations limited area size to l-degree quadrangles and time periods to 1 month. During the four experimental surveys, BI's were taken every half hour. Thus,it was possible to reduce area size to 10-minute quadrangles and time division to 5-day periods. The mean, standard error of the mean, and the standard deviation of the various thermal structure parameters were computed for each of the four experimental cruises and are presented in tables 21 through 2h, (appendix B). The 2-way analysis of variance and the t test also were applied to each 5-day-10-minute quadrangle sort. The resulting probabil- ities are presented in tables 11 through 20. The 5-day means of adjacent 10-minute quadrangles and alternate 10-minute quadrangles are results of testing means of all data recorded within adjacent and alternate 10-minute quadrangles during the same 5-day period. The successive 5-day and alter- nate 5-day means are results of testing means of all data recorded during successive and alternate 5-day time periods within the same 10-minute quad- rangle. Blank spaces in the tables indicate lack of data. If the data are assumed to have been taken at random over the 10-min- ute quadrangles during the same 5-day periods, the tests of adjacent and alternate 10-minute quadrangles indicate significant difference in the indicated thermal structure parameter over approximately 10- and 20-mile distances. Referring to entries in table 11 reflecting results of experimental observations (columns involving 5-day means and 10-minute quadrangles), there is good probability of no significant difference between adjacent areas for all four experiments, whereas there is probably a significant difference between 5-day means for the experiments in March, May, and November, indicating significant short-term thermal changes which affect- ed all areas more or less simultaneously. These short-term changes are of broad scope affecting major portions of the ocean. RESULTS OF ANALYSIS Appendix C contains graphs of the population mean monthly values of each parameter of the thermal structure (historical data from the 20-minute quadrangle centered at 35°N,48°w). Experimental data were used as a reliability check of the historical data. If the means of the experimental data fell within the range of the historical maximum and minimum means, the historical data were considered to be reliable. Means for March generally were not valid because of the lack of data, or because comparisons indicated that the historical data were in error. Comparisons also indicated that the mean gradient is dependent on the type of BT employed (450 or 900 feet). Thus, parameters of the mean gradient of the historical data are not accurate. All compar- isons can be observed in the graphs in appendix C. They are also listed in column 5 of table 25 (appendix B). When the population mean monthly values were plotted the resulting curves were sinusoidal. If the comparison of the means (historical ver- sus experimental data) indicated reliable historical data for all months, the parameter curve was smoothed by Fourier analysis on the LGP-30 com- puter. The results of the Fourier fitting are: Surface Temperature (2) y =71.60- 6.61 sin x - 2.68 cos x+1.29 sin 2x+0.36 cos 2x Maximum Gradient-Gradient (3) y=4.81 - 1.328 sin x - 1.068 cos x+0.456 sin 2x - 0.034 cos 2x Maximum Gradient-Thickness (4) y=91.0 - 44.9 sin x - 35.2 cos x+18.3 sin 2x+9.0 cos 2x Maximum Gradient-Temperature of the Upper Bound (5) y=71.90 - 5.36 sin x - 2.12 cos x+1.63 sin 2x - 0.20 cos 2x First Gradient-Thickness (6) y=107.0 - 80.6 sin x - 66.2 cos x+22.7 sin 2x+8.0 cos 2x where y=the desired parameter mean for a given month, x=15° for January ,; =h5° for February, =75° for March, etc. Minimum and maximum values could be determined from these curves. These values usually occur 6 months apart; however, month of occurrence varies from parameter to parameter. Minimums and maximums of some pa- rameters may persist for a period of 2 months, as shown in columns 2 and 3 of table 25 (appendix B). This indicates that thermal structure change occurs at a relatively slow rate during maximum and minimum pe- riods. The minimums and maximums of certain parameters, however, do not consistently occur in the same month from year to year. Owing to use of a 450-foot BT to obtain the historical data, minimums and maximums of certain parameters could not be computed with any degree of reliability during January, February, March, and April. Maximum surface temperature can be expected during August or Sep- tember. The minimum occurs during March or April. The layer depth and depths of the upper bound of the maximum gradient and first gradient are maximum in January or February and are minimum about 6 months later. The minimum gradients occur in winter — usually a month or two after the maximum depths. The gradients and their thicknesses are usually maximum during August. The maximum standard deviations for surface temperature, as recorded in appendix B, were compared month by month for each parameter. This compar- ison showed that November surface temperatures yielded the largest standard deviations, indicating that temperature changes were greatest during this month. April had the next largest standard deviations; however, these were not nearly as large as those for November, indicating that spring warming oceurs at a slower rate than autumnal cooling. Months of minimum surface temperature change are January, February, August, and September. Although the probability values given in tables 11 through 20 are only approximate, the indicated trends probably are valid. A study of the individual probabilities indicates considerable variation. This may be 8 a true condition or may be due to lack of adequate data samples. To eliminate the variation and to obtain a clearer picture of trends, means of the probabilities for all months were computed (table 20). The results indicate that probability of persistence is highest for all thermal struc- ture parameters when comparing means of areas during the same time periods. The highest probability is found by comparing monthly means of adjacent l-degree quadrangles. With exception of surface temperature, all param- eters have a mean probability greater than 90 percent that no significant difterence exists (95% level of significance). This indicates that vari- ability between adjacent 1l-degree quadrangles is partially masked by the use of monthly means. The next highest mean probability resulted from comparison of 5-day mean adjacent 10-minute quadrangles. However, this probability was only slightly higher than that for the comparison of 5-day means of alternate 10-minute quadrangles. Thus, the variability within a 10-minute quad- rangle over a 5-day period is nearly the same in an area roughly 20 miles away as in one 10 miles away. In general, all thermal structure parameters varied more from one 5-day period to the next in one area than they do between 10-minute quadrangles during the same 5-day time period. The lowest mean probability of all parameters was recorded for 10-minute quad- rangle, alternate 5-day means. It was the only recorded paramet*r with mean probability below 50 percent. Parameters exhibiting greatest spatial persistence are the gradients of the first and maximum gradients and the thickness of the maximum gra- dient. Parameters exhibiting least spatial persistence are the gradient of the mean gradient, the layer depth, and the temperature of the upper bound of the maximum gradient. As mentioned previously, the magnitude of the mean gradient is related to the BT type (450 or 900 feet) and is not a reliable statistic. The only parameter exhibiting a high degree of temporal persistence is the thickness of the first gradient. The gradients of the first and maximum gradients apparently persist from one 5-day period to the next but vary from year to year. Surface temperature and the temperature of the upper bound of the maximum gradient show the greatest temporal vari- ability. One objective of this study is determination of area size for which a@ point temperature structure forecast is applicable within statistical limits. A direct solution of this problem necessitates comparison of individual observations. Since locations of individual observations may be in error by as much as 5 miles, such comparisons may be invalid. It is hoped that errors may be minimized through processing of large amounts of data. Thus, the quantity of data available may indicate the analysis potential or limitations. If the spatial variation in the thermal structure occurring at any given instant within a 10-minute quadrangle is assumed to be equal to or less than the variation in a 5-day period within the same area, table 26 can be used to give an estimate of the spatial variation. For example, variation in surface temperature during March within a 10-minute quad- rangle is (+3 x e637) or + 1.11°F for 100 percent probability; and (+2 Kies) Ores 74 OR for 95 percent probability. This estimate should be fairly accurate, because errors in the method tend to cancel each other. Months of maximum and minimum variability for each thermal structure parameter are listed in table 26 (appendix B). These values were determined by computing the mean standard deviation for all 5-day, 10-minute quadrangles and 3-week, 10-minute quadrangles. The results were checked against histor- ical data and found to be in approximate agreement. However, both sets of data were insufficient for determining months of maximum and minimum vari- ability. QUALITY OF THE DATA AND STATISTICAL ANALYSIS The magnitude of the various errors involved in the methods of obtain- ing, processing, reading, and analyzing the data properly are of sufficient importance to warrant a separate study. Thus only a brief qualitative discussion is presented here. A number of reports dealing with BT errors are available. The most comprehensive study is probably that of Bralove and Williams (4). By use of their gualitative report and the SERC deck, some of the errors associ- ated with BI data can be quantitatively analyzed. They result from instru- ment limitation (limited accuracy), calibration (malfunctions), operational (human error), reference temperature, data processing, and location error. The magnitude of the location error, which cannot be determined, varies from cruise to cruise and from station to station and certainly reduces the reliability of the analyses. Conclusions based on the analysis of variance technique are valid if observations are randomly chosen from normally distributed populations having approximately equal variances. However, the observations were not taken at random over any given area (e.8e, a l-degree quadrangle), rather they tend to be concentrated about the central location of 35N,48w. Also, times of observation are not random within each area. Fortunately, inves- tigation shows that the results of the analysis are changed little by mod- erate departure from the assumptions. Distribution curves were plotted for each month and parameter. The analysis of variance and the t test were applied only to groups of data having approximately normal distributions and equal variances. Because of extreme care exercised on the four experimental cruises, instrument and operator errors were assumed to be minimal for comparison purposes. To obtain an indication of the magnitude of the instrument errors, the ratios of the standard deviations of the historical data to the experimental data for the 20-minute quadrangle centered at 35°N, 48Ow were computed. If the size of the area and the time period were the same for both sets of data, the standard deviations should be approximately the same for any given parameter. If a ratio of the two standard deviations did not approach unity, 10 the excess of one deviation over the other was attributed to causes other than space and time variations, e.g., instrument error or data processing errore Normally, both experimental and historical data might contain instrument error. The standard deviations were not directly comparable, because the time periods of the experimental data were only two-thirds those of the historical data. The ratios (table 25) for various parameters related only to depth varied from 0.95 to 1.14, well within the 33 percent variation that can be attributed to the difference in length of the time periods. Thus, the magnitude of error incorporated into the standard deviations is approximately the same for the historical and experimental data. However, the standard deviation ratios of various parameters related to temperature consistently fell beyond the 33 percent tolerance and varied between 1.45 and 2.66. This indicates that standard deviations of historical data related to temperature contain a large error factor. CONCLUSIONS Conclusions drawn from analysis of the data are pertinent to vari- ations in the thermal structure only at ocean weather station ECHO. Stud- ies are contemplated for other stations. The following specific conclu- sions are made: 1. Because experimental cruise data are of much greater value than historical data, samples should be collected at other ocean weather stations for comparison purposes. 2. Monthly means of parameters of the thermal structure show sinus- oidal annual curves. 3. The temperature element of the 450-foot BT appears to be subject to considerable error; the pressure element appears to be relatively stable. Temperature errors may indicate reference temperature errors. 4. The probability of persistence for all thermal structure parameters is highest when comparing means of all observations taken over a period of @ month within adjacent l-degree quadrangles. This result supports the persistence theory explained by Perlroth and Simpson (5). 5.- The probability of persistence is quite low when comparing year- to-year mean monthly values of all observations within a l-degree quadrangle. 6. The probability of persistence for any parameter during the same 5-day period is generally greater between adjacent 10-minute quadrangles than it is between consecutive 5-day time periods within the same 10-minute quadrangle. ‘ 7- The gradients of the first and maximum gradients and the thickness of the maximum gradient exhibit greatest spatial persistence. 8. The only parameter exhibiting high temporal persistence is the thickness of the first gradient. 11 12 9. Conclusions 4 through 8 are limited to months and parameters that exhibit normal distribution. ACKNOWLEDGEMENTS All historical BT and weather observations were collected by U.S. Coast Guard personnel at ocean weather stations. Appreciation is also due various personnel of the Oceanographic Office who provided helpful suggestions, who carried out the field surveys, or who assisted in the many phases of data processing and programming. Special acknowledgement is due Mr. R. Bolton who wrote the SERC thermal structure program for Datatron use (appendix A). be REFERENCES U.S. Navy Electronics Laboratory A BL Coding System for Shallow Water Data, by L. A. Harvey. San Diego, California, 21 July 1954. (Tech Memo No. TM=39). 5 pe Kendall, M. G. The Advanced Theory of Statistics. London: Charles Griffin and Co. Limited. Vole II. 1946. pp 220-229 Worthington, L. C. "The 18° water in the Sargasso Sea," in Deep-Sea Research, Vol. 5, No. 4, May 1959, pp. 297-305. Bralove, A. Le, and E. I. Williams. A Study of the Errors of the Bathythermograph. National Science Laboratories, Inc., Washington De Gy Uslsas Gila Perlroth, I. and L. Simpson. "Persistence of Sea Surface Temperature Patterns," in Undersea Technology, Vol. 3, No. 4, July/August 1962. APPENDIX A DESCRIPTION OF THE DATATRON 205 PROGRAM 13 p rc ‘ Th) gee i APPENDIX A DESCRIPTION OF THE DATATRON 205 PROGRAM The five main functions of this program are; 1. Determination of the depth at which speed of sound is maximum. This level is defined as the layer depth. Sound velocity is computed from the following polynomial: Sound velocity = a+T; [e +T;(-c +a T;)| + eZ; where a = 4742.2h73 b= 15.316241 e = 18545565 ad = .00103379 e = 05938308 Tj; = Temperature (°C) at 4; = Water depth in meters If the maximum computed sound velocity is at the lowest depth on the BT trace; this depth is recorded as the layer depth with an X overpunch in column 58. 2. To search the digitized BT trace between the surface and 80 feet for the surface effect. The surface effect must have a nearly constant slope with an absolute value greater than 1°F/100 ft between its lower bound and the surface. A leeway factor of 0.5°F/100 ft is allowed between slopes. If this slope extends below a depth of 60 feet, the surface effect is recorded as 60 feet with an X overpunch in column 76 of the master card for ecard output and is preceded by a negative sign on print out. In all other eases the depth of the surface effect is recorded as the upper bound of the first slope interval that fails to meet the stipulated requirements. The mean gradient of the surface effect in °F/100 ft is also recorded. If the search indicates no surface effect, zero is entered in all appropriate eolumns of the master card. 3- To determine the maximum gradient, each depth interval below the recorded surface effect is examined.* The BI depth intervals are always considered to be 20 feet. Thus all 40-foot intervals (360 to 880 feet) are linearly interpolated into two 20-foot intervals. The upper bound of the first interval having a slope equal to or less than -2°0R/100 ft is recorded (in the computer program -3°F, etc., are less than aor) e *When this program was written, temperature data were assumed to be continuous. Occasionally a temperature value was omitted from the punch card at an intermediate depth. The card was punched 000, indicating no data. The Datatron program recognized this depth as the last recorded interval and accordingly computed the gradients only to this depth. Expe- rience shows that a linear interpolation over the adjacent depths should be made. Gradients computed by use of the interpolated values are more realistic. 15 16 When two consecutive intervals are found with a slope greater than -2°F/100 ft or when one interval is found with a slope greater than 0°/100 ft, the lower bound of the last slope with value less than -2°F/100 ft is recorded. The slope between the two recorded bounds is computed and recorded as a gradient. An identical search is begun at the last examined interval. When all such gradients have been examined, the data for the gradient with the greatest absolute value is recorded for output as the maximum gradient.* If no gradient meets the requirement, all columns for the maximum gradient are recorded as zero on the master card. Exceptions to this procedure are: a. Gradients less than 40 feet thick are not recorded unless the slope is less than -25°F/100 ft. be If a maximum gradient continues to the end of the trace and the last interval meets the requirements for inclusion in the gradient, the depth of that interval is recorded as the lower bound of the maximum gra- dient. If the last interval has a negative slope but does not meet the requirements of a maximum gradient and the next to the last interval is included in the maximum gradient, the lower depth of the latter interval is recorded as the lower bound of the maximum gradient. In either event, column 68 of the master card is X overpunched and the value of the maxi- mum gradient is preceded by a minus sign on print out. 4. To determine the mean gradient the digitized trace is searched for the first interval below a recorded surface effect with slope less than -1°F/100 ft. The upper bound of this interval is recorded as the upper bound of the mean gradient. A search is made below this point for the lowest temperature of the digitized trace. The depth of the lowest temperature is recorded as the lower bound of the mean gradient. The slope between the upper and lower bounds is computed and recorded as the mean gradient. If positive gradients exist in the mean gradient, column hO of detail card no. 3 is X overpunched, and the mean gradient is pre- ceded by a negative sign on print out.** If no gradient meets the requir- ement, all columns for the mean gradient are recorded as zero. 5. To determine the first gradient the portion of the digitized trace below the recorded surface effect is searched for the first gradient with slope less than -1°F/100 ft. The upper bound of this gradient is recorded and the remainder of the trace is examined until either slopes in two adjacent intervals equal to or greater than -1°F/100 ft are found or until a slope greater than 0°/100 ft is found. If the first gradient is not found in the digitized BI trace, all columns for that entity are recorded *Some key punch and coding errors escaped a cursory check. The program was written to reject any observation as being in error when the computa- tion resulted in a gradient greater than 100°F/100 ft. Experience has shown that this threshold value should be reduced to 20°F/100 ft. **Experience shows that positive gradients are never detected by this search. The entire BT trace should be searched for a positive gradient, as well as the mean gradient. as zeroe The bottom bound of the last interval with slope less than -1°F/100 ft is then recorded. The slope between the upper and lower bounds is computed and recorded as the first gradient. The following are except- ions to this procedure: ae A gradient with thickness less than 40 feet and slope greater than -2°F/100 ft is discarded, and a new search is begun from the last interval examined. be If the first gradient persists to the end of the trace and the last interval meets the requirements for inclusion in the first gradient, the depth of the last recorded temperature is designated as the lower bound of the first gradient. If the last interval of the digitized graph has a negative slope but does not meet the requirements of a first gradient, and the next to the last interval is included in the first negative gradient, the lower depth of this interval is designated as the lower bound of the first gradient. In either event, column 68 of detail card no. 3 is X overpunched and the first gradient is preceded by a minus sign print out. 17 jek uatrwoniupe Batis ives ao * a mal ce Ve paling? bs bhai nrliet . re ‘ius ‘him fee ia han ei nie ye ae “at yk {aa Veo at at . Ne 2 ca | is f sa ea Bo Ase a wy 5a et Vie. | ne a Pr Ds ; Lim AFR a hhes aint prorky Paes WM Pomeet ite Pty OES Wiest ea \ ahs ANT: Be eae : Lf ee ae er a ae ied ain Ghat a ee i APPENDIX B STATISTICAL ANALYSIS OF PARAMETERS ug) Statistical Analysis of Historical Data for Chosen Parameters One = Degree Quadrangle 35, 47W 35N, 48w 35N,48W x Monthly Sea Surface Temperature (°F) Number of Years of Data 0 Ow NW AA Wo 19 AO AAW Fr CO Ow FW AWW Ww Table 1 Maximum Minimun Mean Mean JANUARY Gileert 66.0 67.8 65.9 68.7 6561 70.3 65.0 69.9 65.0 FEBRUARY 65.8 65.8 67-6 64.8 67-4 64.7 67.5 64.4 asee 64.3 MARCH 65-7 64. 66.7 64.2 66.8 307 APRIL 66.7 66.3 66.0 65-3 66.3 6501 67.0 61.5 66.7 61.9 MAY 70.0 65.4 69.1 67-3 68.3 65.0 69.6 64.4 69.6 66.8 JUNE 1503 724 Th.9 Tec2 Th el (lventi 74.2 67.8 T4.5 67.8 * 20-minute square centered at this location Maximum Standard Error Maximum Standard Deviation al Table 1 (con) One= Number Maximum Maximum Degree of Years Maximum Minimum Standard Standard Quadrangle of Data Mean Mean Range Error Deviation JULY 34.NL-7W 2 Se) Titiole 0.5° e271 1.10 34 N48W 5 1905 76.8 2el @ 1.91 35NL-7W 3 796 hee 2 ol 36 1.52 35N48W 7 78.8 154 304 ool 2.13 36NL8W 1 76.8 76.8 ~~ ook Asis} 35N48W* 8 78.8 “ST Beil Seri 2.19 AUGUST 34N47W 2 1907 1961 0.6 od 1.61 34NL8W h 80.7 78.1 2.6 oS 1.50 35NL8W 8 80.2 76.0 4.2 016 1.65 35NUSWe 8 80.1 T7103 Bie{s} 19 1.68 SEPTEMBER 34NL-7W 2 80.8 78.2 2.6 256 vero Zu NEW 6 81.8 76 4 54 a) fil 141 35NL-7W 3 192 77-0 2.2 ol 141 35N48W 7 80.3 tee Shall Hey 1.65 3 5NLSWe 8 80.6 Eitee 34 eis} 1.67 OCTOBER 34NL-7W wh, 762 1602 ae 266 2.08 3uNL8W 2 1905 1905 == 055 1.92 35N4-7W 2 ya PS) 74.9 320 eer eas 35NL8W 7 78.6 74.26 4.0 oy) 2.51 35NL8W 7 78.4 Tee 4.2 48 2025 NOVEMBER 34NL-7W 3 ated TECH hk 085 3.60 34 N4SW 5 76.0 7203 307 1.28 4.23 35NL-7W 5 1505 7109 3.6 oT 3019 35N48W 6 [607 7129 4.8 261 4.09 35NLEW* 8 76.8 69-1 Tiel oS 3.86 DECEMBER 3LNk8w 3 ToD 68.2 563 e91 2.87 35NL7W h Tals) 69.1 322 263 2.19 35N48Wx 7 eee 69.3 2.9 31 2.06 * 20-minute square centered at this location 22 Table 2 Statistical Analysis of Historical Data for Chosen Parameters Monthly Layer Depth (ft) One. Number Maximum Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obs.e> Quadrangle of Data Mean Mean Range Error Deviation Max. BI Depth JANUARY 3hNL-7W 3 357 200 157 (ied: 45.4 70 ZL NYSW h 370 327 3 5323 92 4 72 35N4-7W 3 400 365 SB) 2329 47.3 72 35NUSW 8 380 273 107 66.3 162.3 57 35N48W* 8 376 289 87 49,2 147-7 60 FEBRUARY 34N48w 6 377 180 197 T1e5 154.9 78 35N4-7W 3 370 250 120 21.3 212.1 76 35NL8W 7 347 90 257 83.5 166.9 90 35NUS We 7 360 72 288 67eL 150.1 80 MARCH 34.N4SW 1 300 300 on 2361 40.0 70 35NL-7W h 360 220 140 86.0 172.0 8h 35N48W 6 360 153 207 83.3 144.2 80 35NLSWx 7 360 129 231 OTe! 202.2 67 APRIL 34NL-TW 2 273 91 182 33-3 110.4 ho 34NL8W 3 298 8 290 49.9 141.2 50 35NL-7W 3 208 91 117 115.7 200.3 5h 35N48W i 306 55 251 146.6 165.5 T 35NL8We 1 303 48 255 32e1 15007 22 MAY 34.Nk-7W 2 70 51 19 hO.2 98.6 3h 34NLoW 2 62 62 =e 10.5 33.3 ) 35N4-7W 5 120 28 92 50 4 142.6 13 35N48W 8 111 20 91 1726 98.0 Tt 35N48W* 9 151 33 118 21.7 119.0 2 JUNE 34NY- TW 3 20 6 14 6.8 26.2 ) 34NLSW h 51 6 h5 10.9 30.0 9) 35N4-7W 3 33 18 15 2.8 30.4 fe) 35N48W 6 h7 10 37 To3 42.3 ) 35N48 We 6 32 h 28 907 6307 0) * 20-minute square centered at this location 23 Table 2 (con) One= Number Maximum Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obs. > Quadrangle of Data Mean Mean Range Error Deviation Max. BT Depth JULY 3u.NL-7W 2 32 20 12 Ted 30.9 fe) 3k N4SW 5 27 8 19 40) 29.2 fe) 35N4-7W 3 yh 12 32 8.9 38.6 ) 35N48W a 27 10 ale 302 26.8 fe) 36NL8W 1 h h eg 2e3 8.5 (@) 35NL8We 8 y ar 2.3 30-1 fe) AUGUST 34NL-7W 2 32 27 5 Gee ee fe) 3kNASwW h hh 29 15 925 31.5 0) 35NL8W 8 ka ily¢ oh. es 3563 ) 35Nu8W* 8 37 18 19 4.8 34.2 0) SEPTEMBER 34NE- TW 2 80 27 53 Tae} 40.8 (e) 34NLow 6 10h. yh 60 11.8 49.6 @) 35N4-7W 3 103 17 26 14.9 51.8 ) 35NLEW Ti 98 26 72 65 58.8 fe) 35N4SW* 8 96 48 48 ier 55.5 (0) OCTOBER 34LNATW 1 138 138 == 2126 68.3 0) 3hN4Sw 2 140 140 “= et 25.6 ) 35N4-7W 2 199 ial 82 pean 98.5 (e) 35N48W if 202 106 96 14.7 68.7 0) 35N48W 7 171 120 51 10.0 68.7 fe) NOVEMBER 3uNL-TW 3 234 219 15 12.6 6507 6) 34. NSW 5 280 162 118 23.0 74.28 fe) 35N4-7W 5 278 203 175 22.2 10.2 9 35N48W 6 269 207 62 14.7 1728 h 35N4S8Wx 8 278 147 131 15.5 196 2 DECEMBER 34N4-7W 2 318 263 55 8.7 OT oh 19 34unhsw 3 366 27h 92 32.5 103.0 28 35N4-7W h 329 264 65 20.2 70.0 5 35N48W 7 374 203 slab 12.3 7506 25 35N4u8w* 7 367 28h. 83 3 6: 679 26 * 20-minute square centered at this location oh Table 3 Statistical Analysis of Historical Data for Chosen Parameters Gradient of the Thermocline (Maximum Gradient) (°F/100 ft ) One = Number Maximum Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obs. > Quadrangle of Data Mean Mean Range Error Deviation Max. BT Depth JANUARY 34NL-7W 3 -- -- -- -- -- 100 34NLSW 4 on = -- -- -- 100 35N4-7W 3 -- =< so -- -- 100 35NL8W 8 4.22 242 1.80 052 eli 8h 35N48W* 8 4.25 3-42 283 49 DST 8h FEBRUARY 34 NL8W 6 2.35 2635 -- -- -- oh 35N47W 3 2s es “= -- =e 100 35N48W Ti 2.00 2.00 fe oat ae 98 35N48W* 7 4.67 2075 1.92 e3L 093 96 MARCH 34 NOW at -< -- -- -- -- 100 35N4-7W 4 -- -- -- -- oe 100 35N4uSW 6 a mn -- -- == 100 35N4Sw* 7 -- -- -- -- -- 100 APRIL Su NL-TW 2 == =< -- — =< 96 34NLSW 3 -- oe -- -- 2 100 35N4-7W 3 3-40 3.37 203 229 1.64 96 35NL8W a 4.00 2.50 1.50 012 1.02 96 35N48W* 7 34h 2.50 9h 268 2.18 95 MAY 34NE-7W 2 7013 425 2.88 085 Bor 50 3uNLSW 2 5.09 3-70 1.39 94 2.98 30 35NL-7W 5 4.80 2074 2.06 260 2.56 52 35N48W 8 5230 3216 Doee 229 3.06 50 35N48W 9 5085 3230 2055 056 son 39 JUNE 34NL-7W 3 8.30 5067 2.63 1.07 3-05 fe) 34N4SW h 8.30 4.23 4.07 Aral 2035 ) 35NL-7W 3 een 5678 1.49 86 2.72 e) 35N48W 6 6.65 4.06 2.59 57 2.62 y 35N48W* 6 7.00 4.63 2.37 076 5.00 2 * 20-minute square centered at this location ’ 2 Number fable 3 (con) of Years Maximum Minimum of Data © Ow V1 WwW AANMNE CON WwW Orv) (eowooy aye) OrPAWwu A FWP Mean Mean Range 1. 1.93 * 20-minute square centered at this location 26 Maximum Maximum Standard Standard Deviation Max BT Depth Error cee EE Percentage of Obs. > ooOo000 ooo°o oOo0o0o0°0 OoOo0000 Table 4 Statistical Analysis of Historical Data for Chosen Parameters Depth of the Upper Bound of the Maximum Gradient (ft) One = Number Maximum Maximum Degree of Years Maximum Minimum Standard Standard Quadr e of Data Mean Mean Range Error Deviation JANUARY 34 NA TW 3 -- -- -- =o -- 34Nu8W h -- -- -- -- -- 35N4-7W 3 -- -- -- -- =< 35N48W 8 390 322 68 12e2 40.5 35N48W* 8 390 3h6 hh 9.8 36.3 FEBRUARY 34NLSwW 6 360 360 “= -- -- 35N4-7W 3 -- =< =< -- -- 35N48W uf -- -- -- = a 35Nu8Wx < 313 271 4a 6.8 20.3 MARCH 34NLSW iL -- -- -- = <2 354-7 4 -- -- -- -- -- 35Nu8W 6 == = ve ee ae 35N48W* Tf -- -- -- -- -- APRIL 344-7 2 -- -- -- =5 ae S4UNLEW 3 -- -- <5 = = 35N4-7W 3 92 92 -- 13.7 43.) 35NL8W 7 133 100 33 37k 64.2 35N48wx Tf ily 72 ks 40.0 56.6 MAY 3uNYTW 2 85 70 15 14.4 49.8 34 NEW 2 92 89 3 14.4 6520 35NL-7W 5 140 80 60 GAT 50.1 35N48W 8 143 Fal 72 22.6 83-4 35N48w* 9 218 TI 141 29.8 98.9 JUNE 34NE TW 3 7 ho 29 18.1 82.8 34NL8w h 82 52 30 14.7 yh 7 35N4-7W 3 86 7h 12 31.0 98.0 35N48W 6 116 56 60 BG 74.0 35NL8W* 6 olate 63 48 NOGY/ 66.0 * 20-minute square centered at this location 27 Table 4 (con) One = Number Maximum Maximum Degree of Year Maximum Minimum Standard Standard Quadrangle of Data Mean Mean Range Error Deviation JULY 34 NL-TW 2 7 56 18 1661 66.2 34. NSW 5 74 28 6 we) 48.4 35NE-7W 3 72 58 14 Siar 56 4 35N48W 7 66 38 28 7.0 59.0 36NL48W a 26 26 =e Tigh 16.5 35N4OW% 8 [2 38 34 129 58.6 AUGUST 3uNL-TW 2 70 65 5 9.5 3Lel 34N48W h 76 69 a 10.2 32 35N4EW 8 98 56 he 5.8 32.6 35N48W* 8 89 ho ho 5.8 Wh 5 SEPTEMBER 34NL-7W 2 148 135 13 2253 43.3 34N4SW 6 141 122 19 10.9 37-6 35N4-7W 3 12) 122 2 TAS 29.5 35N48W 7 131 106 25 1.60 Sle 35N4SWx 8 145 110 35 6.9 45.9 OCTOBER Su NLTW 1 190 190 =< 18.0 56.8 34 NEW 2 152 152 2. 8.0 27.6 35NL7W 2 287 149 138 12.9 54.9 35NL8W 7 261 LAL 120 14.0 576 35NLEW* 7 270 Lh 126 10.5 59.2 NOVEMBER Sh 7W 3 270 223 47 9.8 393 3 NSW 5 3h9 233 116 18.6 67 el 35N47W 5) 312 239 133 23-4 TOmls 35N48W 6 276 237 39 14.8 726 35N48W* 8 Shy 235 109 13.4 7509 DECEMBER 3uNYTW 2 331 331 22 905 28.5 34 NLSwW 3 hoo 320 80 353} 40.0 35N4-7W h 350 2hs8 102 11.9 40.9 35N48W 6 400 262 138 OAT yh 2 35N48W* i 391 321 70 ILS) 43.7 * 20-minute square centered at this location Table 5 Statistical Analysis of Historical Data for Chosen Parameters Thickness of the Maximum Gradient (ft) One = Number Maximum Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obs. > Quadrangle of Data Mean Mean Range Error Deviation Max. BT Depth JANUARY 34N4-7W 3 -- =< -- -- -- 100 34NL8W h == -- -- -- -- 100 35N4-7W 5 -- -- -- -- =< 100 35N4oW 8 ho 16 4.8 WSAT/ 86 35N4SW* 8 56 ho 16 4.8 16.3 92 FEBRUARY 34NL8W 6 -- -- -- -- -- 100 35N4-7W 3 -- -- -- -- oe 100 35N48W 7 = -- -- =-- -- 100 35NLSW* i -- -- =-- -- == 100 MARCH 34NLoW 1 -- -- -- =< -- 100 35N4-7W 4 -- -- -- -- o 100 35N48W 6 -- -- -- -- -- 100 35N48W* T -- -- -- -- -- 100 APRIL 3uNLTW 2 -- -- -- -- -- 100 34NL8W 3 -- -- -- -- -- 100 35N4-7W 3 60 60 == 8.8 26.5 88 35N48W 7 7 ho 7 Gan 11.5 ok 35N48w* 7/ hg HTT@) 9 509 LST 96 MAY 34NL-7W 2 ho 17 6.9 23.9 55 34N48W 2 66 52 14 Mee 19.0 39 35N4-7W 2 55 5D == 16.3 21.1 35N48W 8 719 h3 36 8.6 43.3 ho 35NA8W* 9 7h 49 25 667 29.8 ho JUNE 34.NL-7W 3 108 70 38 18.6 39.3 aa 3LN48w k 171 72 99 14.6 Th el 9 35N47W 3 108 100 8 14.3 59.2 5 35N48w 6 131 5h 17 10.8 53.6 15 35N48W 6 Alaiye 86 31 10.9 65-2 12 * 20-minute square centered at this location 29 Table 5 (con) One — Number Maximum Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obs.> Quadrangle of Data Mean Mean Range Error Deviation Max. BI Depth JULY 34NL-7W 2 194 180 14 25-0 85.9 13 34. N48W 5 TSO” 149 39 qo ch 60.6 ) 35NLTW 3 192 152 ho 14.0 59.9 8 35NLSW 7 185 1h9 36 8.5 lie 3 13 26NLEW ai irels alial oe 13.9 51.9 fe) 35N48W* 8 186 150 36 8.9 6567 aa AUGUST | 34 NL TW 2 188 174 14 21.9 69.3 Tl 3uNu8w 4 219 175 yh Ged: 53.8 9 | 35NL8W 8 215 1h9 66 ol! 78.3 22 | 35N48W* 8 215 181 3h 10.4 WS ah 22 | SEPTEMBER 3uNuTW 2 20h 133 val 25.6 62.8 30 | 34 NEW 6 210 158 52 13.4 59.3 16 35NL-7W 3 188 151 37 16.8 52.8 17 35NL8W Ve 198 167 31 16.3 6563 16 35Nu8w* 8 200 153 h7 9.2 64.1 15 OCTOBER 34 N4-7W 1 134 134 -- 18.4 48.6 30 34N48W 2 169 169 -~ 8.6 22.7 ho 35NL-7W 2 172 172 2 Sisal 41.3 33 35N48W ff 15 114 5S 17-1 59 4 37 35NLEW* Fi 168 115 53 12.6 59.2 34 NOVEMBER Su TW 3 120 85 35 20.0 3529 59 34 NEW 5 98 ho 58 IL) 39.8 35 35N4-7W 5 ala 56 61 apa TT) 36 35N48W 6 106 72 3h 10.8 47.2 34 35N4SW* 8 108 57 51 8.0 41.6 ok DECEMBER Su NY-TW 2 65 65 -- 18.9 37-9 80 3h. Nk8w 3 67 ho 27 607 Lees 88 35N4-7W 4 TT 63 14 Gel 23.0 mt 35N48W 7 80 53 27 8.9 20.3 68 35N48W* 7 80 52 28 Lie 23-1 76 * 20-minute square centered at this location 30 Table 6 Statistical Analysis of Historical Data for Chosen Parameters Temperature of the Upper Bound of the Maximum Gradient (°F) One —- Number Maximum Maximum Degree of Years Maxinun Minimum Standard Standard Quadrangle of Data Mean Mean Range Error Deviation JANUARY 34k 7W 3 -- =< -- -- -- 34N48W h -- -- -- -- == 35N47W 3 =< ae a == == 35N4SW 8 69.6 65-6 TeXe) 039 296 35N48W* 8 69.6 6526 4.0 039 096 FEBRUARY 34.N4SW 6 67.0 67.0 -- — ise 35N4-7W 5 -- -- -- -- -- 35N48W 7 -- -- -- -- -- 35N48W* 7 1007 67.8 2.9 3 oh 5.97 MARCH 34 NLSW aL -- -- -- -- -- 35N4-7W 3 -- -- =< -- -- 35N48W 6 -- -- -= -- ~= 35N48W* 7 66.3 66.3 -- ol 1.00 APRIL 34NLTW 2 -- -- -- -- -- 34N48w 3 -- -- -- = = 35N4-7W 3 66.9 66.9 -- 51 1.62 35N48W 7 68.3 60.7 706 e1l5 026 35N48W* uv ALA 62.4 9.2 a 2.99 MAY 34N4-7W 2 69.7 69.7 -- ody ee 34NL8w 2 69.5 670 2.5 oY 1.65 35N47W 5 68.0 64.67 303 1.14 2054 35N48W 8. 69.2 66.2 320 263 2.18 35NuoW* 9 69 66.4 3.0 039 1.38 JUNE 34NL-7W 3 Fl Peal TleT 204 256 2.59 34NL8W h Teel [007 304 e716 2.29 35NL-7W 3 729 7203 6 49 1.54 35N48W 6 Tel 66.5 dee 49 2.88 35NL8W* 6 74.0 66.5 Te5 oT 2.90 * 20-minute square centered at this location Table 6 (con) One = Number Maximum Maximum Degree of Years Maximum Minimum Standard Standard Quadrangle of Data Mean Mean Range Error Deviation JULY 34NL-7W 2 Toe 7720 52) 42 Lea 34 NL8W 5 719 02 76.4 2.8 260 2.07 35N4-7W 3 TI el 76.6 2.5 49 2.24 35N48W 7 78.4 74.6 3.8 o 3h 246 36N48W 1 7603 7663 -- “38 22 35N48W* 8 78.4 1520 304 029 247 AUGUST 34N4-7W 2 T1901 78.8 43 49 GES 34 NL8W h 199 tee 2.5 046 14h 35N48W 8 719 ot Omit Qe e2l 1.21 35N48W* 8 1905 76.8 Dar cule ee SEPTEMBER 344-7 2 798 W901 Pye 083 2.63 34 Now 6 80.8 1605 4.3 6 1.60 35NL-7W 3 790 76.8 2.2 © 36 1.26 35N48W Ti 799 (our 3.2 ° 33 1.61 35N4SwW* 8 8001 "eit 304 033 eSB OCTOBER 34uNL7W a 154 1504 Coard e(9 2.48 34NL8w 2 1903 1923 -- 055 1.92 35NL-7W 2 eo 74.0 36 °30 1.17 35NL8W i 7825 V2 4.3 oy 3206 35NL8W* 7 78.3 720 4.3 -68 2.05 NOVEMBER 34NL-7W 3 We 72.03 5.3 289 3.46 Zu NSW 5 Toee 719 39 1.48 Woh 35NL-7W 5 1503 71.9 34 1.15 4.06 SNuSw 6 (eo) 7.5 5.5 262 oh 35NLSW* 8 769 68.7 8.2 48 3.93 DECEMBER 34NL-7W 2 69.0 69.0 -- 53 293 3h NSW 3 7320 69.2 B18 eel 247 35N4-7W h 726 67 4 562 60 2.00 35N48W e TEHe 68.0 4.6 088 2.14 35N48W* 7 729 68.8 Heng 255 2015 * 20-minute square centered at this location 32 Table 7 Statistical Analysis of Historical Data for Chosen Parameters Gradient of the Mean Gradient (°F/100 ft) One = Number Maximun Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obs.> Quadr e of Data Mean Mean Range Error Deviation Max. BT Depth JANUARY 34NL-7W 2 -- -- -- -- -- 100 34Nu8W 3 3.07 1.35 1.72 2230 4.76 Ted 35NL-7W i! -- -- -- == -- 100 35N48W 6 2.94 092 2.02 069 oe 56 35N4uSW* 8 3-10 250 2.60 1.80 4.06 70 FEBRUARY 34NLSW 2 1.97 Ay(o) 1.27 250 rfl 88 35N4-7W 3 2.20 °02 1.38 1.04 2.08 Te 35N48W 5 1.03 Ay (0) 538 027 Aon 90 3 5N4SW* 7 en 9 281 086 2.34 88 MARCH 35N4-7W h 1.00 1.00 30 62 91 35N48W 5 5.67(2) 45 Ce = 5eb2(2)F © 69. 50(2)) 85 35N48u* 8 3-50(? ° Gain § SSO) Ny eiesoCz) 83 APRIL 34.N4-7W 2 053 ALal 202 iC) e31 25 34 NASW h 82 34 48 fie 025 46 35N47W 3 1.05 34 Ayal °20 1.01 32 35NL8W 5 1.23 30 093 013 082 57 35N48W* 6 1.20 035 085 ily 1.38 54 MAY 344 7W 2 1.99 ira 228 018 065 ail 34.NLEW 1 1.32 1.32 =< 016 e5L 0) 35N4-7W h 2.17(7) 262 (2) e61( 7) 2.43(2) 19 35N4EW 6 1.59 098 6. 016 Lol 3 35Nu8Ww* 9 1.50 60 090 ale Aste) h JUNE 34NYTW 3 4.20 1.86 2634 02h 095 0 34N48w h 3.83 1.89 1.94 AIL 286 fe) 35N4-7W 3 3-09 1.95 ab sallh ails) 095 @) 35NuSW 5 3.69 TAral 1.98 pis) 1.88 fe) 35N48W* 6 3.51 1.66 1.85 018 1.88 0 * 20-minute square centered at this location 33 (2) Original data believed to be in error Table 7 (con) One = Number Maximum Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obs. > Quadrangle of Data Mean Mean Range Error Deviation Max. BI Depth JULY 34Nk7W 3 41h 2.88 1.26 232 1.00 ) 34NL8w h 3-50 BOs oS 025 LUT fe) 35NL-7W y 4.06 Bela 095 © 36 1.42 ) 35N48W 6 6.78 BASH | 3.91 230 3238 @) 35NL8Wx 7 4.76 2.93 1.83 323 1.89 @) AUGUST 34N-TW 2 3-78 Beil 203 ol} 5 fe) 34 N48w y 413 3-59 5 Fully 255 ) 35N4-7W 1 3.89 3.89 -- 6a. 230 f¢) 35N48W y 6.78 3268 3210 230 3238 fe) 35N48W* 7 6.49 ST eee 025 3.06 (0) SEPTEMBER 34k 7W 2 4.50 4.03 alae 229 092 ) 34 N48w 6 453 4.09 oy ell eT3 fe) 35N4-7W 2 6.00 3292 2.08 etl Le42 0) 35N48W 6 5.32 3266 1.66 018 1.53 9) 35N48w 7 540 ei ef 026 1.49 ) OCTOBER 34N4-7W iL 3259 3259 -- 33 1.05 0 34N48W 2 5.36 5236 -- asil 1.09 fe) 35NL-7W 1 5222 5.22 -- 029 eal 0) 35Nu8wW "7 5.30 3.16 aul 256 2.31 @) 35NL8w* 7 5.36 2.04 2.52 e2l 1.60 fe) NOVEMBER 344 7W 2 6.61 3212 49 e719 3-32 ) 34N48W 5 4.97 1.95 3.02 e15 2.48 ) 35NL-7W 4 451 2.64 1387 038 ey 7 35N4SW 5 5.56 2.76 2.80 037 e719 9 35N4uSW* 8 3.98 ies: 2.67 ° 32 2.68 3 DECEMBER 34NETW 2 3205 296 2.09 Asil 093 34uNL8W 3 3-79 1.46 2.33 A 1.79 36 35N4-7W 3 3.35 1.29 2.06 228 1.02 13 35N48W 5 3.57 oily) 1.40 235 1.82 36 35N48Ws 7 3037 1.91 1.46 © 36 2.19 30 * 20-minute square centered at this location 3h Table 8 Statistical Analysis of Historical Data for Chosen Parameters Gradient of the First Gradient (°F/100 £t) One = Number Maximum Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obs.> Quadrangle of Data Mean Mean Range Error Deviation Max. BI Depth JANUARY 34 NL TW 3 2.00 == -- -- -- 92 34Nu8W 3 3.80 1.40 2.40 2.22 4.76 TT 35N4-7W al -- -- -- -- -- 100 35N48W 6 443 1.92 2.51 3-54 7-08( 7?) 66 35N48W* 8 3.68 1.98 ney (0) eoO(7)e e602(7) 73 FEBRUARY 34 N4EW 2 2.10 1.25 085 1.49 ITT 88 35NL-7W 3 2.35 1.34 iLa@ul 1.08 217 82 35N4oW 5 4.50 1.40 3.10 2.98 149 93 35N48W* 7 36-75 1.66 2.09 1.13 2.54 89 MARCH 35N4-7W 2 = == 25 = = 100 35N4SW 5 12.5(7) LT (2) 10.25(?) 17.-76(2) 88 35N4SW* 8 8.4(2) °70 aTd ey WoW) alei/stol(@)) 89 APRIL 34.N4-7W 2 2.50 1.00 1.50 ° 34 TSS} 29 34Nu8w 3 3280 1.70 2210 of 1.54 61 35N4-7W 3 3015 1.87 1.28 . 1.40 59 35N48W 6 2071 2205 266 ody 1.74 71 35N48W* 6 2073 2.05 268 “eal. 1.20 61 MAY 34.NY-7W 2 4.68 3-70 098 263 ee Oy() 35 3u NSW ite 3-91 3-91 -- 267 Dons} 0) 35N4-7W 3 4.16 Dail 1.59 54 2.18 22 35N48W 6 3-78 1.28 2.50 S7/ 22h 6 35N48W* 9 3685 2.34 2.51 027 2.00 6 JUNE 34NL-7W 3 525 Bo Bi 1.68 81 3015 ) 34.N48W h 5-19 3-11 2.68 “73 2.52 fe) 35N4-7W 3 57 3.90 1.57 °50 2.46 © 35N48W 5 5.12 3.18 1.94 230 1.49 @) 35N48Wx 6 5.30 3239 1.91 035 1.96 0 * 20-minute square centered at this location 39 Table 8 (con) One = Number Maximum Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obs. > Quadr e of Data Mean Mean Range _Error Deviation Max. BI Depth) JULY 34.N4-7W 3 6.40 411 2.29 268 Pelt ) 34N48W h 546 4.08 1.38 o5 2657 ) 35NL-7W h 5.63 467 296 230 123 ) 35N4u8W 6 7229 4.80 249 037 3.08 0) 35N48W* 7 7230 4.34 2.96 Ay (eo) 2.67 (0) | AUGUST | 34 7W 2 5.65 5.00 265 238 127 0 3kN48W 4 6.92 1550 qeaehe 43 1.57 0 354-7W al 6.02 6202 = 66 1.85 re) | 35N46W h 7-00 4.65 2.35 029 3633 a) | 35N4Sw* Quadrangle of Data Mean Mean Range Error Deviation Max. BI Depth JANUARY 34.4 7W 2 340 340 -- -- -- 92 3uN4SW 3 390 190 200 10.0 20.0 Wat 35NL-7W 1 -- -- -- -- -- 100 35NLoW 6 38h. 300 8h. 48.1 127-4 66 35NuSw* 8 385 100 285 539 161.8 73 FEBRUARY 34uN48w 2 387 250 137 -- -- 88 35N4-7W 3 373 210 163 100.6 174.3 82 35N48W 5 313 0) 273 559 137-3 93 35N48W* 7 3 al 267 62.3 153-0 89 MARCH 35NX7W 2 -- =< -- -- -- 100 35Nu8W 5 327 60 267 110.2 190.8 88 35N48W* 8 320 h3 PT 634 141.8 89 APRIL 34NA7W 2 129 116 13 31.4 91.4 29 3LNLSW 3 140 25 115 5267 126.5 61 35N4-7W 3 105 23 52 34.20 1372 59 35N48W 6 203 ho 163 52.4 128.3 7 35N48W* 6 205 58 147 40.3 12250 61 MAY 34.N47W 2 83 72 11 3509 89.8 35 34.NL8W a 86 86 -- 79 oe: ) 35N4-7W 5 100 93 7 Sos 111.8 22 35N48w 6 132 Ms) 8h 9el 99.6 6 35N4SwW* 9 112 51 61 alfeeal Sima 6 JUNE 34NL-7W 3 51 27 peut Ts3 28.2 ) 34NL8W h 67 38 29 10.9 43.5 @) 35N4-7W 3 58 hs 13 6.8 28.6 fe) 35N48W 5 67 Ta 26 Tak 34.2 0) 35N48W* 6 67 25 he TO et 53-3 (0) * 20-minute square centered at this location 37 Table 9 (con) One = Number Maximum Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obse > Quadrangle of Data Mean Mean Range Error Deviation Max. BT Depth JULY 34NL7W 3 48 TS 3 HAS 30 4 0) 34 NSW y 51 25 26 607 31 oy ) 35NL7W h 68 30 38 8.3 86a 0) 35N48W 6 h6 35 eye Le oie 43.0 ¢) 35N48W* if hg 30 19 2.6 3Lel ) AUGUST 34NL7W 2 53 h9 h 9.9 32.67 0) 34uNkSw h Tal oh a7, 8.1 29.7 ) 35N4-7W 1 60 60 -- WabAs} 32.61 ) 35NLoW iT 88 7) k6 6.5 33-5 0) 35NUu8W* 7 80 ho 38 5.0 33.4 fe) SEPTEMBER 34.NL-7W 2 126 SEE 15 TLE 36.6 ) 34NLSOW 6 114 93 21 11.9 41.3 ) 35N4-7W 2 118 106 12 8.3 28.9 ) 35N48W 6 122 97 25 8.0 42.7 @) 35N48W* ct PES, 38 (5) 64 50-3 e) OCTOBER 3LNL7W 1 162 162 == 12.5 39 4 0 34uNLSW 2 145 145 -- ——s-T 0 2h.3 ) 35N4-7W iL 147 147 == 4.6 18.0 @) 35N48W ve 236 135 101 aa eesl 56 4 (0) 35N48W* a 215 Tele 98 14.3 7861 ) NOVEMBER 34N-7W 2 ahh 198 h6 18.6 Tee 0) 34NL8W 5 261 229 32 3226 108.2 3 35N4-7W Tt 270 225 5 28.5 106.3 8 35NL8W 5 266 228 38 15-2 159 11 35N48W* 8 281 180 101 21 of 104.0 5 DECEMBER 34 NET W 2 326 ; 197 129 56.6 133-5 10 34 NEW 3 4.00 317 83 29.6 726 39 35N4-7W 3 332 2ho 92 56.6 150.1 NF 35N48W 5 379 290 89 TSAI 92.1 37 35N48W* 76 382 237 1h5 22 2 121.0 30 * 20-minute square centered at this location 38 Table LO Statistical Analysis of Historical Data for Chosen Parameters Thickness of the First Gradient (ft) One. Number Maximum Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obs.> Quadrangle of Data Mean Mean Range Error Deviation Max. BIT Depth JANUARY 34NL-7W 2 20 20 -- -- -- 96 3u.NL8w 3 iY) 20 20 -- -- 99 35N4-7W 1 == -- -- -- -- 100 35N48W 6 69 20 hg 9.6 35.0 89 35N48W* 8 69 20 hg 9.0 34.0 85 FEBRUARY 34Nk8w 2 120 20 100 -- -- 95 35N47W 3 33 20 13 -- -- 90 35N48W 5 32 26 6 TLS 26.0 93 35NLoW vi 31 it 20 vi) 19.5 93 MARCH 35N4-7W 2 -- -- -- -- -- 100 35N48W 5 3h 20 14 S07 151 91 35N48W* 8 Ff) 13 27 99 24.2 89 APRIL 34NL-7W 2 36 36 -- 6.8 27.28 37 34 N4SW 3 aS 23 22 12.4 2502 50 35N4-7W 3 53 29 2k 8.2 36.9 46 35NL8W 6 80 23 57 59 Otel 70 35N4u8W* 6 37 13 24 4.6 322 59 MAY 34.N4-7W 2 106 ho 66 13.1 47.2 34 34 N47W ay 76 76 ac 8.8 28.0 ) 35N4-7W 5 89 51 38 2323 699 28 35N48W 6 107 ho 67 11.6 65.6 19 35N48W* 9 108 yh 64 11.4 121.5 10 JUNE 34.4 7W 3 157 112 5 279 96.8 21 34 NLSW h 191 103 88 24.3 97-3 17 35N4-7W 3 156 118 38 17.8 119 8 35N48W 5 193 121 72 25el 105.0 14 35N48W* 6 167 121 h6 16.6 83.0 12 * 20-minute square centered at this location Si) Table 10 (con) One = Number Maximum Maximum Percentage Degree of Years Maximum Minimum Standard Standard of Obs. > Quadrangle of Data Mean Mean Range _Error Deviation Max. BT Depth JULY 34NL-7W 3 238 222 16 30.8 110.6 iL 34 NLSW in ohy 209 35 22.9 90.1 4 35N4-7W y 22h 218 6 ts) 6867 iat 35N48W 6 222 199 23 12.2 99 4 16 35N48wx 7 228 202 26 10.7 96.4 15 AUGUST 3h.NA TW 2 29 233 16 29.9 89.6 6 3L NASW Tt 285 214 Wak 25.0 7304 20 35NL-7W a, 2k5 ahs -- 21.3 60.2 fe) 3 SNLSwW \ 282 112 170 28.2 126.0 43 35NL8W* 7 281 147 134 16.0 101.4 38 SEPTEMBER 34 N4-7W 2 270 148 122 41.3 92.3 61 34 N48w 6 208 abeul 77 37-2 123.4 51 35N4-7W 2 260 217 43 23.9 58.5 60 35N48W 6 218 170 48 52.6 105.2 43 35N48W* Fi 220 170 50 24.7 Oey 43 OCTOBER 34.N4-7W 1 207 207 -- 69.6 120.4 70 34uN4Sw 2 200 200 -- 8.2 16.3 67 35N4-7W ai 20h. 204. -- a Sal 43.4 67 35N48W T e1h 81 133 30.9 87.5 58 35N48W* T 193 81 We 27-8 100.4 NOVEMBER Su NA TW 2 89 73 16 6326 Ose 61 34. NL8W 5 130 43 87 37-0 7309 65 35N4-7W h 147 ho 107 20.0 54.2 63 35N48W 5 125 (as 0) 21.3 67 4 64, 35N48W* 8 118 59 59 18.6 69.3 63 DECEMBER 3k N4-7W 2 100 20 80 -- -- 70 34 N48W 3 80 35 KS 18.3 36.5 78 35NE7W 3 82 27 55 10.0 28.8 66 35N48W 5 80 7 33 14.3 37.8 8h 35N48W* 7 95 33 62 14.3 ho.7 76 * 20-minute square centered at this location h0 Table 11 Analysis of Variance Results Sea Surface Temperature Probability (%) of No Probability (%) of No Significant Difference Significant Difference Between Areas Between Time Periods (Constant Time Period) (Constant Area) Mean Monthly | 10" Quadrangle Mean Monthly Adjacent Alternate | in Adjacent Successive |Alternate |in 1-Degree 10* Quad- 10" Quad- 1-Degree 5-Day 5-Day |Quadrangle Month | X--Of) |pq |rangles rangles Quadrangles Means Means |Year to Year 0 33 Mean Probability Xee= mean of the monthly mean l-degree quadrangle for all years P = number of years having 10 or more observations @ = number of l-degree quadrangles having 10 or more observations During March, May, September, and November when an "experimental" cruise occurred, interpret column pq as follows: Pq = number of 5-day periods x number of 10-minute quadrangles Pq = number of years of observations x number of l-degree quadrangles Tal ho Table 12 Analysis of Variance Results Layer Depth Probability (%) of No Probability (%) of No Significant Difference Significant Difference Between Areas Between Time Periods (Constant Time Period) (Constant Area) 10° Quadrangle Mean Monthly Successive |Alternate |in 1-Degree 5-Day 5-Day Means Means Adjacent Alternate 10° Quad- 10" Quad= Month | X.-(#+4) |pa |rangles rangles Mean Monthly in Adjacent 1-Degree Quadrangles Jane 54% of la Feb. 55% of ld March | 630 3x3} 100 April 90% of layer depths] below BT May @ 2x3} 1oO June ale 3h July (oe 3x3 100 Aug. 29 lix3 90% of ob Sept. | 78 6x2 63 100 30 oa LG es 100 2x3 Nove | 235 = 67 56 100 Dece | 321 26% of obs. >4ho! pal «|e | ele Mean Probability All Months Quadrangle Year to Year Table 13 Analysis of Variance Results Gradient of the Maximum Gradient (Thermocline) Probability (%) of No Probability (%) of No Significant Difference Significant Difference Between Areas Between Time Periods (Constant Time Period) (Constant Area) Mean Monthly] 10* Quadrangle __|Mean Monthly [@) ( F / 109 ft) Adjacent Alternate | in Adjacent | Successive |Alternate jin 1-Degree 10° Quad- 10° Quad- 1-Degree 5-Day 5-Day /Quadrangle Month | X.-(OF) [pq |rangles rangles Quadrangles Means Means {Year to Year of me S 6 Jane 3-50 Feb. | 3060 of may March | 4.00 April | 3-10 May 4.20 June | 6.32 20 July | 6.03 56 eels 3h. Thy Sept. 7.03 25 Oct. De Dt Nov. | 4.68 56 Dec. | 3.61 Mean Probability h6 43 Table 14 Analysis of Variance Results Depth of the Upper Bound of the Maximum Gradient Probability (%) of No Probability (%) of No Significant Difference Significant Difference Between Areas Between Time Periods (Constant Time Period) (Constant Area) Mean Monthly Mean Monthly Adjacent Alternate | in Adjacent | Successive |Alternate jin 1-Degree 10* Quad- 10" Quad- 5-Day 5-Day jQuadrangle Month | X.-(¢¢) [pa _|rangles rangles oe Means |Year to Year Oct. 190 2x3 Nov. | 26 ov Datah x3 Dec. a of max. ee beLow BT rangg ( >4ho*) Mean Probability All Months Sul yd Table 15 Analysis of Variance Results Thickness of the Maximum Gradient Probability (%) of No Probability (%) of No Significant Difference Significant Difference Between Areas Between Time Periods ou Time Period) (Constant Area) Oct. = ae Nove 92 Dec. : Mean Probability All Months ae of mat. grad. ee | SeDay Mean _—si{ Mean Monthly | 10" Quadrangle Mean Monthly ce Alternate | in Adjacent | Successive |Alternate jin 1-Degree 10* Quad- 10° Quad- 1-Degree 5-Day 5-Day j|Quadrangle rangles Quadrangles Means Means {Year to Year Month | X.-(ft )|pa |rangles 91 100 20 80 100 25 19 alow BT range ( >440") 5 Month | X.-("r) [pa |rangles rangles Mean Probability All Months 46 Table 16 Analysis of Variance Results Temperature of the Upper Bound - Maximum Gradient Probability (%) of No Significant Difference Between Areas (Constant Time Period) Mean Monthly Probability (%) of No Significant Difference Between Time Periods (Constant Area) 10" Quadrangle Mean Monthly Adjacent Alternate | in Adjacent Successive |Alternate jin 1-Degree 10* Quad= 10° Quad- 1-Degree 5-Day 5-Day j|Quadrangle Quadrangles Means Means |Year to Year Table 17 Analysis of Variance Results Gradient of the Mean Gradient Probability (%) of No Probability (%) of No Significant Difference Significant Difference Between Areas Between Time Periods (Constant Time Period) (Constant Area) (°F ee ft) Mean Nonthly Mean Monthly Adjacent Alternate | in Adjacent Successive |Alternate |in 1-Degree 10! Stee 10" Quad- 1-Degree 5-Day 5-Day |Quadrangle Month Tx. -(OF) [pa | rangl rangles Quadrangles Means Means |Year to Year Jan. | 1-71 Feb. 1.27 May 1.12 June | 2.33 July {3.14 [3x3 89 100 Aug. | 4.238 |4x2 100 100 ‘x3 Sept. 4.23 6x2 100 50 Oct. | 3-93 |3xe 100 33 a Nove | 3.30 [Rx 89 iT Dece | 2073 ane of grad. obs. below BT range Main ) Mean Probability 7 Table 18 Analysis of Variance Results Gradient of the First Gradient Probability (%) of No Probability (%) of No Significant Difference Significant Difference Between Areas Between Time Periods (Constant Time Period) (Constant Area) (pr /100 ft) Mean Monthly] 10" Quadrangle Mean Monthly Adjacent Alternate | in Adjacent Successive |Alternate |in 1-Degree 10* Quad- 10" Quad- 1=-Degree 5-Day 5-Day Quadrangle Month | X--Op) [pa |rangles rangles Means Means |Year to Year Quadrangles Jane eto 71% of grad. below Feb. | 3092 90% of grad. below March | 1-40 90% of grad. below 3 April | 1.70 |60% of grad. below 3 May | 3.02 June | 4.74 July | 5.02 Auge 5032 Sept. Oct. Nove Dec. a 3 Mean Probability All Months 100 100 Tay Table 19 Analysis of Variance Results Depth of the Upper Bound - First Gradient Probability (%) of No Probability (%) of No Significant Difference Significant Difference Between Areas Between Time Periods (Constant Time Period) (Constant Area) Mean Monthly] 10* Quadrangle Mean Monthly Adjacent Alternate | in Adjacent Successive |Alternate |in 1-Degree 10° Quad- 10" Quad- 1-Degree 5-Day 5-Day |Quadrangle Month | X.-(t) |pa |rangles rangles Quadrangles Means Means |Year to Year April ase of grd4d. below BIT range May 86 = 100 67 90 June 6 |3xh 100 90 Jay | ho x 100 90 Aug. 62 4x2 100 90 Sept. 108 100 Octo 2) exe 100 6x2) 248 100 eae Hime pane [+ [|e 210 Mean Probability All Months Nov. hg Table 20 Analysis of Variance Results Thickness of the First Gradient Probability (%) of No Probability (%) of No Significant Difference Significant Difference Between Areas Between Time Periods (Constant Time Period) (Constant Area) Mean Monthly|10' Quadrangle Mean Monthly Adjacent Alternate | in Adjacent Successive |Alternate |in 1l=-Degree 10* Quad- 10" Quad- 1-Degree 5-Day 5-Day j/Quadrangle Month X(t) pq. | rangles rangles Quadrangles Means Means [|Year to Year Jane Bde below BI range HeDe nd. below } March Ade below April nde below B May 67 100 90 June 92 Sept. Oct. Nove Dec. Mean Probability Mean of ALL Parameters Goa: 80.8 95.6 706 oe 59.6 50 Tia sole 89569) ete 7S #8618 ce le B99 «Tin ET 26 eee ko? 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Cle sOce OS Simms Ce GLe gT° On°T Ee Gece etce OS°T gf ae Xg aS UMM TOD 0°69 ou} FO aes SUuOT}eATESgO JO Tequnu GTOT Te10L 469 «eT = StlHxerse S°99 LT = Lxe*GE 9°99 €2 as°gnxr°se 4°69) 0 Li | T° GHXT°SE G°g9 09 O*gHXT°SE g°6é9 eS G°LHXT°Se 1°99 «Set oa LHXT°SE G°g9 LET T°gXO°SE Z°69 €G o°gyxorSe 6°89 THE «= S°LHXO°SE T°69 «OLT 4° LyxorSe €°69 «TE €°LnxXo°Se S°g9 LT T° ghxXGeHe H°89 ST O° QHXG HE 6°69 «LE Ge LHXG HE 1°69 Oh 4° LHXG HE G°69 OT Co LyxG He 9°19 ET O° eux’ HE X PCE a ammypetodmay, soeyang Statistics of Experiment #21 Surface Temperature Area* N 25cOK fel MELD 3500X47 ot 32 350X475 23 350X480 alate 351X473 Te) Sibyl ales 351X475 73 35-1X48.0 72 35-2x47 12 25 OMeS 7) ke 35-2X48.0 Lb Total ee of Observations Mean of the Column * Denotes area 52 =) ll i TA PX Me i TM TU X SE 63.8 1 63-5 09 E805 cil 6369 §S9E. 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Goh) Sou, L°9L Xx emjereduey, soeszans T06 zh at oT ce get xl Te90 T°QuxXT°SE O° QHXT°SE 2° QuyXO°SGE T°gtxo°SE O° gyxo°Se G° LnXxO°S€ 4° Litx0°SE T° trxG ° HE O° tTXS °HE G° LAXG HE xXBOLy 2c 36 iLO. Table 25 Months of Maximum and Minimum Values for each Parameter Parameter Surface Temperature Layer Depth Gradient Maximum Gradient Depth Upper Bound Maximum Gradient Thickness = Maximum Gradient Temperature Upper Bound Maximum Gradient Gradient - Mean Gradient Gradient - First Gradient Depth Upper Bound First Gradient Thickness of the First Gradient Maximum Value August or September Jan, Feb, or March August January or February August August or September September August December or January August Minimum Value March or April dune or July Feb, March, or April July Jan, Feb, March, or April March or April April February June or July Jan, Feb, March, or April Instrument Error' 1.90 1.10 1.35 1.14 1.04 1.46 2.66 1.45 0.98 0095 Comparison Fourier of Means? Analysis Yes Yes March = No No May, Sept, Nov - Yes March, May, Yes Nov - Yes Sept = No March, Sept - No May, Nov = Yes Yes Yes No March, May, Nov =- Yes Sept = No May, Sept, Nov = Yes March = No Yes 'Mean Standard Deviation of the Historical Data Mean Standard Deviation of the Experimental Data “Yes or No indicates whether the data from experimental cruises fall within the range established by historical data. No Yes Yes No No No Yes 22 Table 26 Mean Standard Deviations Within 5-Day and 3-Week Periods For a 10-Minute Quadrangle Area (Experimental Data) Parameter 5-Day 3=-Week Month of Cruise Month of Cruise March May Septe Nove March May Sept. Nov. Surface ASY/ 050 4 “Gill, oS 262 ~60 Os Temperature ( OF) Layer Depth (ft) 68 5h ho 56 67 51 52 67 Gradient e449 Helene dass N.D. 1.64 Len, 2.12 Maximum Gradient anes ft) Depth Upper Bound N.D. 37 31 43 N.D. h6 35 53 Maximum Gradient (ft) Thickness - N.D. 13 46 29 N.D. 13 54 31 Maximum Gradient (ft) Gradient = e 48 Pale) 043 025 C) 59 wilt 46 e 39 Mean Gradient (°F/100 ft) Gradient - First 058 083 oO} 093 60 eal 1.22 TOS Gradient (°F/100 ft) Depth Upper Bound 237 yy 37 55 238 hy 51 60 First Gradient (ft) Thickness of the if 33 96 5h. 27 3h 116 58 First Gradient (ft) Temperature N.D. seal is 073 N.D. 283 1.26 isealal Upper Bound Maximum Gradient (°F) APPENDIX C ANNUAL STATISTICS FOR VARIOUS THERMAL STRUCTURE PARAMETERS Pit centss fot: "habe 5 “Wires cred, ion Ses oie te a Us ay VLVG IWLN3SWIYSdx3s O V1LVG TIVOINOLSIH e GQN3931 Hld3d Y¥S3AV1 2-9 SYNDIS ANNf AWN ‘YdvV YVAN “a4 ‘AON “190 “1ld3S ‘9NvV AINC SYNLVYAdW3L JOVSYNS VAS “AON 190 ‘Id3S ‘ONV ANC 1-9 3YNSIS SNNC AVN ‘YdvY “YVAN ‘34 BAYND d3LLis YalwnNOd — VLVG IVWINSWIY3dx3 O VLVG IVOINOLSIH e QN3931 ool 002 foXoys (14) Hid 30 OOv oos 009 002 (do) SYNLVYSdW3L 29 LNSIGVYS WOWIXVI SHL JO GNNOG YaddN SHL SOHLdAG v-9 AYNSIS ‘YVN 834 NUE ‘0530 “AON 190 “ldS3S ‘9NV AINC ANN AVW ‘Ydv ‘YVAN ‘834 Nur 002 00 pa [ae| alla 00s vivd IWINSWIYadxa O eee 009 VLVG TIVOINOLSIH e aN3931 002 (LNSIGVYS WOAWIXVW) SNITDOWYSHL SHL SO LNSIGVYD €-9 JYNDIS ‘WN gad NWP 03d AON 1100 ‘“ld3S ‘OMv AIM? 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