MASS, SALT, AND HEAT TRANSPORT ACROSS uCn LATITUDE IN THE ATLANTIC OCEAN BASED ON IGY DATA AND DYNAMIC HEIGHT CALCULATIONS Tommy Darell Greeson DUDifY KNOX LIBRARY NAVAL HJSTGRADL'ATE SCHOOL mONTLRlY. CALIFORNIA 9(fi being the angular velocity of the earth, the latitude of the station), L is the distance between stations A and B, and D. and DR the dynamic heights (depths) at the two stations. As stated previously, it is necessary to establish a level of no motion when using this computational procedure. In this study the two criteria which must be satisfied for the determination of this depth are 22 /pV dA = 0 (5) A n and fpSV dA = 0 (6) A n where S is the salinity. These equations assert that the net transports of total mass and salt must equal zero when computed across an entire latitude section of the ocean of area A. Having used these criteria to establish the level of no motion, a value is obtained for the heat transported across the vertical cross section by ocean currents. 23 IV. PROCEDURE A. DATA SOURCES To perform the calculations described in the preceding sections one needs the distribution of temperature and salinity over the vertical cross section of ocean under investigation. The oceanographic data collected during the International Geophysical Year provides the numerous obser- vations of temperature and salinity required for the compu- tation of the transports of mass, salt, and heat across the vertical cross section within the North Atlantic Ocean at 40°N. The oceanographic ship, Crawford, transited the North Atlantic Ocean along 40°N from 2 to 22 October 1957, occupying a total of 38 oceanographic stations with observations of temperature and salinity being collected at each station. This particular transit was designated Crawford 16, stations 218 to 255, and hereafter, will be referred to only by these station numbers. These 38 stations extend along 40°N from a point off the New Jersey coast to a point off the coast of Spain (see Figure 1). The maximum distance between any pair of stations is 170.93 km or approximately two degrees of longitude. The horizontal and vertical extent of the data coverage of the cross section is shown in Figure 2. Due to the relatively short period of time in which the data were collected, it 2k Figure 1. Crawford' s transit of the North Atlantic Ocean at 40°N, 2-22 October 1957. Dots indicate stations occupied. is assumed that the data are completely representative of the thermal and saline distribution occurring that October along this parallel of latitude. Even though the temperature and salinity data collected by Crawford provides considerable coverage for this cross section of ocean, there are areas along this parallel for which there are no data during the time interval of the Crawford cruise. Two of these regions is that west of sta- tion 218 to the North American coast and that east of station 255 to the European coast. The other areas lacking data are the regions between the deepest Crawford observations of temperature and salinity and the ocean floor. The largest of these areas, that from station 218 to the New Jersey shore, has dimensions of 489 km in the horizontal by 165m in the vertical at station 218 to Om at the New Jersey shore . 25 tit Crawford 16 Station Numbers 2SO ZM 1*1 j»£ — m Figure 2. Vertical cross section of the North Atlantic Ocean at 40°N showing the vertical and horizontal extent of temperature and salinity observations. Dots indicate observations of temperature and salinity. 26 In order to determine the relative importance of the mass, salt, and heat transports for the area west of station 218 it was necessary to arrive at reasonable estimates of the average density, velocity, temperature, and salinity for this area. The average temperatures for October for this section were taken from the "Serial Atlas of the Marine Environment." Values of the average October temperatures were obtained at one degree longitude increments from 4o°N, 69°W to 40°N , 74°W at various depths ranging from 0 to 330 feet. These monthly averages were then averaged again to obtain a single space average value of 13.11°C. The monthly average of the surface current velocity was taken from the "Pilot Chart of the North Atlantic Ocean" for October 1973- In the section from station 218 westward, the surface current indicated on this chart is in a southerly direction with a velocity of 25.7 cm/sec, which is assumed to approach the geostrophic current due to the east-west orientation of the entire vertical cross section. The geo- strophic current at the bottom is assumed to be zero and an average of the surface current and the bottom current is taken to arrive at a single average value of 12.85 cm/sec. The average value for the salinity of this section was determined from the work of Ketchum and Keen (1955) in which they used depth mean salinities to show a seasonal variation in the concentration of river water on the continental shelf 27 between Cape Cod and Chesapeake Bay. In this study, their winter depth mean salinities at 20, 30, 40, and 100 fathoms are averaged to arrive at the value of 33.175 ppt for the salinity of the section from station 218 to the coast of New Jersey. An estimated average density value of 1.02395 g/cm^ is obtained from the work by Howe (1962). This value is an average of values as read from his graph of Section C, Figure 4. The average values of temperature, salinity, density, and current velocity obtained in the preceding paragraphs are used to compute estimates of the transport of mass, salt content, and heat in that part of the vertical cross section westward from Crawford station 218 to the New Jersey shore. The distance from station 255 to the coast of Spain is 67km and the depth of the water is less than 150m. There- fore, it was assumed that the conditions were the same as those between stations 254 and 255. With this assumption, it was possible to take a percentage of the transports of mass, salt, and heat between stations 254 and 255 based on the area eastward of station 255 to the area between stations 254 and 255. The procedure for obtaining the estimates of the trans- ports of mass, salt, and heat for those areas near the ocean floor is described in a later section. 28 B. DEVELOPMENT OF THE COMPUTER PROGRAM An existing computer program, held by the Department of Oceanography of the U.S. Naval Postgraduate School, Monterey, California, which computes absolute current velocities and volume transports between pairs of oceanographic stations was modified so as to compute values for the transport of mass, salt content, and heat. Additional modifications were made to allow the program to perform the necessary summing pro- cesses in order to obtain the integrated transports for each pair of stations, and the net transports for the entire cross section. Also the program's capacity for the number of standard depths and stations was increased from 24 to 48 and 48 to 60, respectively. A copy of the computer program is included in Appendix A. C. SELECTION OF THE INTERPOLATION METHOD Since the observed values of temperature and salinity at each station must be interpolated to standard depths for computing the velocity and the various transports in the conventional manner, the problem of selecting an interpola- tion scheme which comes nearest to approximating the real ocean distribution of temperature and salinity is of major significance. A comparison was made of four interpolation methods. These methods include linear, mean linear-parabolic , mean A mean linear-parabolic interpolation method Is a numerical average of one linear plus two parabolic interpolations . 29 parabolic, and piecewise-cubic polynomial interpolation. The comparison was accomplished with the aid of computer plots of each of these methods at each of the 38 Crawford stations. Visual comparison of the actual temperature and salinity profiles with the interpolated values at 10m incre- ments made it readily apparent that no one method was satis- factory in all cases. It was determined that some combina- tion of a linear and a higher order interpolation method was necessary to give the desired results, especially when there was an isothermal layer near the surface. The results of the comparison of the four different interpolation methods and the specific interpolation method chosen for the rest of this study are included in Section V.A. D. COMPUTATIONS OF VELOCITIES AND THE TRANSPORTS OF MASS, SALT CONTENT, AND HEAT With the assumption of geostrophic balance it is possible to use the procedure of computing dynamic heights so as to obtain the velocity estimates for the latitude section. A detailed description of the flow of computations is included in the following paragraphs to aid the reader in understanding the computer program in Appendix A, and the exact procedures used in obtaining the transport values. The data from Crawford Cruise 16, stations 218 to 255, are at various depths and have to be interpolated to standard depths. This is accomplished by the subroutine "LGTP" (Appendix A) which is the programmed version of the combination 30 linear and parabolic mean interpolation method. The observed values of temperature and salinity are interpolated to the following standard depths: 0, 50, 100, 150,200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1050, 1100, 1150, 1200, 1250, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2250, 2500, 2750, 3000, 3250, 3500, 3750, 4000, 4250, 4500, 4750, 5000, 5250, and 5500m. After obtaining the interpolated values of temperature and salinity at the standard depths, the computer subroutine "SGTSVA" (Appendix A) is called to compute the sigma-t, specific volume anomaly, and specific volume for each standard depth. With the specific volume anomaly values calculated for each standard depth, the next step is to compute the dynamic heights, D. This process is accomplished in the main com- puter program. An average specific volume anomaly between each pair of standard depths for each station is computed according to the following equation: J = z (z+Az) /-n where 6 is the mean specific volume anomaly, and 6 and 6, , . x are the specific volume anomalies at the standard (z+Az) depths, z and z+Az, respectively. The increments, Az, are in standard depth increments only. The equivalent of an integration is then accomplished using: 31 AD = 7[z-(z+Az)] (8) where AD is the difference in the dynamic heights (depths) between the standard depths. A vertical summation of the AD's is carried out for each station: lZQ AD = D (9) The distance L between stations in (*J) is computed with use of the computer subroutine "DSTSTA" (Appendix A) using the following method. The length, in meters, of one degree of latitude and one degree of longitude for each station is computed using the equations based on Clarke's spheroid of 1866. These lengths are functions of the latitude and longitude of each station. The two values for one degree of latitude are averaged as are the two values for one degree of longitude. The difference in the latitudes and the difference in the longitudes of the two stations are computed. The differences in degrees in latitude and longitude of the pair of stations are multiplied by the average values for the length of one degree of latitude and p The earth is approximately an oblate spheroid (a sphere flattened at the poles). Its dimensions and the amount of flattening are not known exactly, but the values determined by the English geodesist A.R. Clarke in 1866 as defined by U.S. Coast and Geodetic Survey in i860 are used for charts of North America. 32 longitude, respectively. This procedure gives two sides of a right triangle and the third side, the distance L, between the two stations, can be obtained by the use of the Pythag- orean relation. The use of the Pythagorean relation to obtain the third side of a right triangle involves a flat earth assumption. This assumption seems to be reasonable since the maximum distance between any pair of stations is 170km. With the distance L computed, the computer subroutine "GEOCUR" (Appendix A) computes the relative velocity between pairs of stations at each standard depth according to (4). The relative velocities can be converted to absolute veloci- ties by setting the geostrophic velocity at an assumed level of no motion equal to zero. The computational procedure used for determining the level of no motion from (5) and (6) is discussed later in this section. The velocity values obtained by the preceding method represent values at standard depths between a pair of sta- tions. The velocity values are averaged in the computer subroutine "GEOCUR" to obtain a velocity in the center of an area bounded by the two stations in the vertical and by a pair of standard depths in the horizontal. This procedure (denoted as Step 1) is illustrated in Figure 3. Density is computed from the following equation: p = —±- (10) o±r Otomp 33 sta zn v, STEP 2 . g ***** T,,T,+T, 1 a STEP 2 STA 220 STEP i .STEP3 *«-— : i — v „ W* • c Z • -*- /! . f -T,»Tt STEP 3 STEP 1 50 M • fs,1».,s3 STEP^ 'ts .Tt+fr 2. STEPfc few. Figure 3. Illustration of the averaging process in order to make values of velocity, density, temperature, and salinity compatible within a sample rectangular area. 3*J where PSTp is density at a particular salinity, temperature, and pressure, and agTp is the specific volume at a particular salinity, temperature, and pressure. Since density is computed at standard depths for each station, one has available values for density for the four corners of the rectangular area described in a preceding paragraph. These four values of density are averaged to obtain a value of average density compatible with the average velocity for that rectangular area. The average values of temperature and salinity are obtained in the same manner. This procedure, illustrated in Figure 3, is accom- plished in two steps. Step 2 is carried out in the main com- puter program and the values are stored in a matrix array until they are needed by the computer subroutine "GEOCUR" where Step 3 is performed. This averaging procedure is per- formed for each rectangular area formed by a pair of stations and a pair of standard depths for the entire vertical cross section. In summary then, the values are either passed to or computed in the subroutine "GEOCUR" for each rectangle are the area, the average density, the average velocity, the average temperature, and the average salinity. The product of the first three gives the mass transport, which when multiplied In turn by each of the remaining averages gives the heat transport and salt transport across a particular rectangular area of the vertical cross section. 35 The transport values computed for each rectangular area are summed both horizontally and vertically. By summing vertically between each pair of stations, one obtains values for the integrated transports of mass, salt, and heat for that pair of stations. The transport values between each pair of standard depths, for example 0 to 50m, are summed horizontally to give the net transports of mass, salt, and heat in a particular layer of the North Atlantic Ocean at 40°N. These layer values are then summed vertically to give the total net transports of mass, salt, and heat across the entire vertical cross section. This process is accomplished by the computer program; an example of the method is shown in Figure 4. Wherein it is understood that the transports of mass, salt, and heat have been computed individually for each of the rectan- gular areas 1 thru 9. For example; the sum of the mass transports for the rectangular areas 1, 4, and 7 gives the integrated mass transport, A, between the pair of stations, 218 and 219. The integrated values for salt and heat trans- port are computed for each pair of stations in the same manner. Similarly, the mass transport values for the rectan- gular areas 1, 2, and 3 gives the net mass transport, B, for the layer between 0 and 50m extending from station 218 to station 221. The computer program computes the transport values for each pair of stations down to the deepest standard depth 36 w -p CD a-p Ocean Surface 218 219 220 221 0 i ? 3 50 ^ 4 5 6 ion 7 8 9 150 t A B Figure 4. Illustration of the summation process performed in the computer program for a sample cross section of ocean, A represents integrated transport for a pair of stations 218-219. B represents the net transport for the layer 0 to 50m. common to both stations. Thus, account is not taken for small areas, mentioned previously, of ocean near the bottom where there are no computed values for the transports. The areas in question are represented in Figure 5 as the areas between the bottom of the ocean and the first solid line above the ocean bottom. The solid line above the ocean bottom indicates the deepest depth common to each pair of stations for which the transports are computed. The method for obtaining the estimates of the transports for these 37 triangles or quadrangles Is described in the following paragraph. Values of temperature and salinity were extrapolated to depths deep enough to cover the entire water area between each pair of stations. In some cases this involved an extrapolation of temperature and salinity into the ocean floor as If the ocean bottom did not exist. The transport values were then computed via the computer program and a percentage value of the water area to the total area present in each rectangle was multiplied by the values of mass, salt, and heat transports for each rectangle. After this process was completed for each of the triangles or quadran- gles, a summation was carried out to obtain the estimated net transport values for mass, salt, and heat. The number of areas involved is illustrated in Figure 6. It is recog- nized that this is only a rough estimate due to the fact that the bottom is not smooth and orderly. Once these values are obtained they are assumed to be constant. Each time the level of no motion is varied the integrated transports will vary. If the integrated transports are recorded for each level of no motion for each pair of sta- tions, it is possible to determine the amount of change in the integrated transports for a change in the level of no motion. For example, the integrated transports are recorded for the pair of stations, 235-236, with the level of no motion set at 1000m and then at 1050m. The difference between the 38 Figure 5. Vertical cross section through the North Atlantic Ocean at 40°N showing the deepest level common to a pair of stations for which the transports of mass, salt, and heat are computed. Numbers across the top of the figure represent Crawford stations 218 to 255 Figure 6. Vertical cross section through the North Atlantic Ocean at 40°N showing the areas for which the estimates of the transports of mass, salt, and heat are made from extrapolated temperature and salinity values. Values of temperature and salinity are extrapolated for every intersection of dashed lines. Darkened areas are considered to have negligible transports of mass, salt, and heat . 39 no 41 transport figures is the amount of change when the level of no motion is shifted from 1000m to 1050m. The above procedure is used only for Crawford stations 222 to 253- The shaded areas in Figure 6 along the conti- nental slope of both the United States and European coasts are considered to have negligible transports of mass, salt, and heat. To show that the mass and salt balance obtained with the inclusion of the mass and salt transport estimates in the areas for which there are no actual data, causes only slight variations in the level of no motion obtained by a mass and salt balances based only on Crawford data, the following procedure was adopted. First a level of no motion was determined by balancing the mass and salt transports across the portion of the vertical cross section covered by the Crawford data only, i.e., all areas not covered by Crawford data were neglected. Next a level of no motion was deter- mined by balancing the mass and salt transports across the vertical cross section which included those estimates of the transports of mass and salt for the areas not covered by Crawford data. If the level of no motion obtained by the first approach agreed reasonably well with the level of no motion obtained in the second approach, it was assumed that the level of no motion obtained from Crawford data only was the best approximation of the level of no motion for this cross section of ocean since It was based on actual data. 42 The level of no motion was determined by balancing the mass and salt transports across the entire vertical cross section. This is accomplished by setting a constant level of no motion equal to a standard depth into the computer program, for all pairs of stations and computing the net transports of mass, salt, and heat for the entire cross section of the ocean. This procedure was repeated for a different standard depth until the net transports of mass and salt change sign. In this particular computer program positive values indicate northward movement and negative values southward movement. If a level of no motion speci- fied for any particular pair of stations was deeper than the data for the two stations, the program automatically used the deepest level common to both stations. Once the net transports of mass and salt have changed sign, the level of no motion is varied (by hand) for pairs of stations until a balance of the mass and salt transports is achieved for the entire vertical cross section of the North Atlantic Ocean at 40°N. 43 V. DISCUSSION OF RESULTS A. COMPARISON OF VARIOUS INTERPOLATION METHODS It was not until this work was completed that the work of Borkowski and Goulet (1971) was discovered. They recom- mend the use of linear interpolation at the top and bottom of the profile and mean parabolic interpolation otherwise. This recommendation came as a result of a comparison of ten different interpolation methods with values obtained from an in situ STD (salinity-temperature-depth) recorder. The same conclusion was drawn by the author after making a comparison of four different interpolation methods at each of the 38 Crawford stations. While comparing these four interpolation methods, it became apparent that two problem areas existed. The first problem area is at stations that have an isothermal layer near the surface; the second problem area exists at all stations that exhibit a permanent thermo- cline. As a general rule, higher order interpolation methods overestimate the temperatures in the isothermal layer while the linear interpolation method overestimates the temperatures in certain areas of the permanent thermocline. Crawford Station 221 is specifically singled out for illustration of the comparison process due to the indications of the isothermal layer at the surface and the steep thermo- cline below this layer. Figures 7, 8, 9, and 10 are computer plots of the vertical temperature profile for this station. W The crosses represent the observed values of temperature while the continuous line represents values of temperature interpolated at every 10m using the various interpolation methods. Figure 7 is a plot of the linear interpolation method. This method provides satisfactory interpolated values for the isothermal layer between the surface and the 2nd observed values in Figure 7, but does not give as good an approxima- tion of the temperature distribution as some of the other interpolation methods in the area of the 3rd, 4th, and 5th observed temperature values. Figure 8 is a plot of the mean linear-parabolic inter- polation method. This interpolation method is a numerical average of the combination of two parabolic interpolations plus one linear interpolation for a specific standard depth. One of the three-point parabolic interpolations includes the observed values two depths above and the observed value one depth below the standard depth. The other three-point parabolic interpolation includes the observed value one depth above and the observed values two depths below the standard depth. It is obvious from the plot that this inter- polation method does not provide satisfactory values for temperature in the region of the isothermal layer between the surface and the 2nd observed temperature value. In Figure 9, a piecewise-cubic polynomial interpolation method is shown. This interpolation method tends to produce 45 even higher values of temperature in the isothermal layer, plus a slight exaggeration of the profile between the 3rd, 4th, and 5th observed temperature values. Another disadvan- tage of the piecewise-cubic polynomial interpolation is that it requires more computer time than the other interpolation methods . The interpolation method finally adopted for use in this research is a combination of linear interpolation between the first two observed values and the last two observed values with a mean parabolic interpolation method for the rest of the profile. The mean parabolic interpolation was used because the work by Borkowski and Goulet (1971) showed, by statistical means, that the mean parabolic interpolation method was more accurate in the nonlinear portion of the profile. This method is illustrated in Figure 10. A comparison of the previously discussed interpolation methods., with the exception of the piecewise-cubic polynomial interpolation method, is made to determine the effect of the interpolation method on the net transports of mass, salt content, and heat across the entire vertical cross section. If the level of no motion is held constant then variation in the transport values is entirely due to the different interpolated values of temperature and salinity as obtained by the different interpolation methods. As can be seen from Table I, there is a considerable difference in the magnitude of the transports computed by 46 Temperature (°C) 020 02S E & o .p O *o Figure 7. Computer plot of the linear interpolation method for the vertical temperature profile at Crawford Station 221. Crosses represent observed values. Continuous line represents values interpolated every 10m, H7 00' Temperature (°C) 023 025 f3 K- V.' s-*. JG e -P o o,o Q) rH n X O 1^ Figure 8. Computer plot of the mean linear-parabolic interpolation method for the vertical temperature profile at Crawford station 221. Crosses represent the observed values. The continuous line represents values •interpolated every 10m. l\S Temperature (°C) 003 00£ OiO OiS 020 025 o C3 — £=> o f— o • ► - Depth (xlOOm) 1 1 ^ < o o > ( ■ Figure 9. Computer plot of the piecewise-cubic polynomial interpolation method for the vertical temperature profile at Crawford station 221. Crosses represent the observed values. The continuous line represents values interpolated every 10m. ^9 oc-c DCS Temperature (°C) 010 211 ozo oze> xi a -P o Figure 10. Computer plot of the combination linear and mean parabolic interpolation method for the vertical temperature profile at Crawford station 221. Crosses represent the observed values. The continuous line represents values interpolated every 10m. 50 TABLE I Comparison of the Effect of Various Interpolation Methods on the Transports of Mass, Salt Content, and Heat at 40°N within the North Atlantic Ocean. (Positive values indicate northward transport and negative values indicate southward transport.) Level of No Motion Held Constant (All Values x 1012) Interpolation Method Mass gm/sec Salt gm/sec Heat gm-cal/sec Linear - 1.75^3 - 53.9933 - 316.9080 Mean Linear- Parabolic - 0.4966 8.8255 + 48.1338 Combination of Linear and Parabolic Mean - 0.2677 - 0.5861 + 114.4340 51 the linear interpolation method when compared with the other two. One explanation for this difference can be traced to the observations of temperature and salinity which are missing between the depths of 200m and 1295m at Crawford Station 220. The other 37 stations have observations of temperature and salinity in this depth region at approximately 100m incre- ments; therefore, the use of the linear interpolation method would not have as drastic an effect at these stations. The cause for the large variation is illustrated in Figure 10. Assume that the observations of temperature and salinity are missing between the 5th and 13th observations for station 221, and that one is using the linear interpolation method. The line drawn in Figure 10 illustrates the resulting linear interpolation for this region. Higher temperatures at the standard depths would be obtained and these values, coupled with large negative velocities, would account for the large deviation in the transport values obtained by this method. In this case, the mean parabolic interpolation method would more closely approximate the actual temperature distribution expected in this region. B. LEVEL OF NO MOTION The determination of the level of no motion for the entire vertical cross section requires that net transports of mass and salt across that section be equal to zero. The level of no motion for each pair of stations based solely on Crawford data is listed in Table II. This level of no motion is based 52 TABLE II Level of No Motion for Each Pair of Crawford Stations at 40°N Within the North Atlantic Ocean (Values in parentheses represent changes in the level of no motion as a result of taking into consideration all the areas in the vertical cross section of ocean not covered with Crawford data.) Level of No Motion Crawford Stations (Meters) 218-219 150 219-220 850 220-221 1150 (1100) 221-222 1200 (1250) 222-223 1200 223-224 1200 224-225 1200 225-226 1250 (1300) 226-227 1200 (1300) 227-228 1300 (1250) 228-229 1200 229-230 1200 (1300) 230-231 1200 231-232 1250 232-233 1200 233-234 1250 234-235 1250 235-236 1200 236-237 1200 237-238 1200 238-239 1250 239-240 125.0 240-241 1250 241-242 1200 242-243 1100 243-244 1200 244-245 1150 245-246 1200 • 246-247 1200 247-248 1200 248-249 1200 249-250 1200 250-251 1200 (1250) 251-252 1200 252-253 1150 253-254 1100 254-255 150 53 upon the balance of the integrated mass and salt transports shown In Table III. The sums of the different columns represent the net transports of mass, salt, and heat across the entire vertical cross section. The near balance of the mass and salt trans- port columns represents an attempt to balance both of these simultaneously. It should be noted that the balance of either one is not equal to zero exactly. If one rounds each of the integrated mass and salt transports to the nearest 12 whole number x 10 then the salt transport balance is off 12 by +1 x 10 while the mass transport balance is off by 12 -1 x 10 from an exact balance. The balance in Table III represents a compromise between the best mass balance and the best salt balance. If one attempts to balance only the salt transport while ignoring the mass balance then it is possible to make the net salt transport value in Table III closer to zero. The opposite is true if the mass transport is balanced without regard for the salt balance. When this is done the variation in the level of no motion is only 50m at three pairs of stations. The second approach in determining the level of no motion was to assume that the mass and salt transports of the areas neglected in the first approach were significant. Once the estimates for the transports of mass, salt, and heat were obtained for these areas, the level of no motion was varied between pairs of stations until a balance of the 54 TABLE III Integrated Transports of Mass, Salt, and Heat (Positive values represent northward transport, negative values represent southward transport) (All values x 1012) Crawford Mass Stations gm/sec 218-219 -0.048 219-220 7.839 220-221 -3.466 221-222 -0.718 222-223 2.588 223-224 0.144 224-225 1.328 225-226 -8.409 226-227 17.277 227-228 -20.877 228-229 3.160 229-230 .969 230-231 9.650 231-232 -9.637 232-233 0.215 233-234 -.539 234-235 9.188 235-236 -9.294 236-237 5.620 237-238 -6.622 238-239 1.301 239-240 6.987 240-241 -7.047 241-242 0.047 242-243 1.881 243-244 2.939 244-245 -1.114 245-246 1.232 246-247 -1.911 247-248 0.449 248-249 -2.800 249-250 0.389 250-251 -0.389 251-252 2.076 252-253 -1.454 253-254 -1.137 254-255 -0.084 Net Transports -0.268 Transports Salt Heat gm/sec gm-cal/sec -1.679 -13.751 276.115 2223.725 •121.334 -967.546 -25.308 -202.166 98.986 854.604 -0.998 -63.565 46.447 367.518 •294.734 -2336.479 634.543 5177.051 •759.727 -6188.070 111.538 900.428 32.936 245.045 352.005 2859.991 •350.146 -2834.232 5.795 3.316 -13.904 -1.416 342.636 2817.137 ■335.634 -2693.083 184.374 1394.852 •223.337 -1721.683 39.190 278.117 251.106 2015.054 •252.019 -2015.903 1.534 II.676 67.120 536.609 105.393 843.956 -40.968 -332.850 42.960 339.036 -70.292 -572.699 19.228 168.333 -98.216 -776.739 12.659 95.273 -14.214 -115.026 72.249 569.122 -51.382 -408.233 -40.494 -318.681 -3.014 -24.269 -0.586 +114.43 55 mass transport occurred. It turns out that the level of no motion has to be varied at only 7 pairs out of 37 pairs of stations, the maximum variation at any one pair of stations being 100m. The new levels of no motion for the 7 pairs of stations are shown in Table II in parentheses. A comparison of the level of no motion obtained by both approaches is shown in Figure 11. The solid line indicates the level of no motion established with the first assumption: that the areas west of station 218, east of station 255, and near the ocean floor make negligible contributions to the transport of mass, salt, and heat. The dashed line indicates the variations to this level of no motion when making the opposite assumption. It can be seen from either Figure 11 or Table II that the maximum variation in the level of no motion using either assumption is 100m, which occurs at two pairs of stations, 226-227 and 229-230. This would indicate that the level of no motion determined solely from actual Crawford data is a good approximation. Table IV shows the magnitude of the estimates for the various transports in those areas not covered by Crawford data. The estimates in the fourth line of Table IV are the estimates obtained from the computer program when the level of no motion is varied to achieve a mass balance for the entire cross section with those areas not covered by Crawford data included. By summing each column in Table IV, one obtains the net transports across the entire vertical cross section of the North Atlantic Ocean. 56 0« o o £ -H to P P -P £ O c -a o c >> cd 0 -H XJ rH C P CO P •H cd cd T3 < E tH 0 0) m m m c x; 0 cd cd •H P p > E M 0 rH u o ■OOJH 0 s .C cd p C P 0 0 O hO ■a .c •H -^ C p P C tH c O 0 13 o c E CO 3 •H tH 0 rH P .G O m O O P C Q £ E-H 0 tH £ rtH 0 H 3 rH P rH W 0 cd T3 0 > 0 0 M 0 c .c .c rH O P co cd •H cd 0 P to Q 10 x: O P cd P 0 C 10 0 • C «M to cd o • O CO 0 P iH cd to U cd p p c o UTJ o cd O M 0 Ex) to o m t3 •H m O T3 £h 0) 0 o C M Cd ,C C «H O Q.P "H £ Cm • co O O 0 >> rH 0 CO M rH ,Q rH .C Cm O to T3 0 cd • >jtH 0 fn O C rH .C M 3 U cd 0 p 0 to a 0 r-H > •H a O O C O fc do w •H O 57 TABLE IV Transports of Mass, Salt, and Heat Including all Areas Not Covered by Crawford Data (Positive values indicate northward transport and negative values indicate southward transport.) (All values x 1012) Mass Salt Heat gm/sec gm/sec gm-cal/sec Estimates of the transport -6. 139 -213.540 -1842. 9^2 of mass, salt, and heat for the area westward from Crawford Station 218 to the coast of New Jersey. Estimates of the transport -.128 -H . 589 -32.026 of mass, salt, and heat for the area eastward of station 255 to the coast of Spain. Estimates of the transport +2.571 +81.734 +670.659 of mass, salt, and heat for the bottom areas not covered by Crawford data. Estimates of the transport +4.003 +149.276 +1304.520 of mass, salt, and heat based on the level of no motion determined by the mass transport balance including the above estimates . Net Transports +.008 +12.881 +100.211 58 An attempt to balance only the mass transport was under- taken since it was felt there was less chance of error in the estimates of density than those of salinity. The values of salinity in the region from Crawford station 218 to the United States coast are highly variable due to considerable river runoff from the Hudson and Delaware Rivers. It is important to understand that various transports of mass, salt, and heat obtained for those areas not covered by Crawford data are very rough estimates and that there is no way of checking their validity. The comparison of the two levels of no motion in Figure 11 shows that there is very little variation resulting from the two different approaches. A comparison of the results in Tables III and IV shows there is also very little resulting variation in the net heat transport values for the vertical cross section. Since by comparison of the two approaches, one obtains approximately the same results, the level of no motion obtained by using only the Crawford data is the one upon which the rest of this work is based. Table V shows the effect on the balance of mass and salt transports, and the net transport of heat by varying the level of no motion for each pair of stations 50m either side of the presently established level of no motion. The level of no motion is not varied between stations 218-219, 219-220, and 25^-255 because of their shallow depths; It is assumed that the level of no motion Is located at the ocean 59 TABLE V Comparison of the Net Transports of Mass, Salt, and Heat for the Vertical Cross Section at 40°N Within the North Atlantic Ocean When the Level of No Motion is Varied 50m Above and Below the Level of No Motion Obtained from Actual Crawford Data (Positive values indicate northward transport, negative values indicate southward transport.) (All values x 1012) 50m above Mass Salt Heat gm/sec gm/sec gm-cal/sec -3.288 -106. 991* -728.523 Level of No Motion (Based on Crawford Data) -0.268 -O.586 +114.43^ 50m below +24.923 +911.009 +7509.230 60 floor for these stations. The differences in the transports are considerable thus providing additional evidence that the level of no motion obtained in this study lies somewhere in between these limits. C. VELOCITIES Within the North Atlantic Ocean at latitude 40°N the Gulf Stream Current System begins to meander and is generally considered to have a west to east flow. It is also a region where the system begins to diffuse; and the surface current velocities are generally recognized as gradually becoming weaker as one proceeds from west to east. Geostrophic velocities were computed for every standard depth that is common to a pair of stations. The geostrophic velocities between each pair of stations at 0, 1000, 2000, 3000, and 4 000m are shown in Figures 12, 13, 14, 15, and 16 respectively. The maximum surface geostrophic velocities occur between stations 226-227 and 227-228: 44.18 cm/sec in the northward direction and -48.45 cm/sec where the minus sign indicates southward flow, respectively. This is probably related to a meander of the Gulf Stream Current that crosses 40°N. The water temperatures in this region are higher than the surrounding water temperatures which is a further indication that these velocities can be associated with the Gulf Stream. Fuglister (1964) showed the path of the Gulf Stream in the vicinity of 40°M to be complex (see Figure 17). The 61 Figure 12 Surface Geostrophic Velocities Figure 13 Geostrophic Velocities at 1000m Figure 14 Geostrophic Velocities at 2000m Figure 15 Geostrophic Velocities at 3000m Figure 16 Geostrophic Velocities at 4000m (In the figures listed above, the vertical axis is in cm/sec. The horizontal axis represents Crawford stations 218 to 255. Positive velocity values represent a northward flowing current while negative values represent southward flow. The solid arrows represent velocities computed from the level of no motion based only on Crawford data.) 62 :$& ■OSS ■■^Z - OfrS - — ozz <&z ■oiz -Ifzg i i i c i i ■ ■ i o -Ofr2 - m ■ SC2 -oes * ► -522 * » -023 " t I I i i . i . 1 1 i 1 " -i i i l i . t i . i i ■ i i o C\! O oas/tno CJ l en •H I 64 ::S£2 • 4 052 ■svs — [ ^ •0fr2 oxq.Lraiq.v-PTH ■se2 .1 1 -J— - •oeg ■ « r622 1 ' ' 1 — •- -022 ■ ' — i — i i ... i i I i i ,. . .. J 0) 00 o oas/uio I 1 I 65 :S£3 . — - • ■ -052 * ~~ ■ ■* - -SfrS. a3pTH OTq-traxq-V-pxH •« -otz- » • m — - (D M ■H cr> vo o oos/uo VO I 67 ,s \ V SURFACE CURRENT OBSERVATIONS, GULF STREAM '60 / I r \ \ r*"a JS> ?\ i.-f I A- I I *& -'V tCX cu»"mr victims - < jo o* i u c — ».t» •* M-Mt -** 2O0CM/SCC tw*v-»o*-. o*irr wm O S-I - * X. o o-z-j-tr J L Figure 17. Surface current observations "Gulf Stream '60" [From Fuglister (1964)] 68 current measurements in his study were obtained with the use of a GEK during 2 April to 15 June i960. A comparison of Figures 12 and 17 indicates some similarities in the north-south pattern of the Gulf Stream even though his measurements were taken in a different season and year than those of this study. His i960 study was chosen for comparison because it happens to be nearer to the time that the IGY data were collected. One major difference between his current pattern and the one obtained in this study is the presence of the large meander shown in his pattern between 6o°W and 6.3°W. The path of the Gulf Stream plotted from various cruises conducted in 19^7, 19^8, 1950, and i960 shows a quasi-stationary pattern with an abrupt change near 62°W. Some years this meander crosses 40°N and in others, it does not. According to Fuglister, this sudden change in the pattern of meanders is a permanent feature of the Gulf Stream. The geostrophic velocities below the level of no motion as determined in this study are shown in Figures lk , 15, and 16. The maximum geostrophic velocity of about +7 cm/sec below the level of no motion occurs at a depth of ^000m between stations 236 and 237. In most cases, for this vertical cross section of the North Atlantic Ocean, the deep ocean velocities are less than 3 cm/sec for the areas below the level of no motion. In general, the stronger geostrophic velocities at depth can be associated with the stronger velocities at the surface. 69 The weak geostrophic velocities below the level of no motion could be another indication that the level for this cross section of ocean has been chosen properly. D. TRANSPORTS OF MASS, SALT, AND HEAT The integrated transports of mass, salt, and heat for each pair of stations are shown in Figures 18, 19, and 20, respectively. These figures closely resemble the geostrophic velocity figures since the transports are directly related to the velocity. One item to note in Figures 18 and 19 is that the transports of mass and salt for one pair of stations tends to be balanced by another pair of stations in close proximity. For example, in Figure 18, the integrated north- ward mass transport value for stations 226 to 227 tends to be balanced by the integrated southern mass transport value for stations 227 to 228. This is in conformity with the assertion of Sverdrup et al . (19^2): "If the section is taken across an ocean, the mass transport to the north must equal the mass transport to the south but the heat transport may differ because the temperature of the water transported in one direction may be higher or lower than that of the water which is transported in the opposite direction." Two methods are available for measuring the meridional heat transport in the oceans. Heat balance computations are used in one method. The addition of geothermal heat through the ocean floor is relatively small, and the heat transport 70 ,«2 •052 -St2 t3 U O O o -ot^ ■sea -0£2 CO to cd 6 o -p o a to c Ctj u ■p TS ■P Ct) W - CD LTv .p LTi C CM H I CO -522 oo rH CM CO CD O U -H 3 -P hO ctf ■H -P Ph co .?0Z2 1 . 1 1 1 ■ , 1 T i i ■ i i t i.l. . , 1 o o CM o O o H O CM O m 1 ■ Ode /w3 1 1 71 * « - ■ * -052 -QbZ ^- ■ ■ ■ "5£2 ■ - ■ ■ * « m ♦ -oez a* ^ — "522 ■ ■ -» i , . i. 1 . 1 ■ , i— ; i . J32.2 . ■ I i i i i i.ii -j o o O o o o cr> vo m o o I o o VO I o o I o cd o u o cd CO in .p LT\ C CM H I CO H • C\J o C\J w CO o U -H 3 -P M cd •H +J pin W 73 can be computed from the distribution of heat sources and sinks at the surface. The second method consists of direct computation based on measurements of velocity and temperature. Sverdrup's heat transport estimates were obtained by utilization of the first method. Budyko constructed maps of the heat balance for the entire earth's surface from which he obtained his estimates. Jung (1955) utilized the second approach based on data from the Meteor expedition and The Naval Hydrographic Office. Bryan (1962) used a completely independent method based on geostrophic calcula- tions from hydrographic data, measuring the integral of covariance of the meridional velocity and temperature of an entire vertical section across an ocean basin. This method included the division of the heat transport into two parts. One part is calculated from hydrographic data alone and is independent of the level of no motion. The other part of the integral does contain information about the level of no motion, and is calculated from the field of surface wind stress . A comparison of the heat transport values determined in this study is made in Table VI with the values obtained by Jung, Budyko, Sverdrup and Byran. Of note is the discrepancy between the author's value and that determined by Bryan. Both studies for this cross section are based on the same IGY data, but the methods are different. The only explanation for the discrepancy Is that Bryan's method is limited by the existing knowledge of the distribution of the wind stress. 7*» TABLE VI Comparison of Heat Transport Values (Positive values indicate northward transport.) TO (All values x 10 gm-cal/sec) Sverdrup Bryan (1957) (1962) 40°N 40°N +11.4 +13.5 +9.5 +18.0 +14.5* +0.0 Greeson Jung (1955) Budyko (1956) i»0°N 36°N 45°N 40°N interpolated value. 75 The methods of Sverdrup and Budyko eliminated seasonal effects by using annual heat balance computations while Jung eliminated them by averaging all data for the cross section. Since the data used in the present study were collected during one month, it should reflect a seasonal variation if one exists; therefore, there is no reason why the values of Sverdrup, Budyko, and Jung should compare favorably. However, due to the favorable comparison of author's heat transport value with those obtained by Sverdrup, Budyko, and Jung, it might be suggested that the meridional transport of heat for this cross section of ocean is quasi-stationary. E. WATER MASSES AND THEIR RELATIVE LOCATION TO THE LEVEL OF NO MOTION Figure 21 is a representation of the distribution of the water masses present at 40°N within the North Atlantic Ocean The basis for this figure are the T-S diagrams of Crawford stations 218-255 included as Appendix B. The horizontal discontinuous line through Regions III and IV represents the level of no motion as determined by the balance of mass and salt transports through the vertical cross section. Sverdrup et al. (19*12) defined the North Atlantic Central Water (Region II) as water that is characterized by a nearly straight T-S curve between the points T=8°C, S=35.10 ppt , and T=19°C, S=36.70 ppt, and North Atlantic Deep and Bottom Water (Region V) as characterized by temperatures between 3.5°C and 2.2°C, and salinities between 3^-97 and 3^-90 ppt. 76 According to Sverdrup, between these two typical water masses are found other water masses, most of which have not been formed in the North Atlantic Ocean but which exercise a considerable influence upon the distribution of temperature and salinity at mid-depths. . The regions depicted as II and V in Figure 21 represent the area for which values of temperature and salinity fall within the limits defined by Sverdrup for the North Atlantic Central Water and the Deep and Bottom Water. Region I represents the surface area that experiences highly variable temperatures and salinities due to evapora- tion and precipitation. Regions III and IV represent areas where the temperatures and salinities fall outside the limits that define the North Atlantic Central, and Deep and Bottom water masses. The reason for dividing this intermediate water region into two areas is that a good portion of it is affected by the high temperature and high salinity water of the Mediterranean Sea, Region III representing the Mediter- ranean influence. The limits of the region were determined from the T-S diagrams in Appendix B. While it Is understood that the limits of the region can not be defined precisely by this method, it does give a good relative picture of the influence of the Mediterranean water at this particular latitudinal cross section. The asterisks indicate the salinity maximum determined from the T-S diagrams. 77 Figure 21. Relative position of the level of no motion to the various water masses within the North Atlantic Ocean at iJ0°N. I. Surface Water II. North Atlantic Central Water III. Intermediate Water with Mediterranean Influence IV. Intermediate Water with no Mediterranean Influence V. Deep and Bottom Water. 78 79 Region IV is the intermediate water area that falls outside the limits of the North Atlantic Central, and Deep and Bottom water masses, and shows no influence of the Mediterranean water. There is a slight indication of the presence of Arctic Intermediate Water in the T-S diagrams for Crawford stations 236, 231, 227, 222, and 220; but this is not indicated in Figure 21. Regions III and IV could probably be more appropriately described as the areas where more than two water masses are mixed and are represented on a T-S diagram as the nonlinear portion that lies between the North Atlantic Central and the Deep and Bottom water masses of the North Atlantic Ocean. As can be seen from Figure 21, the level of no motion lies in the intermediate water regions. III and IV. These regions probably represent areas of considerable vertical mixing vice lateral mixing since the level of no motion established in these areas requires no horizontal water movement. Weak horizontal velocities would be prevalent in the close proximity of this level. The author knows no reason why the level of no motion should fall in this region except that this is where the balance of the transports of mass and salt occurs. 80 VI. CONCLUSIONS AND RECOMMENDATIONS This study represents the first attempt to determine mass, salt, and heat transports based strictly upon the dynamic method from data which are completely homogeneous and consistent. The results indicate that the transport of heat is quasi-stationary; but this requires additional investigation based upon data taken during different seasons. Agreement between the heat transport of this study and those of other authors is surprisingly good even though the methods and the data were completely different. A level of no motion has been determined that gives a reasonable geostrophic velocity picture for the entire cross section. It was further established that this level is net necessarily related to any characteristic of the water nor to a specific water mass and is shown to lie in a region where the water masses appear to have been thoroughly mixed. The volume of calculations for this type of study can be accommodated easily with the aid of high speed computers. Through the use of the computer program in Appendix A, the remainder of the IGY data at other latitudinal cross sections of the North Atlantic Ocean can be used to piece together a complete picture of the heat transport. Not only can the heat transport picture be established in the North Atlantic, but in other oceans as well. 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'': j. en 2 ?! 6 102 33.5 28 34.1 34.7 35.3 35.9 36.5 I 24 20 16 12 x X X X X X X C r v \vf o r d st a t i r >:i 227 103 33.5 28 r- 34.1 — T- 34.7 35.3 35.9 36.5 24 20 X 16 X X frav/ford station "22! X 104 33.5 28 34.1 34.7 35.3 35.9 36.5 24 20 16 12 X X X X X X » .-..-. -for3 station 229 105 33.3 28 24 20 16 12 34.1 34.7 1 — 2±2 359 36-3 i r X X X X !r:.v;ford station 230 106 33.5 28 34.1 34.7 35.3 35.9 — r~ 36.5 24 20 16 12 X rt^tr...rPr.^,A _j.0j.^ nri* p "5-1 X X X 107 33.5 28 34.1 34.7 33.3 35.9 36.5 24 20 16 12 < - 1 ■■ 1 1 I • • ' • - X X • - X X - X X X X XX X £> . • 'ord station "32 108 33.5 28 34.1 3*4.7 35.3 35.9 i 1 r— 34.5 24 20 16 12 X xx Crawford station 233 109 33.5 28 34.1 34.7 1 — 35.3 J— 35.9 36.5 24 20 16 12 X X X X X X X X 2k »■ Irawford station "234 110 33.5 38 34.1 34.7 35.3 35.9 36.5 1 24 30 16 13 X X* & Crav:ford station 235 111. 33.5 28 34.1 34.7 35.3 35.9 36.5 24 20 xx 16 12 X X X / X X X X X X Iraw '•,"■' si bion 236 112 33.3 38 3.4.1 y4.7 35.3 35.9 34.5 24 20 16 12 X Z X Crawford station 237 113 33.3 28 34.1 34.7 1 — 35.3 35.9 36.5 24 20 X X 16 X 12 X X X X X X X X X •hi nn P ■ 111 33.3 28 34.1 T- 34.7 35.3 35.9 1 — 34.5 24 20 X X 16 12 X X X Crawford station 23S 115 33.5 38 34.1 34.7 35.3 35.9 36.5 34 20 - 16 12 1 r i 1 - 1 .— • X - - X * X X X - X X X • X X % X Crawford c tat ion "240 116 33.3 28 34. 34.7 35.3 1 — 35.9 36.5 24 20 X X 16 12 X X X # X X X X n ■*».-...,•? or stction ■h-inn p/11 117 33.5 28 34.1 34.7 35.3 1 1 — 35.9 1 — 36.5 24 20 16 12 X X ^ X X X X X X X Crawford station 118 33.3 28 34.1 r- 34.7 35.3 1 — 35.9 36.5 24 20 X X 16 12 X X X X X X X X tf Crawford station 243 119 33.5 28 34.1 34.7 35.3 35.9 34.5 24 20 - 16 12 1 1 1 » 1 X . X 1 ■ X X X • ■ X* X X f X X . - X X ' f • Crawford station 244 120 33.3 28 34.1 3-4.7 1 — 35.3 1 — 35.9 36.5 24 20 16 X 12 X X X X X X X .-X Crav/ford station 245 121 33.5 28 34.1 34.7 35.3 35.9 3d. 5 24 20 *x 16 12 X # X X X X X X X X M C r c.v;i o r d s t at i o n 2 • ' 6 122 33.5 28 34.1 34.7 1 — 35.3 1 — 35.9 1 — 36.5 24 20 16 12 8 - X >F X X s X X X X Jrav-ford station 247 123 ~3> 33.5 28 ■^*L 34.1 34.7 24 -..:"■. •• ' >," 20 16 12 35.3 35.9 r- X X X X *x X X X # # 36.5 Crawford station 24° 124 33.3 28 34.1 — T" 34.7 — r — 35.3 1 — 35.9 36.5 24 20 XX 16 X 12 X X XX . X X X .X 3$ bat ion 249 125 33.3 28 S 34.1 34.7 33.3 1 — 35.9 36.5 24 20 X 16 12 X X X X X X Crawford station 250 126 33.5 28 34.1 r~ 14.7 35.3 35.9 34.5 24 20 16 X 12 x * X X X Crawford station 251 127 33.5 28 3<.l 3*1.7 35.3 35.9 1 — 36.5 24 20 16 X X X x x *x X X X Crawford station 25 ICC 128 33.5 28 34-1 34.7 1 — 33.3 35.9 34.5 24 20 16 12 X X X* xxxx X X X Crawford station 253 129 33.3 28 34.1 *4.7 35.3 35.9 36.5 24 20 16 - 12 A - 1 i 1 • < - X m X ■ • X X ■ X >xx > - X X X X " Crawford station 2 [ • ' 130 33.5 28 34.1 34.7 — r- 35.3 35.9 36.5 24 20 16 12 Crawford station" 255 X # 131 APPENDIX C LATITUDE AND LONGITUDE FOR CRAWFORD STATIONS 218-255 Crawford Station Number Date Oct 57 Latitude 40° 15'N Loni 68° gltude 218 2 25'W 219 2 Oct 57 40° 15'N 67° 58'W 220 7 Oct 57 40° 15'N 67° 20 'W 221 7 Oct 57 40° 15'N 66° 28'W 222 8 Oct 57 40° 14'N 64° 40'W 223 8 Oct 57 40° 16'N 62° 56'W 224 8 Oct 57 40° 10'N 61° 07'W 225 9 Oct 57 40° 16'N 59° 35'W 226 9 Oct 57 40° 12'N 57° 39'W 227 10 Oct 57 40° 16'N 55° 59'W 228 10 Oct 57 40° 15'N 54° 12'W 229 11 Oct 57 40° 10'N 52° 18'W 230 11 Oct 57 40° 12'N 50° 42'W 231 12 Oct 57 40° 15'N 49° OO'W 232 12 Oct 57 40° 14'N 47° 12'W 233 13 Oct 57 40° 03'N 45° 39'W 234 13 Oct 57 40° 17'N 43° 40'W 235 14 Oct 57 40° 15'N 41° 56'W 236 14 Oct 57 40° 12'N 40° 18*W 237 15 Oct 57 40° 12'N 38° 34'W 238 15 Oct 57 40° 14'N 36° 44'W 239 16 Oct 57 40° 14'N 34° 58'W 240 16 Oct 57 40° 15'N 330 13'W 241 16 Oct 57 40° 15'N 31° 29'W 242 17 Oct 57 40° 14' N 29° 4 8'W 243 17 Oct 57 40° 14'N 27° 58'W 244 18 Oct 57 40° 14'N 26° 13*W 245 18 Oct 57 40° 03'N 24° 27'W 132 Crawford Station Number Date Latitude Longitude 246 18 Oct 57 40° l4'N 22° 4l'W 247 19 Oct 57 40° 16'N 21° OO'W 248 19 Oct 57 40° 14'N 19° 12'W 249 20 Oct 57 40° l8'N 17° 26'W 250 20 Oct 57 40° 15'N 15° 46'W 251 21 Oct 57 40° 13'N 14° OO'W 252 21 Oct 57 40° 14'N 12° 09'W 253 22 Oct 57 40° 15'N 10° 50'W 254 22 Oct 57 40° 16'N 09° 53'W 255 22 Oct 57 40° 14'N 09° 33'W 133 BIBLIOGRAPHY 1. 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Fomin, L.M., The Dynamic Method in Oceanography. Chap. IV, Methods for Computing the "Zero" Surface in the Sea, Elsevier Publishing Co., New York, pp. 117-148, 1964. 8. Fuglister, F.C., Gulf Stream '60, Ref. No. 64-4, Woods Hole Oceanographic Institution, Woods Hole, Mass., pp. 265-383, 1964. 9. Hidaka, K. , Depth of motionless layer as inferred from the distribution of salinity in the ocean. Trans. Am. Geophys. Union, V. 30, No. 3., 1940 10. Howe , M.R., Some direct measurements of the non-tidal drift on the continental shelf between Cape Cod and Cape Hatteras, Deep-Sea Research, 9, 445-453, 1962. 11. Jacobsen, J. P., Contribution to the hydrography of the Atlantic. Medd. Komm. Havundersgelser , Ser. Hydrografi, V. 2. , 1916. 134 12. Jung, G.H. , Note on meridional transport of energy by the oceans. J. Marine Res., 11_ (2), pp. 139-146, 1952. 13. Jung, G.H. , Heat transport in the Atlantic Ocean, Ref. 53-34T, Dept. of Oceanography, A. and M. 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Soc, Boston, ppT 568-574 , 1951. 20. Stommel, H. , On the determination of the depth of no meriodional motion. Deep-Sea Research, 3, PP • 273-2783 1956. 21. Sverdrup, H.V. , M.W. Johnson and R.H. Fleming, The Oceans. Prentice-Hall, New York, 1087 PP., 1942. 22. Sverdrup, H.V. , Oceanography, Handbuch der Physik. Springer Verlag, Berlin, 1957. 23. Walford, L.A., and Wicklund, R.I., Monthly Sea Temperature Structure from the Florida Keys to Cape Cod, Serial Atlas of the Marine Environment, U.S. Dept. of Sport Fisheries and Wildlife, 1968. 24. Wiist, G. , Schichtung und Zirkulation des Atlantischen Ozeans. Die Stratosphare . WIss Ergeb . Deut. Atlant. Exped. "Meteor", V. 6, Part 2., 1925-1927, 1935. 135 INITIAL DISTRIBUTION LIST No. Copies 1. Department of Oceanography, Code 58 3 Naval Postgraduate School Monterey, CA 939^0 2. Oceanographer of the Navy 1 Hoffman Building No. 2 200 Stovall Street Alexandria, VA 22332 3. Office of Naval Research 1 Code 480 Arlington, VA 22217 4. 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