Tables for Computing Geopotential Distances between Isobaric Surfaces

1051

## Tables for Computing Geopotential Distances between Isobaric Surfaces [PDF]

### Contents

 TABLE I. Specific volume of sea water of salinity 35 ‰ and temperature O°C, and at stated pressure, α35,0,p exprwsed in cm2/g or m3/ton. (From Bjerknes and Sandstrilm, 1910.) TABLE II. Geopotential distances from the sea surface to stated isobaric surfaces in sea water of salinity 35 ‰ and temperature O°C, D35,0,p, expressed in dynamic meters. (From Bjerknes and Sandström, 1910, expanded by ms. data.) TABLE III. 105Δs,ϑ as function of σ. (From Sverdrup, 1933.) TABLE IVa. 105Δs,p as function of salinity and pressure. (From Sverdrup, 1933.) TABLE IVb. 105Δs,p as function of salinity and pressure. (From Sverdrup, 1933.) TABLE Va. 105Δϑ,p as function of temperature and pressure. (From Sverdrup, 1933.) TABLE Vb. 105Δϑ,p as function of temperature and pressure. (From Sverdrup, 1933.)

### Symbols and Definitions

α35,0,p: Specific volume of sea water of salinity 35 ‰ and temperature O°C, and at pressure p.

δ: Anomaly of specific volume of sea water of salinity S and temperature ϑ and at pressure p (see p. 58):

where

(DlD2)s: Standard geopotential distance between the isobaric surfaces p1 and p2 (equation XII, 6, p. 408):

1052

ΔD: Anomaly of the geopotential distance between the isobaric surfaces p1 and p2 (equation XII, 7, p. 409):

### Explanation

If σt has been computed by means of Knudsen's or other tables, the specific volume anomaly, δ, can be found from tables III, IV, and V. If numerous computations are to be made, special tables should be prepared with closer intervals of the arguments. In order to facilitate such preparation and in order to avoid accumulation of errors, the terms have been tabulated with one more decimal place than warranted by the accuracy of the temperature and salinity observations.

When the specific volume anomalies have been found, the geopotential anomalies can be computed by numerical integration (table 61, p. 411).

## Bibliography

Bjerknes, V., and J. W. Sandström. 1910. “Dynamic meteorology and hydrography” . Pt. I, Statics. Carnegie Inst. Washington, Pub. no. 88, 146 pp. + tables. 1910.

Knudsen, Martin. 1901. Hydrographical tables. Copenhagen. G. E. C. Gad. 63 pp. 1901.

Sverdrup, H. U.1933. Vereinfachtes Verfahren zur Berechnung der Druckund Massenverteilung im Meere. Geofysiske Publikasjoner, v. 10, no. 1, 9 pp. 1933. Oslo.

1053
SPECIFIC VOLUME OF SEA WATER OF SALINITY 35 ‰ AND TEMPERATURE 0°C, AND AT STATED PRESSURE, α35,0,p, EXPRESSED IN cm3/g OR m3/ton
Pressure (decibars) 0 100 200 300 400 500 600 700 800 900
0 0.97264 0.97219 0.97174 0.97129 0.97084 0.97040 0.96995 0.96951 0.96907 0.96863
1000 0.96819 0.96775 0.96732 0.96688 0.96645 0.96602 0.96559 0.96516 0.96473 0.96430
2000 0.96388 0.96345 0.96303 0.96261 0.96219 0.96177 0.96136 0.96094 0.96053 0.96011
3000 0.95970 0.95929 0.95888 0.95848 0.95807 0.95766 0.95726 0.95686 0.95646 0.95606
4000 0.95566 0.95526 0.95486 0.95447 0.95407 0.95368 0.95329 0.95289 0.95251 0.95212
5000 0.95173 0.95134 0.95096 0.95057 0.95019 0.94981 0.94943 0.94905 0.94867 0.94829
6000 0.94791 0.94754 0.94717 0.94679 0.94642 0.94605 0.94568 0.94531 0.94494 0.94457
7000 0.94421 0.94384 0.94348 0.94312 0.94275 0.94239 0.94203 0.94167 0.94132 0.94096
8000 0.94060 0.94025 0.93989 0.93954 0.93919 0.93883 0.93848 0.93813 0.93778 0.93744
9000 0.93709 0.93674 0.93640 0.93605 0.93571 0.93537 0.93503 0.93469 0.93434 0.93401

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GEOPOTENTIAL DISTANCES FROM THE SEA SURFACE TO STATED ISOBARIC SURFACES IN SEA WATER OF SALINITY 35 ‰ AND TEMPERATURE 0°C, D35,0,p, EXPRESSED IN DYNAMIC METERS

(From Bjerknes and Sandstrom. 1910. expanded by ms data)

p (decibars) D35,0,p (dynamic meters) p (decibars) D35,0,p (dynamic meters)
10     9.7262   1200 1163.9534
20   19.4520   1400 1357.3295
30   29.1773   1600 1550.5327
40   38.9021   1800 1743.5639
50   48.6265   2000 1936.4246
75   72.9356   2500 2417.8360
100   97. 2417   3000 2898.2041
150 145.8457   3500 3377.5445
200 194.4382   4000 3855.8733
300 291.5898   4500 4333. 2053
400 388.6965   5000 4809.5559
500 485.7584   6000 5759.3685
600 582.7759   8000 7647.8173
800 776.6777 10000 9522.0255
1000 970.4032

1055
105Δs AS FUNCTION OF σt

(From Sverdrup. 1933)

σt .00 01 0.2 .03 .04 .05 .06 .07 .08 .09 .10
23.0 .487.8 486.8 485.9 484.9 484.0 483.0 482.0 481.1 480.1 479.2 478.2
.1 478.2 477.2 476.3 475.4 474.4 473.4 472.5 471.6 470.6 469.6 468.7
.2 468.7 467.7 466.8 465.8 464.9 463.9 462.9 462.0 461.0 460.1 459.1
.3 459.1 458.1 457.2 456.3 455.3 454.3 453.4 452.5 451.5 450.5 449.6
.4 449.6 448.6 447.7 446.7 445.8 444.8 443.8 442.9 441.9 441.0 440.0
.5 440.0 439.0 438.1 437.2 436.2 435.2 434.3 433.4 432.4 431.4 430.5
.6 430.5 429.5 428.6 427.6 426.7 425.7 424.7 423.8 422.8 421.9 420.9
.7 420.9 419.9 419.0 418.1 417.1 416.1 415:2 414.3 413.3 412.3 411.4
.8 411.4 410.4 409.5 408.5 407.6 406:6 405.6 404.7 403.7 402.8 401.8
.9 401.8 400.8 399.9 398.9 398.0 397.0 396.0 395.1 394.1 393.2 392.2
24.0 392.2 391.2 390.3 389.4 388.4 387.4 386.5 385.6 384.6 383.6 382.7
.1 382.7 381.7 380.8 379.9 378.9 377.9 377.0 376.1 375.1 374.1 373.2
.2 373.2 372.2 371.3 370.3 369.4 368.4 367.4 366.5 365.5 364.6 363.6
.3 363.6 362.6 361.7 360.8 359.8 358.8 357.9 357.0 356.0 355.0 354.1
.4 354.1 353.1 352.2 351.3 350.3 349.3 348.4 347.5 346.5 345.5 344.6
.5 344.6 343.6 342.7 341.8 340.8 339.8 338.9 338.0 337.0 336.0 335.1
.6 335.1 334.1 333.2 332.2 331.3 330.3 329.3 328.4 327.4 326.5 325.5
.7 325.5 324.5 323.6 322.7 321.7 320.7 319.8 318.9 317.9 316.9 316.0
.8 316.0 315.0 314.1 313.2 312.2 311.2 310.3 309.4 308.4 307.4 306.5
.9 306.5 305.5 304.6 303.7 302.7 301.7 300.8 299.9 298.9 297.9 297.0
25.0 297.0 296.0 295.1 294.1 293.2 292.2 291.2 290.3 289.3 288.4 287.4
.1 287.4 286.4 285.5 284.6 283.6 282.6 281.7 280.8 279.8 278.8 277.9
.2 277.9 276.9 276.0 275.1 274.1 273.1 272.2 271.3 270.3 269.3 268.4
.3 268.4 267.4 266.5 265.6 264.6 263.6 262.7 261.8 260.8 259.8 258.9
.4 258.9 257.9 257.0 256.1 255.1 254.1 253.2 252.3 251.3 250.3 249.4
.5 249.4 248.4 247.5 246.6 245.6 244.6 243.7 242.8 241.8 240.8 239.9
.6 239.9 238.9 238.0 237.1 236.1 235.1 234.2 233.3 232.3 231.3 230.4
.7 230.4 229.4 228.5 227.6 226.6 225.6 224.7 223.8 222.8 221.8 220.9
.8 220.9 219.9 219.0 218.1 217.1 216.1 215.2 214.3 213.3 212.3 211.4
.9 211.4 210.4 209.5 208.6 207.6 208.6 205.7 204.8 203.8 202.8 201.9
26.0 201.9 200.9 200.0 199.1 198.1 197.1 196.2 195.3 194.3 193.3 192.4
.1 192.4 191.4 190.5 189.6 188.6 187.6 186.7 185.8 184.8 183.8 182.9
.2 182.9 181.9 181.0 180.1 179.1 178.1 177.2 176.3 175.3 174.3 173.4
.3 173.4 172.4 171.5 170.6 169.6 168.6 167.6 166.8 165.8 164.8 163.9
.4 163.9 162.9 162.0 161.1 160.1 159.1 158.2 157.3 156.3 155.3 154.4
.5 154.4 153.5 152.5 151.6 150.6 149.7 148.7 147.8 146.8 145.9 144.9
.6 144.9 144.0 143.0 142.1 141.1 140.2 139.2 138.3 137.3 136.4 135.4
.7 135.4 134.5 133.5 132.6 131.6 130.7 129.7 128.8 127.8 126.9 125.9
.8 125.9 125.0 124.0 123.1 122.1 121.2 120.3 119.3 118.4 117.4 116.5
.9 116.5 115.5 114.6 113.6 112.7 111.7 110.8 109.8 108.9 107.9 107.0
27.0 107.0 106.0 105.1 104.1 103.2 102.2 101.3 100.3 99.4 98.4 97.5
.1 97.5 96.6 95.6 94.7 93.7 92.8 91.8 90.9 89.9 89.0 88.0
.2 88.0 87.1 86.1 85.2 84.2 83.3 82.3 81.4 80.4 79.5 78.5
.3 78.5 77.6 76.6 75.7 74.8 73.8 72.9 71.9 71.0 70.0 69.1
.4 69.1 68.1 67.2 66.8 65.3 64.3 63.4 62.4 61.5 60.5 59.6
.5 59.6 58.7 57.7 56.8 55.8 54.9 53.9 53.0 52.0 51.1 50.1
.6 50.1 49.2 48.2 47.3 46.3 45.4 44.5 43.5 42.6 41.6 40.7
.7 40.7 39.7 38.8 37.8 36.9 35.9 35.0 34.0 33.1 32.1 31.2
.8 31.2 30.2 29.3 28.3 27.4 26.4 25.5 24.6 23.6 22.7 21.7
.9 21.7 20.8 19.8 18.9 17.9 17.0 16.0 15.1 14.1 13.2 12.3
28.0 12.3 11.3 10.4 9.4 8.5 7.5 6.6 5.6 4.7 3.7

1056
105δs,p AS FUNCTION OF SALINITY AND PRESSURE

(From Sverdrup. 1933)

Pressure (decibars) Salinity ‰
30 31 32 33 34 35 36 37 38 39 40
0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
100 −0.8 −0.6 −0.5 −0.3 −0.2 0.0 0.2 0.3 0.4 0.6 0.7
200 −1.5 −1.2 −0.9 −0.6 −0.3 0.0 0.3 0.6 0.9 1.2 1.5
300 −2.3 −1.8 −1.4 −0.9 −0.5 0.0 0.5 0.9 1.3 1.8 2.2
400 −3.0 −2.4 −1.8 −1.2 −0.6 0.0 0.6 1.2 1.8 2.4 3.0
500 −3.8 −3.0 −2.3 −1.5 −0.8 0.0 0.8 1.5 2.2 3.0 3.7
600 −4.5 −3.6 −2.7 −1.8 −0.9 0.0 0.9 1.8 2.6 3.6 4.4
700 −5.3 −4.2 −3.2 −2.1 −1.1 0.0 1.1 2.1 3.1 4.2 5.1
800 −6.0 −4.8 −3.6 −2,4 −1.2 0.0 1.2 2.3 3.5 4.7 5.9
900 −6.8 −5.4 −4.1 −2.7 −1.4 0.0 1.4 2.6 4.0 5.3 6.6
1000 −7.5 −6.0 −4.5 −3.0 −1.5 0.0 1.5 2.9 4.4 5.9 7.3
1100 −3.3 −1.7 0.0 1.7 3.2 4.8 6.5 8.0
1200 −3.6 −1.8 0.0 1.8 3.5 5.2 7.0 8.7
1300 −3.9 −1.9 0.0 1.9 3.8 5.7 7.6 9.4
1400 −4.1 −2.1 0.0 2.1 4.1 6.1 8.1 10.1
1500 −4.4 −2.2 0.0 2.2 4.4 6.5 8.7 10.8
1600 −4.7 −2.3 0.0 2.3 4.7 6.9 9.3 11.5
1700 −4.9 −2.5 0.0 2.5 4.9 7.3 9.8 12.2
1800 −5.2 −2.6 0.0 2.6 5.2 7.8 10.9 12.9
1900 −5.5 −2.7 0.0 2.7 5.5 8.2 10.9 13.6
2000 −5.8 −2.9 0.0 2.9 5.8 8.6 11.5 14.3
2500 −7.2 −3.6 0.0 3.6 7.1 10.7 14.2 17.7
3000 −8.5 −4.3 0.0 4.2 8.5 12.7 16.8 21.0
3500 −9.9 −4.9 0.0 4.9 9.7 14.6 19.4 24.2
4000 −11.1 −5.6 0.0 5.5 11.0 16.5 22.0 27.4

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105δs,p AS FUNCTION OF SALINITY AND PRESSURE

(From Sverdrup. 1933)

Pressure (decibars) Salinity ‰
34.4 34.6 34.8 35.0 35.2
2000 −1.7 −1.2 −0.6 0.0 0.6
2500 −2.2 −1.4 −0.7. 0.0 0.7
3000 −2.6 −1.7 −0.9 0.0 0.8
3500 −2.9 −2.0 −1.0 0.0 1.1
4000 −3.4 −2.2 −1.1 0.0 1.1
4500 −3.7 −2.5 −1.2 0.0
5000 −4.1 −2.7 −1.4 0.0
5500 −4.4 −3.0 −1.5 0.0
6000 −4.8 −3.2 −1.6 0.0
6500 −5.1 −3.4 −1.7 0.0
7000 −5.5 −3.6 −1.8 0.0
7500 −5.8 −3.8 −1.9 0.0
8000 −6.1 −4.1 −2.0 0.0
8500 −6.4 −4.3 −2.1 0.0
9000 −6.7 −4.5 −2.2 0.0
9500 −7.0 −4.6 −2.3 0.0
10000 −7.3 −4.8 −2.4 0.0

1058
105δϑ,s AS FUNCTION OF TEMPERATURE AND PRESSURE

(From Sverdrup. 1933)

Pressure (decibars) Temperature °C
−2 −1 0 1 2 3 4 5 6 7 8 9 10 15 20 25 30
0. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
100 −0.6 −0.3 0.0 0.3 0.5 0.7 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.9 3.5 3.9 4.2
200 −1.1 −0.6 0.0 0.6 1.1 1.5 2.0 2.4 2.8 3.2 3.5 3.9 4.3 5.8 7.0 7.8 8.4
300 −1.7 0.9 0.0 0.8 1.6 2.3 3.0 3.7 4.3 4.8 5.4 5.9 6.5 8.8 10.4 11.6 12.5
400 −2.2 −1.1 0.0 1.1 2.1 3.0 4.0 4.9 5.7 6.4 7.2 7.9 8.6 11.7 13.9 15.5 16.7
500 −2.8 −1.4 0.0 1.4 2.6 3.8 5.0 6.1 7.1 8.0 9.0 9.9 10.8 14.6 17.4 19.4 20.9
600 −3.3 −1.7 0.0 1.6 3.1 4.6 6.0 7.3 8.5 9.7 10.8 11.9 12.9 17.4 20.8 23.2 24.9
700 −3.9 −2.0 0.0 1.9 3.7 5.3 6.9 8.4 9.8 11.2 12.5 13.8 15.0 20.2 24.1 27.0 29.0
800 −4.4 −2.2 0.0 2.1 4.2 6.1 7.9 9.6 11.2 12.8 14.3 15.7 17.1 23.1 27.5 30.7 33.0
900 −5.0 −2.5 0.0 2.4 4.7 6.8 8.8 10.7 12.6 14.3 16.0 17.6 19.2 25.9 30.8 34.5 37.1
1000 −5.5 −2.8 0.0 2.7 5.3 7.6 9.8 11.9 14.0 15.9 17.7 19.5 21.3 28.7 34.2 38.3 41.1
1100 −6.0 −3.1 0.0 3.0 5.8 8.3 10.7 13.0 15.3 17.4 19.4 21.4 23.3 31.4 37.5
1200 −6.5 −3.3 0.0 3.2 6.3 9.1 11.6 14.1 16.6 18.9 21.1 23.3 25.4 34.1 40.7
1300 −7.1 −3.6 0.0 3.5 6.8 9.8 12.6 15.3 17.9 20.4 22.8 25.1 27.4 36.9 44.0
1400 −7.6 −3.8 0.0 3.7 7.3 10.6 13.5 16.4 19.4 21.9 24.5 27.0 29.5 39.6 47.2
1500 −8.1 −4.1 0.0 4.0 7.8 11.3 14.4 17.5 20.5 23.4 26.2 28.9 31.5 42.3 50.5
1600 −8.6 −4.3 0.0 4.2 8.2 12.0 15.4 18.6 21.8 24.9 27.8 30.7 33.5 44.9 53.6
1700 −9.1 −4.6 0.0 4.5 8.7 12.7 16.3 19.7 23.1 26.3 29.5 32.5 35.4 47.6 56.8
1800 −9.6 −4.8 0.0 4.7 9.2 13.4 17.2 20.8 24.3 27.8 31.1 34.3 37.4 50.2 59.9
1900 −10.1 −5.1 0.0 5.0 9.7 14.1 18.1 21.9 25.6 29.2 32.7 36.1 39.3 52.9 63.1
2000 −10.6 −5.3 0.0 5.2 10.1 14.7 19.0 23.0 26.9 30.7 34.4 37.9 41.3 55.5 66.2
2500 −13.1 −6.5 0.0 6.3 12.3 18.1 23.4 28.3 33.1 37.7 42.2 46.6 50.7 68.2
3000 −15.4 −7.6 0.0 7.4 14.4 21.2 27.6 33.4 39.1 44.6 49.9 55.0 59.8 80.4
3500 −17.7 −8.7 0.0 8.4 16.4 24.2 31.5 38.3 44.9 51.2 57.3 63.1 68.6 92.2
4000 −19.9 −9.9 0.0 9.5 18.4 27.0 35.2 43.0 50.5 57.6 64.4 70.9 77.1

1059
105δϑ,p AS FUNCTION OF TEMPERATURE AND PRESSURE

(From Sverdrup. 1933)

Pressure (decibars) Temperature °C
−1.0 −0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
2000 −5.3 −2.6 0.0 2.6 5.2 7.7 10.1 12.4 14.7 16.9 19.0 21.0 23.0
2500 −6.5 −3.2 0.0 3.2 6.3 9.3 12.3 15.2 18.1 20.8 23.4 25.9 28.3
3000 −7.6 −3.7 0.0 3.7 7.4 11.0 14.4 17.8 21.2 24.5 27.6 30.6 33.4
3500 −8.7 −4.3 0.0 4.2 8.4 12.5 16.4 20.3 24.2 28.0 31.7
4000 −9.9 −4.9 0.0 4.8 9.5 14.0 18.4 22.7 27.0 31.3 35.6
4500 −11.0 −5.4 0.0 5.3 10.4 15.4 20.3 25.0 29.6
5000 −12.0 −5.9 0.0 5.7 11.2 16.7 22.1 27.2 32.1
5500 −13.0 −6.4 0.0 6.1 12.1 18.0 23.9
6000 −13.9 −6.9 0.0 6.5 12.9 19.3 25.6
6500 −14.8 −7.3 0.0 6.9 13.7 20.5 27.3
7000 −15.7 −7.8 0.0 7.4 14.6 21.7 28.9
7500 −16.6 −8.2 0.0 7.8 15.4 23.0 30.5
8000 −17.4 −8.6 0.0 8.2 16.1 24.1 32.0
8500 −18.2 −9.0 0.0 8.6 17.0 25.3 33.5
9000 −18.9 −9.3 0.0 9.0 17.8 26.4 34.9
9500 −19.6 −9.7 0.0 9.4 18.6 27.5 36.2
10000 −20.3 −10.0 0.0 9.8 19.4 28.6 37.5

1060

Tables for Computing Geopotential Distances between Isobaric Surfaces