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Thermometric depth and gravity variations
Deep-Sea Research, 1968, Vol. 15, pp. 645 to 646.
LETTER
Pergamon Press.
TO
THE
Printed in Great Britain.
EDITORS
Thermometric depth and gravity variations Tim FORMULAcommonly used for computing thermometric depth from hydrographic data fails to include the magnitude of local gravity, and this omission introduces an error which warrants consideration in work of high accuracy. The formula used is that of Wt~ST (1933). Depth, D, is given as 10 At D -- Qpm '
(l)
where Q is the so-called "pressure coefficient" of the unprotected thermometer, p,~ is the mean density of the sea-water column above the observation, and At is the difference in corrected readings of the protected and unprotected thermometers. (The factor of 10 results from the units commonly used.) Equation (1) should contain, in the denominator, the magnitude of gravity at the latitude of the observation, because hydrostatic pressure depends on gravity. The derivation is trivial, but the omission seems not to be widely recognized. The depth calculated from the corrected formula will vary with latitude. As the magnitude of gravity increases from the equator to the pole, the extreme difference affects thermometric depth by slightly more than 5 m/km of depth. This amount is less than the precision usually ascribed to the method (see FOFONOFF, 1963), but when the best instruments are used with care this effect may be large enough to be considered (see WHITNEY, 1957; BARRETt, 1967). The effect, in equation (1), of the verticalvariation of gravity becomes marginally significant only at extreme depths. Uncertainty in the value of density at great depths, however, limits accuracy to about 0.1 ~ (see ECgART, 1958). The value reported as the "pressure coefficient" of the thermometer, Q, is actually Qgo, where go is the magnitude of standard gravity (as revealed by the dimension of Q, degrees kg -1 cm-e). Formula (1) could be corrected by multiplying it by the ratio go~g, where g is gravity at the latitude of the observation. This ratio is 1.0026 at the equator and 0.9974 at the poles; it departs from unity by 0"1 ~ at 34 ° and 56 °, and by 0 . 2 ~ at 20 ° and 70 °. (This correction is analogous to the standard correction of mercurial barometers for the variation of gravity with latitude.) An awkward question now arises: why report thermometric depth ? Oceanographers are accustomed to the interchange from meters to decibars. Pressure is measured directly, and it is the variable of integration in the calculation of geopotential anomaly. The common practice of converting pressure to depth and then using depth instead of pressure in the integration of geopotential anomaly appears ill advised. It is desirable to use and report the observed pressure for an observation. Since the drafting of this note, the author has learned (J. CREASE, personal communication) that the National Institute of Oceanography in Great Britain now reports depth and pressure f o r each observation. Wider use of this practice seems desirable, although pressure alone would be sufficient in published or archived data. I have benefited from discussions of this topic with Dr. N. P. Fofonoff, and I am happy to express my thanks to him. This work was done while the author was supported in part by the Office of Naval Research.
University of Rhode Island, Kingston, R.L 02881, U.S.A.
WILTON STURGE$
REFERENCES
B~Tr
(1967) On the precision of the Deep-Sea Res., 14 (2), 2?7-278. J. R .
--
2 ° to 6°C Richter and Wiese reversing thermometers.
645
646
Letter to the Editors
ECKART CARL (1958) Properties of water, part H. The equation of state of water and sea water a*. low temperatures and pressures. Am. J. Sci., 256, 225-240. FOFONOrF N. P. (1963) Precision of oceanographic data for sound-speed calculations. J. acoust. Soc. Am., 35 (6), 830-836. WHITNEY G. G. Jr. (1957) Factors affecting the accuracy of thermometric depth determinations J. Cons. perm. int. Explor. Mer, 22 (2), 167-173. W0ST GEORG (1933) Thermometric measurement of depth. Hydrogr. Rev., 10 (2), 28-49.
LETTER
Pergamon Press.
TO
THE
Printed in Great Britain.
EDITORS
Thermometric depth and gravity variations Tim FORMULAcommonly used for computing thermometric depth from hydrographic data fails to include the magnitude of local gravity, and this omission introduces an error which warrants consideration in work of high accuracy. The formula used is that of Wt~ST (1933). Depth, D, is given as 10 At D -- Qpm '
(l)
where Q is the so-called "pressure coefficient" of the unprotected thermometer, p,~ is the mean density of the sea-water column above the observation, and At is the difference in corrected readings of the protected and unprotected thermometers. (The factor of 10 results from the units commonly used.) Equation (1) should contain, in the denominator, the magnitude of gravity at the latitude of the observation, because hydrostatic pressure depends on gravity. The derivation is trivial, but the omission seems not to be widely recognized. The depth calculated from the corrected formula will vary with latitude. As the magnitude of gravity increases from the equator to the pole, the extreme difference affects thermometric depth by slightly more than 5 m/km of depth. This amount is less than the precision usually ascribed to the method (see FOFONOFF, 1963), but when the best instruments are used with care this effect may be large enough to be considered (see WHITNEY, 1957; BARRETt, 1967). The effect, in equation (1), of the verticalvariation of gravity becomes marginally significant only at extreme depths. Uncertainty in the value of density at great depths, however, limits accuracy to about 0.1 ~ (see ECgART, 1958). The value reported as the "pressure coefficient" of the thermometer, Q, is actually Qgo, where go is the magnitude of standard gravity (as revealed by the dimension of Q, degrees kg -1 cm-e). Formula (1) could be corrected by multiplying it by the ratio go~g, where g is gravity at the latitude of the observation. This ratio is 1.0026 at the equator and 0.9974 at the poles; it departs from unity by 0"1 ~ at 34 ° and 56 °, and by 0 . 2 ~ at 20 ° and 70 °. (This correction is analogous to the standard correction of mercurial barometers for the variation of gravity with latitude.) An awkward question now arises: why report thermometric depth ? Oceanographers are accustomed to the interchange from meters to decibars. Pressure is measured directly, and it is the variable of integration in the calculation of geopotential anomaly. The common practice of converting pressure to depth and then using depth instead of pressure in the integration of geopotential anomaly appears ill advised. It is desirable to use and report the observed pressure for an observation. Since the drafting of this note, the author has learned (J. CREASE, personal communication) that the National Institute of Oceanography in Great Britain now reports depth and pressure f o r each observation. Wider use of this practice seems desirable, although pressure alone would be sufficient in published or archived data. I have benefited from discussions of this topic with Dr. N. P. Fofonoff, and I am happy to express my thanks to him. This work was done while the author was supported in part by the Office of Naval Research.
University of Rhode Island, Kingston, R.L 02881, U.S.A.
WILTON STURGE$
REFERENCES
B~Tr
(1967) On the precision of the Deep-Sea Res., 14 (2), 2?7-278. J. R .
--
2 ° to 6°C Richter and Wiese reversing thermometers.
645
646
Letter to the Editors
ECKART CARL (1958) Properties of water, part H. The equation of state of water and sea water a*. low temperatures and pressures. Am. J. Sci., 256, 225-240. FOFONOrF N. P. (1963) Precision of oceanographic data for sound-speed calculations. J. acoust. Soc. Am., 35 (6), 830-836. WHITNEY G. G. Jr. (1957) Factors affecting the accuracy of thermometric depth determinations J. Cons. perm. int. Explor. Mer, 22 (2), 167-173. W0ST GEORG (1933) Thermometric measurement of depth. Hydrogr. Rev., 10 (2), 28-49.