Equation Of State For Seawater Research Articles

Practical Conversion of Pressure to Depth

A conversion formula between pressure and depth is obtained employing the recently adopted equation of state for seawater (Millero et al., 1980). Assuming the ocean of uniform salinity 35 NSU and temperature 0°C the following equation is proposed, namely, z = (1-c1)p − c2p2. If p is in decibars and z in meters c1 = (5.92 + 5.25 sin2ϕ) × 10−3, where ϕ is latitude and c2 = 2.21 × 10−6. To take account of the physical conditions in the water column a dynamic height correction is to be added but for many purposes this may be ignored.

Available Potential Energy for MODE Eddies

Available, potential energy (APE) is defined as the difference between total potential plus internal energy of a fluid in a gravity field and a corresponding reference field in which the fluid is redistributed (leveled) adiabatically to have constant stably-stratified densities along geopotential surfaces. Potential energy changes result from local shifts of fluid mass relative to geopotential surfaces that are accompanied by local changes of enthalpy and internal energy and global shifts of mass (because volumes of fluid elements are not conserved) that do not change enthalpy or internal energy. The potential energy changes are examined separately by computing available gravitational potential energy (GPE) per unit mass and total GPE (TGPE) per unit area. A technique for estimating GPF, in the ocean is developed by introducing a reference density field (or an equivalent specific volume anomaly field) that is a function of pressure only and is connected to the observed field by adiabatic vertical displacements. The full empirical equation of state for seawater is used in the computational algorithm. The accuracy of the estimate is limited by the data and sampling and not by the algorithm itself, which can be made as precise as desired. The reference density field defined locally for an ocean region allows redefinition of dynamic height ΔD (potential energy per unit mass) relative to the reference field. TGPE per unit area becomes simply the horizontal average of dynamic height integrated over depth in the region considered. The reference density surfaces provide a precise approximation to material surfaces for tracing conservative variables such as salinity and potential temperature and for estimating vortex stretching between surfaces. The procedure is applied to the MODE density data collected in 1973. For each group of stations within five 2-week time windows (designated Groups A–E) the estimated GPE is compared with the net APE based on the Boussinesq approximation and to the low-frequency kinetic energy measured from moored buoys. Changes of potential energy of the reference field from one time window to the next are large compared with the GPE within each window, indicating the presence of scales larger than the station grid. An analysis of errors has been made to show the sensitivity of the estimates to data accuracy and sampling frequency.

A new high pressure equation of state for seawater

A new high pressure equation of state for water and seawater has been derived from the experimental results of Millero and coworkers in Miami and Bradshaw and Schleicher in Woods Hole. The form of the equation of state is a second degree secant bulk modulus K = Pv 0 (v 0−v p =K 0+AP+BP 2 K = K w 0+aS+bS 3 2 A = A w+cS+dS 3 2 B = B w+eS where ν 0 and ν P are the specific volume at 0 and P applied pressure and S is the salinity (ℵ). The coefficients K W O , A W , and B W for the pure water part of the equation are polynomial functions of temperature. The standard error of the pure water equation of state is 4.3 × 10 −6 cm 3 g −1 in ν W P . The temperature dependent parameters a, b, c, d, and e have been determined from the high pressure measurements on seawater. The overall standard error of the seawater equation of state is 9.0 × 10 −6 cm 3 g −1 in ν P . Over the oceanic ranges of temperature, pressure, and salinity the standard error is 5.0 × 10 −6 cm 3 g −1 in ν P . This new high pressure equation of state has recently (1979) been recommended by the UNESCO Joint Panel on Oceanographic Tables and Standards for use by the oceanographic community.

The use and misuse of pure water PVT properties for lake waters

ALTHOUGH dissolved substances affect the thermodynamic properties of lake waters,1,2 many limnologists still consider lake water as pure water3–8. This can be a good assumption if used with caution: lake water is by no means pure water, especially when the precise pressure, volume, temperature (PVT) properties are considered. PVT properties of lake water can be determined from an equation of state for sea water provided that the total mass fraction of dissolved salts in seawater and lake water are equated9. In addition, the total mass fraction of dissolved salts affects calculations concerning the temperature of maximum density and thus stability10. Therefore, in the absence of direct PVT measurements on a particular lake, it is at present most appropriate to use an equation of state for seawater when examining effects of PVT properties in lakes. We present here a short equation of state determined with a precision of 2 × 10−6 g cm−3 in density over the appropriate range for most fresh water lakes, 0–0.6‰ salinity, 0–30 °C, and 0–180 bar. The equation of state is based on the 1 atm pure water density and compressibility equations of Kell11, the pure water temperature and pressure effects of Fine and Millero12, and the effects of dissolved salts of Millero et al.13 and Chen and Millero14: where dp and d0 are the densities of lake water at applied pressures P and 0 (sea level), respectively, t is the temperature in °C, S(‰) is the salinity: where gT is the total grams of dissolved salt in 1 kg of lake water15. The values of gT usually increase with depth due to the increase of HCO3−, Ca2+ and nutrients16. The small changes in composition in a lake can be accounted for by making the appropriate changes in gt. Further, Millero9 and Millero et al.17 showed that the densities calculated from the seawater equation of state for Lake Tanganyika water and artificial river water agree with the measured values to within ±2×10−6g cm−3 despite the large composition difference between the two waters. This verifies the validity of our equation of state for fresh waters.

Precise equation of state of seawater for oceanic ranges of salinity, temperature and pressure

Abstract A 24-parameter equation of state for sea water was established for use in the open ocean (30 to 40‰ S , −2 to 38°C and up to 1000 bars). The equation of state is in the form: V P = V 0 − V 0 P/K 0 + AP + BP 2 ), where V P and V 0 are the specific volumes of seawater at applied pressures P and 0 (atmospheric pressure), respectively. V 0 , K 0 , A and B are all salinity- and temperature-dependent parameters. The short form equation of state is in excellent agreement (±2 × 10 −6 cm 3 g −1 in specific volume, ±1 × 10 −6 deg −1 in thermal expansibility and ±0.02 × 10 −6 bar −1 in isothermal compressibility) with the full, 48-parameter, equation of state for seawater (C. T. Chen and F. J. Millero , The specific volume of seawater at high pressures, Deep-Sea Research , 23 ,595–612,1976a) and is recommended for usage with calculations concerned with oceanic ranges of salinity, temperature, and pressure.

Prediction of the refractive index of seawater as a function of temperature, pressure, salinity and wavelength

Abstract An equation is given for predicting the absolute refractive index of seawater as a function of wavelength (in the visible region), temperature, pressure and salinity. This equation is based on the pure-water equation of H. Eisenberg, on the Tammann hypothesis and the Tait-Gibson equation of state for seawater. Comparison with experimental results (to 1380 bars) indicate an accuracy of ca. 0.0001 or better is achieved in the T-P range of oceanographic interest.