APPLICATION NOTE NO.
Compressibility Compensation of Sea-Bird Conductivity Sensors
Revised May 2013
Sea-Bird conductivity sensors provide precise characterization of deep ocean water masses. To achieve the accuracy of which the sensors are capable, an accounting for the effect of hydrostatic loading (pressure) on the conductivity cell is necessary. Conductivity calibration certificates show an equation containing the appropriate pressure-dependent correction term, which has been derived from mechanical principles and confirmed by field observations. The form of the equation varies somewhat, as shown below:
SBE 4, 9, 9plus, 16, 19, 21, 25, 25plus, 26, 26plus, and 53 BPR
SBE 16plus, 16plus-IM, 16plus V2, 16plus-IM V2, 19plus, 19plus V2, 37, 45, 49, and 52-MP
Sea-Bird CTD data acquisition, display, and post-processing software Seasoft for Waves (for SBE 26, 26plus, and 53 only) and Seasoft (for all other instruments) automatically implement these equations.
Conductivity cells do not measure the actual conductance (the desired property), but rather the conductance of a specific geometry of water. The ratio of the cell's length to its cross-sectional area (cell constant) is used to relate the measured conductance to the actual conductance. Under pressure, the conductivity cell's length and diameter are reduced, leading to a lower indicated conductivity. The magnitude of the effect is not insignificant, reaching 0.0028 S/m at 6800 dbars.
The compressibility of the borosilicate glass used in the conductivity cell (and all other homogeneous noncrystalline materials) can be characterized by E (Young's modulus) and ν (Poisson's ratio). For the Sea-Bird conductivity cell, E = 9.1 x 106 psi, ν = 0.2, and the ratio of indicated conductivity divided by true conductivity is:
1 + s
Note: This equation, and the mathematical derivations below, deals only with the pressure correction term, and does not address the temperature correction term.
For a cube under hydrostatic load:
ΔL / L = s = - p ( 1 - 2 ν) / E
Since this relationship is linear in the forces and displacements, the relationship for strain also applies for the length, radius, and wall thickness of a cylinder.
To compute the effect on conductivity, note that R0 = ρ L / A , where R0 is resistance of the material at 0 pressure; ρ is volume resistivity, L is length, and A is cross-sectional area. For the conductivity cell:
A = p r 2
Under pressure, the new length is L (1 + s ) and the new radius is r (1 + s ). If Rp is the cell resistance under pressure:
Rp = ρ L (1 + s) / (p r 2 [1 + s ] 2) = ρ L / p r 2 (1 + s ) = R0 / (1 + s )
Since conductivity is 1/R:
Cp = C0 (1 + s ) and C0 = Cp / (1 + s ) = Cp / (1 + [CPcor] [p])
A less rigorous determination may be made using the bulk modulus of the material. For small displacements in a cube:
ΔV/V = 3 ΔL/L = - 3p (1 - 2ν) / E or ΔV/V = - p / K
In this case, ΔL/L = - p / 3K.
|May 2004||Update to include SBE 26plus.|
|July 2005||- Update to include SBE 52-MP and
- Provide more details on 26, 26plus, and 53.
|March 2008||Update to include V2 SeaCATs (16plus V2, 16plus-IM V2, 19plus V2).|
|October 2012||Update to include SBE 25plus.|
|May 2013||Update language, replacing ‘specific conductance’ with ‘actual conductance’ to avoid confusion (specific conductance is conductivity normalized to 25 °C, typically used for fresh water applications).|
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