2
The SBE 43 is expected to provide an output voltage that is linear with respect to oxygen concentration. Normal
calibration drift manifests itself as a loss of sensitivity and is evident as a change of slope (and less so in offset) in
the linear relationship between oxygen concentration and voltage output. The coefficients A, B, C, and E correct for
small secondary responses to temperature and pressure. Because these coefficients change very slowly over time, the
values given on the SBE 43 calibration certificate will be used in this analysis, and we will concern ourselves with
estimating changes in the slope (Soc) and offset (Voffset).
Setting
t
V
∂
∂
to zero, we rearrange equation 1 into a linear form and perform a linear regression to obtain a new
Soc and Voffset.
Let:
()
)
*
(
32
****0.1),(
K
PE
eTCTBTASTOxsol +++∗=
φ
eqn 2
The oxygen equation then reduces to the form in equation 3:
+∗= )()/( VoffsetVSoclmlOxygen eqn 3
This may be expressed in a linear form in equation 4.
BVMVoffsetVSoc
lmlOxygen
+∗=+∗= )(
)/(
φ
eqn 4
Where:
Soc = M
Voffset = B / M
A linear regression is calculated using Winkler oxygen concentration divided by φ as the dependent variable and
SBE 43 output voltage as the independent variable.
237
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