2.2 Data quality control
2.2.3 Thermal lag correction
Salinity is estimated using measurements of seawater conductivity, which is mostly dependent on seawater temperature, significantly less on salt ions and weakly dependent on pressure. Salinity can be derived from measurements of pressure, temperature and conductivity. The accuracy of the salinity mea- surements will depend on the matching of the temperature and conductivity sensors response times. The signal of the conductivity sensor in a CTD depends on three factors: the flushing of the inside of the sensor, the bound- ary layer of the fluid against the wall of the sensor and the heat stored in the wall of the sensor (Lueck and Picklo, 1990). The first two factors are “short-term” while the heat stored in the sensor (sensor’s thermal inertia) induces a “long-term” response. This long-term response, hereafter referred to as “Thermal lag error”, is about one order of magnitude larger than both short-term responses. Correcting for this long-term response is particularly important for data that are going to be used to estimate ocean mixing since estimating mixing requires highly precise density estiamtes.
Thermal lag error
The Sea Bird conductivity sensor is mostly composed of glass, which has a high thermal inertia. The heat stored in the glass walls of the sensor takes a few tens of seconds to diffuse through the water inside the sensor, chang- ing the temperature of the water being sampled. This leads to an incorrect estimate of conductivity and thus salinity, with characteristic thermal-lag
timescale error of tens of seconds. The thermal lag error is highest in large in-situ temperature gradients. During a downcast, for example, the sensor travels from warmer waters to colder waters (Figure 2.5). As the instru- ments descends, the heat stored in the conductivity sensor warms entering water, raising the conductivity measurement and therefore the salinity read- ing. Similarly, on an upcast, the sensor is moving from colder to warmer water, lowering the conductivity and salinity measurements. A pumped in- strument will minimize this error but not eliminate it.
Mixed layer depth
Figure 2.5: Theoretical example of temperature and salinity profiles for de- scending (left) and ascending (right) profiles. The solid lines show observed values that include the thermal lag effect; dashed lines show the theoretical or thermal lag corrected data.
Correction method
The thermal lag correction involves deriving a “corrected” temperature of the seawater in the conductivity sensor and then re-calculating salinity. This
is done applying a discrete time domain, recursive filter scheme with two parameters: α, which describes the initial amplitude of the conductivity error and τ, which describes the time constant of the conductivity error (Morison et al., 1994). The temperature correction (Tc) at sample index
(n) is subtracted from the measured temperature to estimate the corrected temperature in the conductivity sensor
Tc(n) =−bTc(n−1) +a[T(n+ 1)−T(n)], (2.8)
where T is the measured temperature and
a= 4fnατ(1 + 4fnτ)−1 b= 1−2aα−1.
Here we follow the method used byJohnson et al.(2007) on SBE-41 CTDs to estimateα and τ. We expect a spike in salinity at the transition between the bottom of the mixed-layer and the ocean interior due to the thermal lag effect (Figure 2.5). A thermal lag signature will be more easily identified for profiles with a well-defined surface thermal mixed-layer and a large vertical temperature gradient. When an ascending float goes from cooler to warmer waters, the deepest measured data point of the thermal mixed-layer typically shows a low salinity spike when compared to the points above (Figure 2.5). We identify all profiles with a well-defined surface thermal mixed-layer and a large vertical temperature gradient and apply the thermal lag correction with a range of values forα and τ.
We then search for theαandτ combination that minimizes the difference between the mean thermal lag corrected potential density of the bottom two points of the thermal mixed-layer and the mean uncorrected potential density in the rest of the thermal mixed-layer. The bottom of the mixed-layer is defined as the depth where dT /dz > 0.0005◦C m−1. The mean uncorrected
potential density is calculated in the mixed-layer from 20 data points below the surface down to 60 data points above the mixed-layer. When the thermal lag correction parameters are accurate, the mixed-layer profile is close to being statically stable (Figure 2.6).
6.5 6.55 6.6 20 21 22 23 24 25 26 27 28 29 Profile 44 Temperature [o C] Pressure [dbar] 33.805 33.81 33.815 33.82 33.825 33.83 20 21 22 23 24 25 26 27 28 29 Salinity Pressure [dbar] Profile 44 1026.53 1026.535 1026.54 1026.545 20 21 22 23 24 25 26 27 28 29 Profile 44 Potential density [kg/m3] Pressure [dbar] Uncorrected Mixed layer depth Thermal lag corrected
(a) Profile 44 of float 3761.
7.35 7.4 7.45 20 21 22 23 24 25 26 27 28 29 Profile 20 Temperature [o C] Pressure [dbar] 33.774 33.776 33.778 33.78 33.782 20 21 22 23 24 25 26 27 28 29 Salinity Pressure [dbar] Profile 20 1026.39 1026.395 1026.4 1026.405 1026.41 20 21 22 23 24 25 26 27 28 29 Profile 20 Potential density [km/m3] Pressure [dbar] Uncorrected Botton of mixed layer Thermal lag corrected
(b) Profile 20 of float 3762.
Figure 2.6: Temperature, salinity and potential density profiles of (a) profile 44 from float 3761and (b) profile 20 from float 3762 where black denotes raw data and blue denotes thermally corrected data. The corrected salinity was derived using median thermal lag correction coefficients α = 0.023 and
Reference CTD α τ [s] α∗τ α IS τ IS
Lueck and Picklo (1990) SBE-4-01 0.028 9 0.25 N/A N/A
Morison et al.(1994) SBE-9 0.0245 9.5 0.23 N/A N/A
Pinot et al. (1997) SBE-25 0.03 14 0.42 N/A N/A
Johnson et al.(2007) SBE-41 0.023 20 0.46 0.019 24 NOAA floats
Johnson et al.(2007) SBE-41 0.028 16 0.45 0.011 32 UW floats
This study SBE-41 0.023 25 0.60 0.031 23
EM-APEX floats
Table 2.4: Weighted median values and interquartile spreads (IS) of sensor response corrections for SBE-41 CTDs.
and large vertical temperature gradients at the bottom of the mixed-layer by applying a careful screening on ascending profiles. The temperature and salinity data are interpolated onto a uniform 1 Hz grid to work in temporal gradients rather than vertical spatial gradients. For each profile we identified the bestαandτcombination that minimizes the difference between the mean thermal lag corrected potential density of the bottom of the thermal mixed- layer and the mean uncorrected potential density in the rest of the thermal mixed-layer (Figure 2.7).
Thermal lag parameters
The median value ofτ is 25 s with an interquartile spread of 23 s. The median value of α is 0.023 with an interquartile spread of 0.031 and the product of the medianαandτ is 0.60 (Table2.4). These values are very close to the val- ues Johnson et al. (2007) derived for the National Oceanic and Atmospheric Administration/Pacific Marine Environmental Laboratory (NOAA/PMEL) and University of Washington (UW) floats (Table 2.4). The fact that the original 1 Hz CTD data from the EM-APEX floats were not accessible makes
correcting for thermal lag difficult. However, it is encouraging that the ther- mal lag correction coefficients for the same CTD but different float types are very similar. The thermal lag correction is described in Section 2.2.1.
0 20 40 60 80 100 120 140 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 o[s] _ Median alpha=0.0235 Median tau=25.5 Float 1901136 Float 1901137 Float 1901138 Float 1901139 Float 1901140 Float 1901141 Float 1901143 !"#$% !"#&% !'()% !"#)% !'($% !'(&% !"#*%
Figure 2.7: Values of thermal lag correction parametersα and τ for selected profiles from EM-APEX floats with SBE-41 CTD (3760, 3761, 3952, 3762, 3950, 3951, and 3764). The median value (red circle) and the curve for constant median value ofα×τ (thin black line) are displayed.