Post-processing SBE oxygen calibrations

To produce the highest-quality oxygen measurements, post-processing procedures were modeled after methods described in Uchida et al. 2010. The following Seabird-recommended calibration equation was used to calibrate the SBE-43 oxygen sensor data:

O2= SOC(V+ Voff)* Oxysol(T,S)*(1 + A*T + B*T2 + C*T3) * eE*p/(273.15 +T) (Equation 1)

where O2 is the CTD oxygen [μmol/kg], V is the output voltage signal processed with the SBE default hysteresis correction [volts], Oxysol is the oxygen saturation [μmol/kg], T is temperature [deg C], S is salinity [psu], and P is pressure [dbar] (SBE Application Note 64-2). Coefficients for the oxygen calibration slope (SOCa; voltage offset at 0 (Voff); temperature-related calibration coefficients of A, B and C; and pressure-related E term were determined initially from an 18-point factory calibration and provided by the manufacturer (Appendix A). Voff, A, B, and C are constant over the sensor life while values for SOC and E can be optimized using discrete water samples measured analytically for dissolved oxygen, and commonly referred to as Winklers.

Calibration coefficients for SOC and E were optimized by applying a non-linear least-squares fit to Winkler samples while calibration coefficients for A, B, C, and Voff were held constant. Oxygen sensor hysteresis due to pressure effects on the sensor membrane was improved by enabling the Seabird default hysteresis correction (Edwards et al. 2010; SBE Application Note 64-3). The optional response time correction, or tau correction, was determined to add excessive signal noise in relatively stable, deep portions of the water column; and, therefore, was not applied in the calibration equation.

While using this approach, a non-linear functional fit of Equation 1 was first attempted using one set of coefficients for the entire data set (whole cruise). Model fits were iterative with outliers discarded. Outliers were determined as values more than three scaled median absolute deviations from the median.

With outliers removed, residuals between CTD values and water sample values were then examined as a function of pressure, temperature, oxygen concentration, and cast number (≈ cruise time). An examination of the residuals as a function of cast number was used to 1) identify episodic events resulting in abrupt changes in SOC values, and 2) determine potential drift in SOC over the course of the cruise. After examining the residuals, cast numbers were grouped if necessary to minimize the residuals with an attempt to limit the number of groups used per cruise. New calibration coefficients were then determined for each group.

If a linear drift as a function of cast number (cn) or cruise time (dt) was determined for a group, a linear correction of the SOC drift was applied to the group while keeping other coefficients constant. The linear drift as a function of cast number/cruise time was then incorporated into the calibration equation, replacing SOC in Equation 1 as a function of cruise number/cruise time as:

SOCcn/dt = SOC1 + F*cn/dt (Equation 2)

where cn or dt is the cast number [-] or time since first cast [d], respectively. SOC1 is the initial SOC value, and F is the rate of SOC change per cast number or day since first cast.

A nonlinear functional fit including the cast or time-dependent SOCcn/dt was then fit to the group determining coefficients for E, SOC1, and F while holding A, B, C, and Voff constant. After iterative fitting and outliers removed, residuals were examined again as a function of pressure, temperature, oxygen concentration and cast number to ensure no linear dependence of residuals as a function of time. Outliers were determined as values more than three scaled median absolute deviations from the median.

For each cruise, CTD-derived measurements of salinity and oxygen solubility were calculated using the TEOS-10 Gibbs-SeaWater Oceanographic Toolbox (McDougall and Barker, 2011). Measurements from primary CTD sensors recorded in line with the SBE43 oxygen sensors were used to calculate oxygen concentrations unless collected data was poor. In these instances, measurements from the secondary CTD sensors were used. Bottle-calibrated CTD salinity measurements were used to produce oxygen concentrations. The measurements of temperature, salinity, pressure and oxygen voltage (processed with SBE default hysteresis correction; Application Note 64-3) used to produce oxygen concentration profiles are included in files for downcasts (indicated with ‘d’ appended) or upcasts (indicated with ‘u’ appended).

Throughout this documentation, oxygen profiles calibrated using a constant SOC value are indicated by SOCk while oxygen profiles calibrated using an SOC term that varies with time or cast (station) number are indicated by SOCdt and SOCcn, respectively. Lastly, oxygen sensor gain is determined as the Winkler-determined SOC value over the factory-determined SOC to assess changes in oxygen calibration slope since factory calibration. Note, the manufacturer recommends factory service inspection and calibration for a SBE43 DO sensor with a gain correction greater than 1.2 from the original factory value (Application Note 64-2).

Deployment Cruise AR45

Summary of Relevant Cruise Information

The AR45 Cruise Report (see cruise report in Pickart & McRaven (2022)) was generated by participants of OSNAP22. The COVID-19 pandemic presented a number of challenges for sea-going operations in 2020. Traditionally, Winkler measurements are made at sea by trained technicians; however, to minimize shipboard personnel in 2020, discrete samples for oxygen were collected and stored according to methods described by Zhang et al. (2002) until subsequent analysis back on land. Results of discrete sample analyses for AR45 are available on BCO-DMO (related dataset: Palevsky et al. 2024).

A total of 163 CTD casts were performed on-board the R/V Armstrong. CTD-derived salinity data were calibrated by Leah McRaven at Woods Hole Oceanographic Institution using discrete bottle samples (Pickart and McRaven 2022). Conductivity and temperature data on this cruise were affected by biofouling issues and CTD pump issues. Issues with the CTD pump resulted in unphysical density inversions and uncharacteristic oxygen profiles in near surface waters for Casts 1-70. These pump-related density and oxygen issues were resolved by replacing the CTD package pump before Cast 71. The biofouling and pump issues are summarized in the AR45 CTD Calibration Report (see CTD calibration report in Pickart & McRaven (2022)) The temperature, bottle-calibrated salinity and depth data from the primary CTD package were used in the oxygen sensor calibration equation to calibrate SBE43 (SN 1960) oxygen sensor data. The hysteresis between upcast and downcast oxygen data due to sensor response time was removed by advancing the oxygen sensor data 5 seconds relative to the pressure sensor data.

Oxygen calibration Results

Calibration coefficients for SOC and E in Equation 1 were determined using a non-linear least squares fit between CTD oxygen values and 68 Winkler samples while calibration coefficients for A, B, C, and Voff were held constant at their factory-determined values (Appendix A). Residuals (Winkler - SOCk model) determined using a constant SOC revealed no relationship between residuals and pressure, temperature, or oxygen concentration (Figure 1, supplemental file: AR45_OxygenCalibration_Results.pdf). The SOCk model (RMSE = 0.78 μmol/kg, R2 = 0.995) flagged 9 Winkler samples (13.2%) as outliers. It was decided that only a constant SOC correction was appropriate for this cruise since 1) Winklers were not measured onboard, 2) Winklers were measured on just 4.3% of casts, and 3) negative relationship observed between SOC and time is not representative of typical electrochemical sensor drift (Application Note 64-2). The Winkler-optimized calibration coefficients and model results are summarized in Table 1. Oxygen data before and after calibration is shown in Figure 2 (supplemental file: AR45_AR6903_OxygenCalibrationResults_FiguresTables.pdf).

Deployment Cruise AR69-03

Summary of Relevant Cruise Information

The AR69-03 Cruise Report (see cruise report in Straneo (2023)) was generated by participants of OSNAP32. Results of discrete sample analyses for AR69-03 are available on BCO-DMO (Related Dataset: Palevsky et al. 2024). A total of 214 CTD casts were performed on-board the R/V Armstrong. CTD-derived salinity data were calibrated by Aaron Mau at Scripps Institution of Oceanography using discrete bottle samples, and results are summarized in the AR69-03 CTD Calibration Report (see CTD calibration report in Straneo (2023)). Temperature, bottle-calibrated salinity and depth data from the primary CTD package were used in the oxygen sensor calibration equation to calibrate SBE43 (SN 1960) oxygen sensor data. The hysteresis between upcast and downcast oxygen data due to sensor response time was removed by advancing the oxygen sensor data 5 seconds relative to the pressure sensor data.

Oxygen calibration Results

Calibration coefficients for SOC and E in Equation 1 were attempted first using a non-linear least square fit between CTD oxygen values and the 585 Winkler samples collected on 82 unique casts. Resulting residuals were linearly correlated with temperature and oxygen concentration. Examination of Winkler residuals revealed issues with relatively high concentration Winklers collected in colder, surface waters. This may either indicate issues in the CTD dissolved oxygen sensor’s sensitivity and fit at these concentrations, or it may indicate a systematic measurement error in the Winkler dissolved oxygen analysis (for instance, due to possible oxygen degassing prior to sample collection and preservation). As such, Winklers greater than 316 μmol/kg were removed from this analysis, leaving 462 Winklers to determine oxygen sensor calibration coefficients.

The calibration coefficient for the E term in Equation 1 was determined using a non-linear least square fit between CTD oxygen values and 311 Winkler samples collected on 38 deep casts (deeper than 1000 m). The SOCk model (RMSE = 0.840 μmol/kg, R2 = 0.993, n = 283) for deep casts flagged 28 Winkler samples (9.0%) as outliers. The calculated E term of 0.0372 was then held constant for the sensor over the duration of AR69-03 and the SOC calibration coefficient was optimized by breaking stations into groups.

Group 1: The calibration coefficient for SOC in Equation 1 was determined for Group 1 using a non-linear least square fit between CTD oxygen values and the 21 Winkler samples collected at Stations 1-2. Residuals (Winkler - SOCk model) determined using a constant SOC revealed no relationship between residuals and pressure, temperature, station or oxygen concentration. The SOCk model (RMSE = 0.191 μmol/kg, R2 = 1.00, n = 18) flagged 3 Winkler samples (14.3%) as outliers.

Group 2: Group 2 consisted of Stations 3-24, and application of the non-linear regression model using a time-dependent SOC term (Equation 2) was found to minimize the residuals between 109 collected Winklers and CTD oxygen. No relationship between residuals (Winkler- SOCdt model) and pressure, temperature, station or oxygen concentration remained with the SOCdt model fit. The SOCdt model for Group 2 (RMSE = 0.517 μmol/kg, R2 = 0.998, n = 98) flagged 11 Winklers (10.1%) as outliers.

Group 3: The calibration coefficient for SOC in Equation 1 was determined for Group 3 using a non-linear least square fit between CTD oxygen values and the 59 Winkler samples collected at Stations 25-63. Residuals (Winkler - SOCk model) determined using a constant SOC revealed no relationship between residuals and pressure, temperature, station or oxygen concentration. The SOCk model (RMSE = 1.23 μmol/kg, R2 = 0.986, n = 51) flagged 8 Winkler samples (13.6%) as outliers.

Group 4: The calibration coefficient for SOC in Equation 1 was determined for Group 4 using a non-linear least square fit between CTD oxygen values and the 47 Winkler samples collected at Stations 64-82. Residuals (Winkler - SOCk model) determined using a constant SOC revealed no relationship between residuals and pressure, temperature, station or oxygen concentration. The SOCk model (RMSE = 0.614 μmol/kg, R2 = 0.998, n = 47) flagged no Winkler samples as outliers.

Group 5: Application of the non-linear regression model using a time-dependent SOC term (Equation 2) was found to minimize the residuals between the 65 Winklers collected and CTD oxygen at Stations 83-99. No relationship between residuals (Winkler- SOCdt model) and pressure, temperature, station or oxygen concentration remained with the SOCdt model fit. The SOCdt model for Group 5 (RMSE = 0.699 μmol/kg, R2 = 0.993, n = 56) flagged 9 Winklers (13.9%) as outliers.

Group 6: The calibration coefficient for SOC in Equation 1 was determined for Stations 100-172 using a non-linear least square fit between CTD oxygen values and 134 Winkler samples. Residuals (Winkler - SOCk model) determined using a constant SOC revealed no relationship between residuals and pressure, temperature, station or oxygen concentration. The SOCk model (RMSE = 0.885 μmol/kg, R2 = 0.988, n = 116) flagged 18 Winkler samples (13.4%) as outliers.

Group 7: Application of the non-linear regression model using a time-dependent SOC term (Equation 2) was found to minimize the residuals between the 27 Winklers collected and CTD oxygen at Stations 173-214. No relationship between residuals (Winkler- SOCdt model) and pressure, temperature, station or oxygen concentration remained with the SOCdt model fit. The SOCdt model for Group 7 (RMSE = 1.13 μmol/kg, R2 = 0.988, n = 25) flagged 2 Winklers (7.4%) as outliers.

Residuals as a function of pressure, station number, temperature, and concentration are shown for all 7 groups in Figure 3. The Winkler-optimized calibration coefficients and model results for the 7 groups are summarized in Table 2. Oxygen data before and after calibration is shown in Figure 4 (supplemental file: AR45_AR6903_OxygenCalibrationResults_FiguresTables.pdf).