This study investigated the effect of hydrostatic pressure of up to 6000 dbar on Aanderaa and Sea-Bird oxygen optodes both in the laboratory and in the field. The overall pressure response is a reduction in the O2 reading by 3%–4% per 1000 dbar, which is closely linear with pressure and increases with temperature. Closer inspection reveals two superimposed processes with an opposite effect: an O2-independent pressure response on the luminophore that increases optode O2 readings and an O2-dependent change in luminescence quenching that decreases optode O2 readings. The latter process dominates and is mainly due to a shift in the equilibrium between the sensing membrane and seawater under elevated pressures. If only the dominant O2-dependent process is considered, then the Aanderaa and Sea-Bird optodes differ in their pressure response. Compensation of the O2-independent process, however, yields a uniform O2 dependence for Aanderaa optodes with standard foil and fast-response foil as well as for Sea-Bird optodes. A new scheme to calculate optode O2 from raw data is proposed to account for the two processes. The overall uncertainty of the optode pressure correction amounts to 0.3% per 1000 dbar, which is mainly due to variability between the sensors.
Oxygen optodes have become a core element of autonomous biogeochemical observations (Johnson et al. 2009). There is rarely a biogeochemical field study that does not measure oxygen (e.g., Fennel et al. 2011; Johnson et al. 2010) because of its core character within fundamental biogeochemical processes, that is, primary production, respiration, and oxidation. The focus of this work is placed on the processing of oxygen optode data with regard to the effects of hydrostatic pressure.
Sensor measurements essentially encompass two separate steps:
Step 1: Data acquisition, that is, the transfer of an environmental state to sensor raw data, for example, the optode’s lifetime information.
Step 2: Translation of the raw sensor data to the parameter of interest, that is, O2 content in our case.
The second step relies on a functional model that mimics the physics of the sensing principle (and the sensor design). For oxygen optodes, the temperature dependence and the pressure dependence are usually dealt with separately and several functional models are in use (see below). Despite some differences, all of them succeed in relating the sensor output—that is, the optode raw data plus salinity and pressure measurements—with the target variable, a temperature-, salinity-, and pressure-corrected O2 value, either expressed as oxygen concentration or partial pressure .
The temperature-dependent part of the functional model has received quite some attention in recent years. It evolved from a polynomial approach (e.g., Aanderaa Data Instruments 2009, appendix 6) over variants of a Stern–Volmer inspired, parametric function (Uchida et al. 2008, 2010; Sea-Bird Electronics 2013) to a model approximating two-site physics (McNeil and D’Asaro 2014). The calculated oxygen quantity is either the (freshwater) (Aanderaa Data Instruments 2009; Uchida et al. 2008; Sea-Bird Electronics 2013), which requires subsequent salinity correction, or the (Bittig et al. 2012; McNeil and D’Asaro 2014), which can be converted to concentration via the oxygen solubility (Garcia and Gordon 1992) [see Eq. (6) in section 2a].
The pressure correction, in contrast, is only poorly constrained. Laboratory experiments of Aanderaa optodes provided a linear dependence of optode on hydrostatic pressure P,
where f is 4% per 1000 dbar (Tengberg et al. 2006). A field study by Uchida et al. (2008) refined this number to 3.2% per 1000 dbar, which is generally used for these sensors today (e.g., Thierry et al. 2013). Sea-Bird Electronics SBE63 optodes use a temperature- and pressure-dependent exponential equation,
with temperature ϑ (°C) (Sea-Bird Electronics 2013), which comes down to approximately 4% per 1000 dbar.
The Tengberg et al. (2006) results are based on few pressure cycles and three Aanderaa optodes with closely succeeding serial numbers—that is, a similar history—only. The Uchida et al. (2008) study is somewhat more extensive in that it used 11 Aanderaa optodes at a total of 279 hydrocasts with Winkler-based oxygen titrations on 8047 discrete samples. This dataset, however, is dominated by one individual sensor (255 casts, 7234 Winkler samples). There is no study known to us that deals with the pressure response of SBE63 optodes.
The aim of this study is as follows:
to reinvestigate the pressure dependence of Aanderaa and Sea-Bird optodes using both laboratory and field experiments,
to properly separate pressure from temperature effects on the optode pressure response,
to reevaluate and improve existing pressure-correction algorithms, and
to characterize the error associated with the pressure correction.
This manuscript first deals with some theoretical background on the conversion of oxygen quantities and the relation between pressure and luminescence quenching. Then the laboratory and field experiments are presented and a pressure-correction rationale is derived from the results. Finally, the pressure response of the Aanderaa and Sea-Bird optodes and its uncertainty is quantified.
a. Oxygen quantity conversion
Oxygen saturation can be expressed in terms of oxygen concentration, as the ratio of to O2 solubility , and in terms of partial pressure, as the ratio of water to the atmospheric equilibrium partial pressure ,
Equation (3) can thus be used to easily convert between concentrations and partial pressures.
At the sea surface, follows
where is the saturation water vapor pressure after Weiss and Price (1980) and is the mixing ratio of O2 in dry air (Glueckauf 1951). Term and thus O2 saturation are therefore dependent on the ambient atmospheric pressure . The temperature (ϑ)- and salinity (S)-dependent seawater O2 solubility is given for a pressure of 1 atm (Garcia and Gordon 1992) and needs to be scaled to ambient pressure for surface applications according to
to give a proper saturation [Eq. (3)]. In the above equation, only components other than water vapor are scaled since depends on temperature and salinity only but not on .
that is, the conversion of to concentration is independent of (since the change in O2 saturation cancels out).
Below the surface, hydrostatic pressure P affects both the oxygen solubility and partial pressure. Enns et al. (1965) describe an exponential increase in of about 14% per 1000 dbar and Taylor (1978) gives a theoretical relationship,
where mL is the molar volume of O2 in seawater (Enns et al. 1965) and J is the universal gas constant. The increase with hydrostatic pressure reflects a higher outgassing tendency with depth, that is, a reduced solubility . Consequently, Eqs. (7) and (6) need to be combined for the conversion between and for subsurface applications.
b. Pressure, chemical potential, and luminescence quenching
The rationale behind the pressure dependence of and is nicely discussed in Ludwig and Macdonald (2005) and in parts reproduced below.
The chemical potential of a species i determines its ability to act in a chemical reaction or state transition. It is defined as
where is the activity of the species and is the chemical potential of an (imaginary) standard state at the same temperature T (kelvins) and P. For dissolved oxygen, the standard state is chosen according to Henry’s law to be an ideal solution where O2 is infinitely diluted in the solvent. In that state, activity equals concentration and the activity coefficient is 1,
According to this definition, activity is an effective concentration and includes only solute–solute interactions but no solute–solvent or solvent–solvent interactions (see case i in Ludwig and Macdonald 2005).
From thermodynamics, the pressure dependence of the chemical potential is
where is the partial molar volume at infinite dilution (i.e., in the imaginary standard state) and is the actual partial molar volume. Experimental data show no apparent difference of in seawater or freshwater (Enns et al. 1965) and there is no concentration dependence (cf. Ludwig and Macdonald 2005), that is, is not significantly different from .
Thus, the concentration (and activity) stays nearly unchanged upon pressurization and the main pressure effect is on the chemical potential of the reference state (see case i in Ludwig and Macdonald 2005). As a consequence, the solubility changes with pressure. The change in and solubility accounts for the structural effect of pressure (on solute–solvent and solvent–solvent interactions). This is reflected in the higher outgassing tendency of O2 with pressure [increased ; Eq. (7); Enns et al. 1965].
There is some confusion in the literature about the pressure effect on luminescence quenching by oxygen. Since increases significantly (ca. 14% per 1000 dbar), one would assume luminescence quenching to increase concurrently (e.g., Taylor 1978; McNeil and D’Asaro 2014). However, no such effect is observed for a luminophore in solution (Carey and Gibson 1976). Instead, the authors see a small increase in fluorescence intensity (5% at 10 000 dbar) attributed to the compression of the solution.
The reason for this at first counterintuitive observation is that dynamic quenching by O2 is a diffusion-controlled process (see Lakowicz 2006). The diffusion of oxygen is driven by the gradient in chemical potential and retarded by frictional resistance. Pressure increases [Eq. (10)], however, it is shifted by the same amount throughout the solvent (since is the same) and the gradient of remains constant, that is, quenching in solution stays the same. The observed marginal increase in fluorescence (Carey and Gibson 1976) can be attributed to changes in geometry (and thus the concentration) as well as viscosity upon compression.
In the case of oxygen optodes, the situation is slightly more complicated since phase equilibrium is involved: The luminophore is embedded in a silicone sensing membrane (M) that is in equilibrium with the ambient liquid seawater (L) with equilibrium condition
With Eq. (8), this yields
where and refer to the standard state in the membrane and liquid, respectively (i.e., they are different). The pressure dependence at equilibrium follows
The ambient seawater as bulk liquid will determine the location of the equilibrium (as a result of its relative size). Following the same argument as given above, its activity will remain constant, that is, . Equation (14) simplifies to
which upon integration from dbar gives
Pressure changes the partitioning of the equilibrium and thus the membrane O2 concentration (activity) because of a difference in the partial molar volumes. In seawater mL (Enns et al. 1965), while in the silicone sensing membrane is larger (39 mL , Kamiya et al. 1990; 46 mL , Kamiya et al. 2000). Accordingly, the O2 concentration inside the sensing membrane (which is relevant for luminescence quenching) is reduced by ca. 3.0% or 5.5% per 1000 dbar. The optodes are thus expected to show a lower O2 under pressure. This equilibrium effect is slightly stronger at low temperatures [see Eq. (16)].
If geometry/viscosity changes are included, then compression leads to both a subtle increase in O2 concentration (order of 0.4% per 1000 dbar; Jordan and Koros 1990) and an increase in viscosity of the sensing membrane. The latter causes oxygen diffusivity to decrease and luminescence quenching as a diffusion-controlled process thus becomes less efficient (Lakowicz 2006). Therefore, lifetimes (phase shift, phase delay) are higher and there appears to be less O2 detected by the optode. However, we consider the μ-increase-caused re-equilibration of O2 between the sensing membrane and ambient water to be the main driver for the optode pressure response, rather than changes in concentration or diffusivity. In fact, silicone is mostly compressed at hydrostatic pressures of 10 dbar, so any effect on physical compression or diffusivity should be limited to mostly the 0–10-dbar range. Still, these effects are superimposed onto the equilibrium effect and may alter the temperature dependence of the pressure response.
a. Laboratory experiments
Two laboratory experiments were performed in March and August 2012 at the high pressure vessel facility of the Technology and Logistics Centre of GEOMAR. The first experiment employed six Aanderaa 3830 optodes and one Aanderaa 4330F optode up to a pressure of 6000 dbar at ca. 4° and 18°C. The second experiment used five Aanderaa 4330 optodes, two Sea-Bird SBE63 optodes, and one of the Aanderaa 3830 optodes of the first experiment up to a pressure of 2000 dbar at ca. 8°, 15°, and 24°C. The sensors varied considerably in age (0.5–9 yr) and their deployment history (newly manufactured vs repeated CTD or multiyear mooring deployments).
The pressure vessel interior (ca. 30-cm diameter, 93-cm height) was split into two separate freshwater-filled volumes by using a commercial watertight dry bag. Thus, contamination of the inside volume by oil spills from the hydraulic pump was prevented. After closure of the dry bag, the water was cooled to cause undersaturation and left to stand for at least 2.5 days (unpressurized) or 12 h (pressurized) to ensure complete dissolution of accidentally trapped air bubbles. The tank was pressurized by means of a hydraulic pump (type EH 1H, LEWA GmbH) with a compression rate around 10 dbar s−1. Decompression at a similar rate was achieved by slowly opening a vent valve. The whole pressure vessel was temperated/cooled with an external heat exchanger and a cryostat (Julabo GmbH). The lower temperature limit was determined by the room temperature of the workshop as a result of diffusive warming of the tank.
The sensors were attached to a holding frame and put into the dry bag inside the pressure vessel, that is, the inner volume. An SBE 5T pump was added to homogenize the inner volume. During the experiment, optodes were in part powered and logged online through a cable connection and in part supplied offline by custom-made loggers. The dry bag was sealed tightly around the cables by means of a stainless steel hose clamp. The logging interval was set to 30 s (online) or 60 s (offline).
Pressure cycles were designed as follows: After 20 min at zero pressure, the tank was pressurized and held at the desired pressure level for 20 min before being depressurized again. Subsequently, it was kept at zero pressure for 20 min again. The first experiment used pressure levels at 500, 1000, 2000, 4000, and 6000 dbar, while the second experiment had pressure levels at 700, 1400, and 2000 dbar. During each pressure cycle, water temperatures increased/decreased because of near-adiabatic compression/decompression by ca. 0.15°C per 1000 dbar.
Different oxygen levels were used: Pressure cycles at ca. 80% O2 saturation served as the high end member in both experiments. For a zero end member, O2 was consumed in the inner volume by the addition of a stoichiometric amount of to the dry bag. In addition, the first experiment featured an intermediate level at ca. 55% O2 saturation and 4°C, a third temperature (10°C) at 80% O2 saturation, and a repetition at 18°C and 80% O2 (see Fig. 1 for an overview). Each pressure cycle was repeated three to four times at each temperature and oxygen level.
For the first experiment, three out of the seven Aanderaa optodes were individually laboratory calibrated according to Bittig et al. (2012), while all five Aanderaa optodes and one of the two SBE63 optodes were laboratory calibrated in the second experiment (see Table 1). Their average O2 reading, validated against Winkler samples at the beginning and end of each experiment, served as reference for the other factory-batch-calibrated optodes.
b. Field experiment
During R/V Polarstern cruise ANT-XXVII/2 (Rohardt et al. 2011) to the Southern Ocean, two Aanderaa optodes were attached to the CTD, a standard model 3830 optode, and a fast-response model 4330F optode. Both were individually multipoint calibrated before the cruise in October 2010 and recalibrated afterward in July 2011 and showed no sign of drift (see Bittig et al. 2012). Laboratory calibrations were linearly adjusted to a total of 2296 Winkler samples at 122 stations.
The ANT-XXVII/2 Southern Ocean field setting covers a very narrow temperature range (Fig. 2). With cold water temperatures throughout the entire water column, the pressure response can be evaluated independently from a possible temperature effect.
Response times τ for the 3830 and 4330F optode are on the order of 25 and 8 s, respectively, and both sensors sampled at 5-s intervals. The response time effect was removed following the procedures of Bittig et al. (2014) by using a temperature-dependent τ parameterization of the mode response time derived for this cruise (see Fig. 6a in Bittig et al. 2014). For the fast-response 4330F optode, there is no significant difference between uncorrected and τ-corrected data. The response time correction of the 3830 optode, however, improves data quality significantly by removing artifacts caused by the sensor’s slow response, for example, the low bias around the surface oxycline (Fig. 2).
a. Laboratory experiments
During the experiments, oxygen levels showed a small and steady drift on the order of −1 to −3 μmol kg–1 h–1 for unknown reasons. It may be related to the combination of different metals (surface of the pressure vessel, sensor housings, screws) or to bacterial respiration inside the enclosed volume. The drift was accounted for by detrending the data before analysis of the pressure response.
Despite the very high (de-)compression rates, the optode pressure response was near instantaneous (within the 60-s resolution) and fully reversible. Reequilibration between the sensing membrane and ambient liquid [Eq. (16)] thus appears to happen on faster time scales than pressure changes. Since the repartitioning/equilibration effect is an optode phenomenon, it is merged into the optode pressure response in the following discussion and is not accounted for separately.
Optodes show a different behavior at high O2 and at very low O2 (Figs. 3a,b, respectively). At high O2, lifetime (phase shift, phase delay) increases with hydrostatic pressure and O2 readings are lower (ca. 3%–4% per 1000 dbar). At zero O2, lifetime decreases with hydrostatic pressure and O2 and readings are thus apparently higher (ca. 0.3 µmol kg−1 per 1000 dbar, being more pronounced at low temperatures). The two opposing effects cancel at around 10 mbar (5% O2 saturation), that is, the apparent reduction of O2 is dominant in most applications.
b. Pressure correction rationale
Having a reduced O2 slope/sensitivity under elevated pressure and a simultaneous opposite effect in the absence of O2 is very similar to observations of optode drift behavior (Bittig and Körtzinger 2015). Our interpretation is analogous: There is one effect that affects oxygen and the quenching process and a second one that affects the luminophore itself.
Increased hydrostatic pressure causes the sensing membrane’s to decrease as a result of a shift in the membrane–seawater equilibrium [Eq. (16)]. At the same time, the sensing membrane is compressed, which increases its viscosity and thus affects the quenching efficiency. The sum of these processes results in higher lifetimes (phase shift, phase delay) and apparently less seawater O2.
Simultaneously, the luminophore properties are affected by hydrostatic pressure. Compression of the sensing membrane (i.e., the matrix) increases the energy level of the luminophore. It seems that, in relative terms, the luminophore’s excited state is more strongly affected than the ground state so that the tendency to return to the ground state is increased. The (excited state’s) lifetime is therefore slightly reduced at high pressures.
Both the O2-dependent effect (changed sensing membrane equilibrium concentration and altered quenching efficiency) and the O2-independent effect (altered luminophore properties) act in parallel but opposite directions and are always superimposed.
Previous parameterizations of the pressure response focused on the O2-dependent part [see Eqs. (1) and (2)]. To derive equations for both the O2-dependent and O2-independent parts, we need to reconsider the order in which the functional model parts are applied. The “classical” approach is described as follows.
step 1a: Compensate for the temperature dependence of quenching, that is, convert the raw sensor phase shift to a (raw) oxygen quantity ( or ).
step 1b: Compensate for the pressure dependence of quenching, that is, convert the raw oxygen quantity to a fully corrected one.
The alternative approach would be to deal with the pressure dependence first (raw phase shift to corrected phase shift) and then correct the temperature dependence (corrected phase shift to fully corrected O2). While this order is in principle feasible, it is less straightforward to arrive at simple parameterizations.
Based on the work presented here, we propose to expand the classical scheme by an additional step to first deal with the pressure effect on the luminophore and then with the quenching process itself.
step 0: Compensate for the O2-independent pressure effect on the luminophore, that is, convert the raw phase shift to a pressure-adjusted one .
step 1a: Compensate for the temperature dependence of quenching, that is, convert the adjusted phase shift to an adjusted oxygen quantity.
step 1b: Compensate for the pressure dependence of quenching, that is, convert the adjusted oxygen quantity to a fully corrected one.
At zero O2, only the O2-independent pressure effect is visible as an offset to unpressurized (surface) conditions. The phase offset and O2 concentration offset are linear with pressure, while the offset follows an exponential trend (Fig. 4a). In contrast to the and offset, the phase offset is nearly temperature independent. Moreover, the phase offset is homogeneous within the Aanderaa and Sea-Bird optodes (Fig. 4b). To compensate for the O2-independent pressure response of the luminophore, the phase shift φ needs to be adjusted according to
where z is a phase offset of 0.1° per 1000 dbar for the Aanderaa optodes and 0.115 μs per 1000 dbar for the SBE63 optodes. Despite using the same PSt3 sensing foil (PreSens GmbH), phase shifts are different between the manufacturers since a different excitation frequency of the luminophore is used (5000 vs 3840 Hz, respectively).
The O2-dependent part (Fig. 5) shows a downward-curved relation in phase offset (phase ratios are inhomogeneous between sensors) and a closely linear trend in the ratio, as well as the ratio with the same slope f. The qualitative picture is the same for the classical approach of neglecting the O2-independent part (Fig. 5a) and the revised approach with a preceding phase offset adjustment according to Eq. (17) (Fig. 5c). In both cases, the slope f increases with temperature.
The magnitude of the O2 reduction matches the magnitude of the equilibrium effect. However, the temperature dependence follows opposite trends, indicating the presence of additional processes. Because of a lack of characterization of these additional processes, we chose to follow a simplistic linear parameterization according to Eq. (1) rather than to empirically adjust Eq. (16) [or Eq. (2)] for the observed temperature dependence.
Except for optode 4330 856, the slope f is in the same range for all Aanderaa optodes (Figs. 5b,d), despite the broad range of sensor (foil) age and deployment history. Without phase adjustment—that is, following the classical approach—there is, however, a difference between Aanderaa and SBE63 optodes (ratio of f ca. 0.9). With the preceding phase offset adjustment, this difference vanishes (ratio of f of 1.0, see Fig. 6). In fact, an analogous pressure response of the quenching process can be expected since both the SBE63 optodes and the Aanderaa optodes with standard foil use the same coated PSt3 sensing membrane material and luminophore. This supports the physical credibility of the proposed new approach to split the pressure response into two separate steps.
The temperature dependence of the O2-dependent pressure effect is shown in Fig. 6 with f being higher at higher temperatures. The temperature slope is very similar between sensors, while there is some variation in the offset (±0.2% per 1000 dbar). With the classical approach, f has an average of 3.3% per 1000 dbar at 1°C that is very close to the 3.2% per 1000 dbar of Uchida et al. (2008). The factor f for the SBE63 is lower by ca. 0.3% per 1000 dbar. With a preceding phase offset, f is about 4.2% per 1000 dbar at 1°C and the Aanderaa and Sea-Bird optodes follow the same trend. Parameters from the laboratory experiment are summarized in Table 2.
There are, however, two caveats to these results: Only two SBE63 optodes were available and their pressure range was limited to 2000 dbar, which somewhat limits the significance of the comparison. The parameters for the SBE63 optodes might thus need to be refined based on further experiments. Moreover, the only fast-response foil (optode 4330F 207) showed a slightly higher O2-dependent pressure response using the revised scheme than the average of the standard foil Aanderaa optodes. Still, it is well within the range of variability of the standard foil optodes and thus not treated separately.
d. Laboratory validation
A third laboratory experiment was performed with three Aanderaa optodes at ca. 80% O2 up to a pressure of 2000 dbar. As no data were obtained at zero O2, this experiment was not included to derive the pressure response. It can thus be used to validate the mean parameterization (Table 2) under laboratory conditions.
Using a constant f of 3.2% per 1000 dbar (Uchida et al. 2008), the mean absolute bias is 0.56% per 1000 dbar. This is reduced to 0.15% per 1000 dbar by inclusion of the temperature dependence of f (Table 2, upper parameter set). With the revised scheme (Table 2, lower parameter set), the error comes down to 0.18% per 1000 dbar.
e. Field experiment
Under field conditions, a clear distinction between O2-independent pressure effect, O2-dependent pressure effect, and its temperature dependence is not possible. Therefore, we will use the phase offset z and the temperature slope of f from the laboratory experiments (Table 2), which were uniform between sensors, and only allow the zero intercept of f to be adjusted according to the field data.
A qualitative picture of the uncompensated pressure effect is given in Fig. 2. The apparent linear slope for the 3830 529 and 4330F 207 optodes is eliminated with an f intercept of 3.2% and 3.6% per 1000 dbar using the classical approach (Fig. 7, left panels) and of 4.0% and 4.5% per 1000 dbar using the revised approach (Fig. 7, right panels), respectively. This mirrors the laboratory observations with the optode 3830 529 being at the low end and the optode 4330F 207 being at the high end of the O2-dependent pressure effect (Figs. 5b,d) and thus confirms the laboratory results.
Quantitatively, the median absolute residuals for the 3830 and 4330F optodes are quite similar between the calculation schemes: 0.66 and 1.06 μmol kg−1 for the classical approach and 0.65 and 1.03 μmol kg−1 for the revised approach, respectively. Here, the classical approach benefits from the very narrow temperature range (Fig. 2) so that the unaccounted temperature dependence does not appear strongly in the residuals. The revised approach performs at least as good as the classical correction in this example. However, it includes improved knowledge about the pressure behavior of optodes and is expected to yield better results in other ocean settings.
f. Pressure correction uncertainty
The uncertainty of the pressure correction consists of two parts. One part is the adequacy of the parameterization and the other part is the uncertainty of the respective coefficients. Based on the laboratory and field evidence, an empirical, linear parameterization seems appropriate. The proposed new scheme incorporates mechanistic elements although the O2-dependent part remains empirical as the interplay between equilibrium effect and changes in quenching efficiency is not yet fully understood.
As for the coefficients, the largest part of the pressure correction uncertainty stems from the variability between sensors themselves (ca. 0.2% per 1000 dbar). Based on the laboratory validation, the practical uncertainty amounts to 0.2% per 1000 dbar for both the classical approach and the newly proposed approach (Table 2, upper and lower parameter sets, respectively). The field experiment, too, indicates an uncertainty of 0.2% per 1000 dbar. Given that the same sensors were used in the laboratory experiment 1 and field experiment, we deem a slightly more conservative overall uncertainty of 0.3% per 1000 dbar realistic.
This level of uncertainty needs to be taken into account when considering an optode drift correction/calibration based on the comparison to a climatological reference at depth (e.g., Takeshita et al. 2013). For a typical Argo O2 float with 2000 dbar profiling depth, this amounts to half a percent uncertainty on top of the uncertainty of the climatology itself. This may exceed the desired level of accuracy, for example, for air–sea gas exchange and eventually net community production calculations. A better constraint for this kind of work is derived from direct in-air measurements (Bittig and Körtzinger 2015).
Oxygen optodes show a systematic pressure response: With increased hydrostatic pressure, they generally read lower O2 than in the ambient seawater. Foremost, this is due to the effect of pressure on the equilibrium between the optode sensing membrane and seawater. Because of a higher partial molar volume of O2 in the membrane, equilibrium concentrations are actually reduced under pressure, which causes the optodes to read a lower O2. In contrast, hydrostatic pressure influences the quenching process only to a minor degree (see section 2b; Taylor 1978; Ludwig and Macdonald 2005). However, the luminophore itself shows a pressure effect that acts in the opposite direction of the equilibrium effect. Consequently, optodes read slightly too high at O2 levels below ca. 5% O2 saturation, while the equilibrium effect dominates above this level and optodes read too low.
The pressure response shows an O2 dependence that is closely linear with O2, both for Aanderaa and Sea-Bird optodes. Its magnitude is somewhat temperature dependent and there is no pressure hysteresis.
Because of the combination of a pressure impact on the luminophore besides the impact on O2 equilibrium concentrations and quenching, we propose a new optode calculations scheme. In this scheme, we first deal with changes to the luminophore caused by pressure (step 0) before addressing oxygen quenching (step 1).
step 0. Compensate for the O2-independent pressure effect on the luminophore.
The measured raw phase shift is pressure corrected to an adjusted one according to
where the phase offset z depends on the manufacturer (Table 2, lower parameter set).
step 1a. Compensate for the temperature dependence of quenching.
Application of a functional model for the temperature dependence of quenching converts the adjusted phase shift to an adjusted oxygen quantity, that is,
It depends on the functional model whether the oxygen quantity is a concentration or a partial pressure .
step 1b. Compensate for the pressure dependence of quenching.
The adjusted oxygen quantity is converted to a fully corrected one by accounting for the pressure effect on quenching, that is,
where is a temperature-dependent factor that is uniform for both Aanderaa and Sea-Bird optodes (see Table 2, lower parameter set). Here, the increase because of hydrostatic pressure (see section 2a) is dealt with explicitly and outside of . It depends on the functional model of the temperature dependence whether this is already included in . The proposed scheme is physically plausible: Both Aanderaa and Sea-Bird use sensing membranes from the same manufacturer but apply different excitation frequencies. This is mirrored in an analogous O2 quenching effect but different phase shift offset of the luminophore. Whenever possible, this scheme should be applied to O2 optode data to properly account for the two opposing pressure effects. If for some (practical) reason, however, the raw phase is not available, then a reasonable pressure correction is still feasible since the O2 effect dominates in most applications. If both processes are lumped together, then the pressure correction is reduced to Eq. (19) and the upper parameter set of Table 1 is used for (note the difference between Aanderaa and Sea-Bird optodes).
There is some variation (offset in f) in the pressure response between sensors on the order of 0.2% per 1000 dbar. This is the most important contributor to the uncertainty of our pressure correction, which is estimated at 0.3% per 1000 dbar.
Moreover, the pressure effect might drift with time as has been seen for the temperature dependence of optodes (Bittig and Körtzinger 2015). Given the broad age range of optodes, especially during experiment 1, the small range of f is encouraging and suggests that aging is of minor importance. Still, a tendency toward lower f with age could be deduced from experiment 1 (Figs. 5b,d). However, we believe this is exceeded by intrinsic variability between sensors (see experiment 2).
This work would not have been possible without the facilities and support of the Technology and Logisitics Centre (TLZ) of GEOMAR. Special thanks go to Martin Steen, Ralf Schwarz, Thomas Brandt, Rudi Link, Wiebke Martens, and Andreas Pinck (all GEOMAR), as well as to the KM Contros team for electronic and mechanical assistance. The authors want to thank the captain, crew, and scientists of R/V Polarstern ANT-XXVII/2 and especially Carolina Dufour (Princeton University) for their assistance with Winkler sampling, as well as three anonymous reviewers for their constructive comments. Financial support by the following projects is gratefully acknowledged: O2 floats (KO 1717/3-1) and the SFB754 of the German Science Foundation (DFG), the FP7-SPACE E-AIMS project (Grant Agreement 312642), as well as SOPRAN (03F0462A) and HGF CV Station (03F0649A) of the German Research Ministry (BMBF).
Pressure Dependence of the Partial Pressure
The discussion of the chemical potential μ in section 2b can be expanded to derive the pressure dependence of the partial pressure [Eq. (7)]. Enns et al. (1965) describe an experiment in which a gas phase (G) at ambient (air) pressure is in equilibrium with a pressurized liquid (L). For a gas dissolved in a liquid, the chemical potential follows Henry’s law, that is,
For the gas phase, the chemical potential follows Raoult’s law, that is,
where is the chemical potential of the standard state at the same temperature and pressure according to Raoult’s law, that is, the pure gas.
The standard state of the gas phase is unaffected by the pressurization of the liquid, that is, , and the pressure-dependent change in needs to be compensated for by a change in the partial pressure . Integration from dbar yields the dependence of partial pressure on hydrostatic pressure P [Eq. (7)].