Oxygen optodes are based on the principle of luminescence quenching by oxygen. One of the first descriptions has been given by Kautsky (1939) and almost all luminophores are quenched by molecular oxygen (Lakowicz, 2006, chap. 8). When a luminophore, L, is excited with a short pulse of light of the correct wavelength, it can transition to an electronically excited state, L^*. From there it may relax to its ground state by non-radiative processes or by light emission (i.e., luminescence). These processes are rate controlled, so that the luminescence intensity I₀ or I decays exponentially with time (Figure 1), where the index 0 denotes the absence of oxygen. The rate of decay is characterized by the luminescence lifetime Λ₀ or Λ, respectively, the time it takes the intensity to decay to 1/e.

Oxygen may quench the luminescence of the excited state L^* by collision with the luminophore and transfer of the excess energy, which is called dynamic quenching¹:

This pathway of radiationless relaxation reduces both the luminescence intensity I and lifetime Λ in the presence of O₂ (Figure 1B). The amount of quenching can be related to the Stern-Volmer equation,

where KSV′ is the Stern-Volmer constant and aO2M or cO2M are the oxygen activity or concentration, respectively, within the sensing foil containing the immobilized luminophore (^M). Oxygen behaves near-ideal, so that its (thermodynamic) activity can be replaced by its concentration. The Stern-Volmer constant is proportional to the diffusivity of oxygen, i.e., dynamic quenching is diffusion controlled (Smoluchowski equation, e.g., Lakowicz, 2006, chap. 8).

Since the equilibrium between sensing foil and ambient seawater is established via equal partial pressures pO₂ (see below), and the O₂ solubility cO2*,M within the sensing foil is generally unknown, the latter can be included in KSV=KSV′·cO2*,M and Equation 2) altered to:

Note that, except for potential secondary reactions of the excited O2* molecules, quenching does not consume any oxygen and optodes therefore do not need to be in a pumped water stream that would continuously replace any consumed oxygen in order to reach a stable (and correct) signal. Steady-state is reached when partial pressures, pO₂, are equilibrated throughout the system.

Luminescence intensity measurements are easily biased by changes in the excitation light source intensity, ambient scattering, and other matrix effects and thus, are prone to enhanced variability and drift. Therefore, all optical oxygen sensors used in marine science measure the luminescence lifetime Λ rather than its intensity I, using a single-frequency phase shift technique: Instead of using a short pulse (compare Figure 1), the excitation is intensity-modulated. The emission is modulated with the same frequency but, due to the finite lifetime Λ of the excited state, phase shifted relative to the excitation (Figure 2). For exponential luminescence decays, the lifetime Λ is proportional to the tangent of the phase shift φ with f being the modulation frequency (Equation 4; derivation given in Lakowicz, 2006, chap. 5). Aanderaa optodes use a modulation frequency f of 5,000 Hz, while Sea-Bird optodes use 3,840 Hz.

Thus phase shift φ and lifetime Λ carry the same information, but they are not equal. The Stern-Volmer equation is not valid for phase shifts φ (Equations 2, 3).

The luminophore in oxygen optodes is immersed and immobilized in an oxygen-permeable sensing foil or thin film, to avoid leaching of the luminophore to the environment and maintain O₂ sensitivity. The sensing foil is placed on the waterside of an optical window and thus exposed to ambient seawater, while the excitation and detection electronics are inside the sensor housing behind the optical window. Sensors are built both for unpumped (e.g., Aanderaa, JFE Advantech, RBR, Contros) and pumped (e.g., Sea-Bird) mode of operation (which does not prevent, of course, unpumped sensors to be used in a pumped flow cell).

When luminophores are dissolved in solution, the high molecular diffusivity ensures that every luminophore has the same environment on timescales of the luminescence lifetime (tens of μs). Consequently, luminophores in solution show linear Stern-Volmer behavior according to Equations (2, 3) (i.e., the ratio of I₀ to I or Λ₀ to Λ is linear with O₂). Note that even for linear Stern-Volmer behavior, the I—oxygen and Λ—oxygen relation is non-linear (Equations 2, 3; Figure 3B).

However, in condensed media such as the sensing foil of oxygen optodes, molecular motion is highly hindered. Thus, different or non-uniform chemical environments around luminophores persist on timescales of the luminescence (tens of μs), i.e., interactions with the matrix are different between luminophores. Because of this heterogeneity, all oxygen optodes show a non-linear Stern-Volmer behavior, i.e., they do not follow Equations 2, 3. Instead, they show a downward curvature of the Stern-Volmer plot (Figure 3).

Oxygen sensing with oxygen optodes imperatively require establishment of chemical equilibrium between the sensing foil, where the luminophore is immobilized, and the ambient seawater. The luminophore responds to the O₂ (thermodynamic) activity in the sensing foil aO2M (since quenching is diffusion-controlled), while the O₂ activity in the ambient medium, aO2L, usually is the quantity of interest to the user. Both phases are in equilibrium when their chemical potentials are equal, i.e., μO2M=μO2L. For a gas dissolved in another medium (i.e., oxygen dissolved in the sensing foil or seawater), Henry's law definition relates the chemical potential of O₂, μ_O2, to the solute's activity, a_O2, according to Equation (5) (see textbooks of physical chemistry)

where μO2∘(T,P) is the chemical potential of an imagined standard state at temperature T and hydrostatic pressure P with an O₂ activity of 1 mol L⁻¹ and dissolved oxygen behaving as if infinitely diluted. This standard state is specific to the medium, i.e., μO2∘,M≠μO2∘,L. For oxygen in the gas phase, the chemical potential is given by Raoult's law,

where μO2⦵(T,P) is the chemical potential of the pure gas at 1 bar (and at temperature T and hydrostatic pressure P) as standard state and f_O2 is the fugacity of O₂. Using the definition of the Henry constant, K_H,O2, or solubility, cO2*, respectively,

the standard potentials of Equations (5, 6) can be related,

For the equilibrium condition between sensing foil and ambient medium, μO2M=μO2L, we can now write

which is equal to

and further simplifies to equal fugacities,

as condition for the phase equilibrium between sensing foil and ambient medium. Since dissolved oxygen behaves near-ideal, activity and fugacity can be replaced by concentration and partial pressure.

In summary, while the sensing principle (luminescence quenching) is a diffusion-controlled process and thus sensitive to the oxygen concentration (again: within the sensing foil), the phase equilibrium between sensing foil and ambient medium renders oxygen optodes, in effect, sensitive to the ambient medium's partial pressure, pO₂. This has important implications for the behavior of oxygen optodes with respect to environmental factors (section 3).

Most studies to characterize oxygen optode behavior for oceanographic applications employed Aanderaa or Sea-Bird optodes, which both use the same silicone-based sensing membrane (PSt3 membrane, PreSens, Regensburg, Germany). Other manufacturers (e.g., JFE Advantech, Contros) use different sensing materials, which are both newer and less well-characterized. In addition, Aanderaa recently started to offer oxygen optodes for shallow water applications with a different membrane (WTW, Weilheim, Germany). Where available, we added preliminary information on these sensors/membranes, but in general focus on the much better studied PSt3 membrane optodes.

Oxygen decreases the luminescence lifetime Λ due to quenching. The relative change ∂Λ/∂O₂ is largest at small O₂ levels, i.e., oxygen optodes are most sensitive at low O₂ (Figures 3B, 4B).

An increase in temperature reduces the lifetime of the excited state, L^*, i.e., both Λ₀ and Λ are reduced (Figure 4B). Moreover, a temperature increase causes oxygen diffusivity to increase and luminescence quenching as a diffusion-controlled process becomes more efficient. In parallel, higher temperature decreases the O₂ solubility, which reduces quenching. The overall effect of these partially counteractive influences, however, is an increase in quenching and a reduction of lifetime with rising temperatures (Figure 4A). These principles are universal for all oxygen optodes.

The characterization of the combined oxygen and temperature response of optodes is the field of classical laboratory calibration. In principle, such calibration setups (e.g., Tengberg et al., 2006; Bittig et al., 2012; Bushinsky and Emerson, 2013) systematically vary oxygen and temperature over adequate ranges while monitoring the optode response (phase shift or lifetime), typically using between 5–10 oxygen and 4–7 temperature levels. A calibration matrix (O₂, T, φ) obtained in this way can then be approximated by a mathematical model F of optode O₂–T–response of choice, that provides a mapping according to:

A variety of mathematical models exist with a common goal to provide an adequate mathematical description of the mapping function F. These models include high-order polynomials (e.g., Aanderaa Data Instruments AS, 2009, Appendix 6), parametric models inspired by Stern-Volmer (Uchida et al., 2008, 2010; Sea-Bird Electronics, 2013; this work), and two-site physics (McNeil and D'Asaro, 2014). Their output can either be an oxygen concentration c_O2 (Uchida et al., 2008; Aanderaa Data Instruments AS, 2009; Sea-Bird Electronics, 2013) or an oxygen partial pressure pO₂ (Bittig et al., 2012; McNeil and D'Asaro, 2014; this work), which both can be converted using temperature and salinity (Bittig et al., 2016). More details about these calculations can be found in section 5.2.

The luminophore is immersed in a sensing membrane, e.g., a hydrophobic silicone matrix (PSt3 membrane) for Aanderaa and Sea-Bird optodes. Only gases (dissolved N₂, O₂, and water vapor) and no salts can penetrate into the membrane, i.e., the oxygen solubility within the sensing foil, cO2*,M(T), is independent of salinity. Thus, the optode response at a given partial pressure, pO₂, is unaffected by salinity. However, seawater oxygen solubility, cO2*,L(T,S), is a function of salinity. Therefore, the conversion between equilibrium partial pressure, pO₂ (i.e., the property which among temperature and pressure determines the O₂ activity in the foil), and seawater O₂ concentration, cO2L, depends on the seawater salinity. This applies to all oxygen optodes.

Since most optodes² do not report partial pressure (which requires no salinity correction) but convert sensor output into O₂ concentration in seawater, a “salinity correction” of the reported concentration is necessary. This correction does not correct the optode sensor response, but simply converts O₂ partial pressure, pO₂, to seawater O₂ concentration, cO2L. We advise to use the SCOR WG142 recommendations on O₂ quantity conversions for this step (Bittig et al., 2016). They apply the Benson and Krause refit of Garcia and Gordon (1992) for the O₂ solubility and also account for the change in atmospheric composition at different salinities (see also section 5.2.3), which is generally neglected in the manufacturer's recommendations.

Oxygen optodes show a pressure effect that is the result of three factors, which are discussed one by one below: the stability of the luminophore's excited state L^>* itself, the O₂ activity inside the sensing foil, and the pressure response of luminescence quenching.

The luminophore's excited state, L^>*, is slightly destabilized at higher pressure with respect to the ground state, L, which can be seen in experiments at low O₂ levels (e.g., Bittig et al., 2015a). The reduction in L^>* stability and thus a decrease in Λ₀ causes an apparent positive O₂ shift in the sensor response, independent whether O₂ is present, i.e., luminescence is quenched, or not.

The most dominant effect originates from a decrease in the sensing foil O₂ activity with pressure caused by the pressure dependence of the chemical potential. From the fundamental thermodynamic relation (definition of the Gibbs energy), pressure affects the chemical potential, μ_O2, according to:

where V_m,O2 is the partial molar volume of O₂, i.e., pressure increases the chemical potential μ_O2. As illustrated in Ludwig and Macdonald (2005), the concentration (and activity) stays nearly unchanged upon pressurization and the main pressure effect is on the chemical potential of the reference state, μO2∘(T,P) (see case i, Ludwig and Macdonald, 2005, and compare Equation 5). As a consequence, solubility changes with pressure (e.g., Taylor, 1978). The change in μO2° and solubility cO2* accounts for the structural effect of pressure (on solute–solvent and solvent–solvent interactions).

This results in a higher outgassing tendency of O₂ with pressure (i.e., an increased pO₂) both in the sensing membrane and in seawater following

Experimentally, Enns et al. (1965) found a 14 % per 1,000 dbar increase of pO₂ in seawater, which corresponds to a partial molar volume Vm,O2L of 31.7 mL mol⁻¹. For a silicone membrane as utilized by Aanderaa or Sea-Bird optodes, literature values for Vm,O2M are between 39 and 46 mL mol⁻¹ (see Bittig et al., 2015a). Since the partial molar volumes and thus the pO₂ increase are different between sensing foil and ambient seawater, oxygen optodes show a pressure effect. The equilibrium condition of equal partial pressures (Equations 11) is true also upon pressurization. After some transformations of Equations (10, 14 Bittig et al., 2015a), one obtains Equation (15) for the change in membrane O₂ concentration due to a re-equilibration of O₂ between sensing foil and ambient seawater upon pressurization from P₀ to P. With Vm,O2M>Vm,O2L, the membrane O₂ concentration cO2M (and activity) decreases at higher pressures.

Luminescence quenching, in contrast, is mostly unaffected by pressure. This at first counterintuitive observation is because 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 μ_O2 (Equation 13), however, it is shifted by the same amount throughout the entire medium (since V_m,O2 is the same throughout). Thus, the gradient of μ_O2 remains constant and quenching within the sensing foil stays the same. In fact, Carey and Gibson (1976) observed only a small increase in fluorescence intensity (5 % at 10,000 dbar) for quenching by O₂ in solution, attributed to the compression of the solution (and thus changes in the concentration).

To our knowledge, pressure experiments were only done with PSt3 membranes, but other sensing membranes can be expected to show similar effects. The pressure response of Aanderaa oxygen optodes has been studied by Tengberg et al. (2006) in the laboratory as well as by Uchida et al. (2008) in the field and more thoroughly by Bittig et al. (2015a) (both laboratory and field), also including Sea-Bird optodes. A two-fold pressure response has been observed:

Pressure affects the lifetime Λ₀ in the absence of O₂ with decreasing Λ₀ under pressure.

The first effect (i) can be explained by a destabilization of the excited state, L^>*. The associated decrease in Λ₀ causes an apparent positive O₂ shift in the sensor response at all O₂ concentrations. The second effect (ii) combines the re-equilibration of O₂ levels between sensing foil and seawater as well as the pressure dependence of quenching. Its magnitude matches the decrease in PSt3 sensing membrane cO2M(P) due to O₂ re-equilibration: Reported O₂ levels decrease by about −4.3 % per 1,000 dbar (see section 5.2.4 or Bittig et al., 2015a) as result of a ca. 14 % per 1000 dbar increase of pO₂ in seawater and an order of 10 % per 1,000 dbar increase of pO₂ in the PSt3 silicone sensing foil (Equation 15). However, the temperature dependence of ii is inverse to the expectation (Equation 15), indicating the presence of additional effects (e.g., a small pressure dependence of quenching, Bittig et al., 2015a). Effects i and ii oppose each other, but the re-equilibration dominates the pressure response: Overall, uncorrected optode readings are biased high at O₂ levels below ca. 5 % O₂ saturation (i dominates over ii), while they are biased low above this level (ii dominates over i; Bittig et al., 2015a).

Previous studies of Aanderaa optode pressure response (Tengberg et al., 2006; Uchida et al., 2008) were unable to separate the pressure effects i and ii, which is why they report an apparently smaller O₂-pressure dependence. Results of Bittig et al. (2015a) (given in detail in section 5.2.4) are consistent with the data of Uchida et al. (2008), however, preference should be given to account for both effects separately, if possible (i.e., if optode phase shift data are available).

Pressure vessel experiments at compression / decompression rates around 10 dbar s⁻¹ showed a near-instantaneous pressure response of optodes with PSt3 membrane (within the 60 s logging interval) that was fully reversible (i.e., without hysteresis) (Bittig et al., 2015a). However, there is sporadic evidence for second-order effects not yet fully understood, e.g., Bittig and Körtzinger (2017) report on a potential pressure conditioning of optodes on two floats after repeated pressure cycling to 2000 dbar (order of 40 pressure cycles, amplitude 1–2 μmol kg⁻¹), being caused by either the Aanderaa 4330 or Sea-Bird SBE63 optode or both.

The time response of oxygen optodes to a change in ambient O₂ levels is not instantaneous. This response is especially noticeable when an optode travels through a large oxygen gradient. Deepening winter mixed layers in the Gulf of Alaska form such gradients and optodes on profiling floats there can underestimate the mixed layer oxygen concentration by 5 μmol kg⁻¹ (Plant et al., 2016, Figure 6). Oxygen has to diffuse in or out of the sensing foil (^M) to reach a new equilibrium with the ambient medium (^L) (Equation 11), which causes a lag in the optode time response. The transfer of O₂ at the interface is determined by the temperature-dependent O₂ diffusivity and solubility in both phases as well as the thickness of the liquid boundary layer. Bittig et al. (2014) developed a simple one dimensional diffusion model that accounts for the temperature dependence of O₂ diffusivity and solubility in both phases but simplifies the liquid boundary layer to a stagnant boundary layer with only molecular diffusion.

The model helps to conceptually understand the processes which are responsible for the dynamic time response of optodes. The response from an equilibrated state with equal partial pressure throughout the system (normalized partial pressure Φ(x≥0, t = 0⁻) = 0) to a step-change in ambient partial pressure (normalized partial pressure Φ(x≥lM+lL,t=0+)=1) is shown in Figure 5A for a silicone membrane with a thickness l_M of 100 μm (Aanderaa optode standard foil) and a stagnant boundary layer thickness l_L of 60 μm, where x is the distance from the optical window. The change in ambient O₂ level has first to diffuse into the boundary layer until a change in sensing foil O₂ is noticeable. Then, the change in sensing foil O₂ levels in response to the change in ambient O₂ is limited by the transfer through the boundary layer. The thicker the boundary layer, the slower the oxygen response of the optode and vice versa (Figure 5B).

Bittig et al. (2014) found that temperature modifies the response time τ, but does not affect the modeled boundary layer thickness l_L. This should be valid for all oxygen optodes. Moreover, they provide a lookup table for response times τ as function of temperature T and l_L for PSt3 membranes with different membrane thickness l_M (see Supplemental Material of Bittig and Körtzinger, 2017; Figure S2 of this work).

The modeled boundary layer thickness l_L, in turn, is determined by the flow in front of the sensing foil (Bittig et al., 2014): High flow speeds erode/renew the boundary layer more efficiently, leading to a faster O₂ transport through the boundary layer and thus shorter response times τ, and vice versa. From laboratory experiments with PSt3 membrane optodes, Bittig et al. (2014) observed an inverse relation between boundary layer thickness l_L and flow V. for pumped applications following

with an uncertainty of 4 μm or 10 %, whichever is greater (Bittig and Körtzinger, 2017, Appendix A). For unpumped applications, the relation between l_L and platform velocity must be established on a case-by-case basis depending on the platform characteristics and optode attachment with respect to flow direction. For typical Biogeochemical-Argo profiling floats, Bittig and Körtzinger (2017) give a characterization for PSt3 membranes following:

where υ is the ascent velocity of the float. The two regimes likely correspond to the shift between laminar and turbulent flow at the sensing foil (Bittig and Körtzinger, 2017) that is not covered by the simple stagnant boundary layer model of Bittig et al. (2014).

Observed boundary layer thicknesses l_L for unpumped Aanderaa optodes translate for the standard PSt3 foils to response times τ on the order of 15–45 s for shipboard CTD applications (Bittig et al., 2014) and of 70–140 s for profiling floats (Bittig and Körtzinger, 2017), depending on flow and temperature. For the Aanderaa fast-response foil, which is a thinner PSt3 foil and without black optical isolation, the corresponding ranges are 8–25 and 35–70 s, respectively. However, there are few oceanographic field data with fast-response foils to support these estimates. Boundary layer thicknesses l_L for pumped Sea-Bird optodes translate to response times τ between 6 and 15 s on a shipboard CTD (flow ca. 7,000 mL min⁻¹) and between 25 and 40 s on a moored or Argo CTD (flow ca. 600 mL min⁻¹), depending on temperature. An unpumped RINKO optode by JFE Advantech showed response times τ between 3 and 7 s on a shipboard CTD during a polar deployment (i.e., cold temperatures with slow time response; Bittig et al., 2014). Preliminary results from a Contros Hydroflash O₂ optode indicate a time response comparable to the Aanderaa fast-response foil or slightly faster (T. Hahn, GEOMAR, pers. comm.).

The estimate of τ can then be used to inverse-filter and correct observations by appropriate algorithms. Care must be taken not to excessively amplify noise. One possible correction algorithm is presented in Bittig and Körtzinger (2017, Appendix A) and Bittig et al. (2014) (reproduced in the Supplementary Material), while Fiedler et al. (2013) used the algorithm of Miloshevich et al. (2004). An example is given in Figure S3 for one CTD and one profiling float profile (after Bittig et al., 2014; Bittig and Körtzinger, 2017).

A time response correction provides a-priori a more accurate estimate of the “true” O₂. However, the impact of the correction strongly depends on the O₂ profile / gradient and response time (and thus on flow). For an unpumped Aanderaa optode mounted on a CTD, Bittig et al. (2014) observed differences between negligible to more than 50 μmol kg⁻¹ between observed and time response corrected O₂ (validated against reference CTD-O₂; see Figure S3a). On a profiling float, median differences between observed and corrected O₂ were between 13 and 15 μmol kg⁻¹ for an unpumped Aanderaa optode and between 6 and 7 μmol kg⁻¹ for a pumped Sea-Bird optode, respectively, in the strongest O₂ gradients (120 μmol kg⁻¹ change over 8 min or 20 dbar). After correction, both sensors agreed to within 2–3 μmol kg⁻¹ (Bittig and Körtzinger, 2017).

In any case, a correction of the dynamic time response works on a time axis and thus requires time stamps for optode samples. These need to be acquired and stored alongside the optode data.

Oxygen optodes with PSt3 foils have been documented to be considerably out of calibration compared to field data (e.g., Takeshita et al., 2013, mean bias of −5.0 % O₂ saturation at 100 % O₂ saturation for 130 Aanderaa optodes). This has been puzzling since field deployments of oxygen optodes indicated high stability in-situ (e.g., Körtzinger et al., 2005; Tengberg et al., 2006). Indeed, there appear to be two distinct regimes: (1) storage regime, i.e., before and/or between deployments, and (2) deployment regime, i.e., when submerged continuously in seawater. When not deployed and stored in air, abundant laboratory data show that optodes can lose O₂ sensitivity on the order of 5 % per year. Given the oceanographic accuracy aim of 0.5 % O₂ saturation / 1 hPa (Gruber et al., 2010), optodes should thus be assumed to be out of calibration after having been stored or not used for a period of several months. This holds in particular for recently produced sensors, whereas old ones tend to drift less (order of 1 % per year or less). During deployments, however, optode O₂ sensitivity drift seems to be drastically reduced and optodes are “stable” within a few tenths of a percent per year. We will discuss both regimes below.

Oxygen optodes should receive an individual multi-point calibration at least once during their lifetime to have their O₂-T-response characterized well. The description of the O₂-T-response by a batch calibration of the sensing foil does not yield satisfactory results since variability between individual sensing foils and optodes is not adequately adjusted using a two-point calibration.

With a once well-characterized O₂-T-response, simpler means of recalibration can be appropriate when taking the optode drift character into account, i.e., a slope factor on optode pO₂ and an offset at zero oxygen. Data for such a recalibration can originate from various sources, e.g., a concurrent depth profile with discrete Winkler samples, optode in-air measurements at the surface together with hydrographic data on a deep isopycnal (to allow for a two-point correction), or a laboratory or on-ship calibration at 0 % and 100 % O₂ saturation (preferably in the temperature range at which the sensor will be deployed). In the latter case, care must be taken to avoid unintended supersaturation for the “100 %” calibration, in particular when using classical bubbling stones⁴. If only one cluster of reference data is available (e.g., only in-air measurements), preference should be given to a slope-only correction on pO₂.

Numerous Aanderaa optodes have been deployed or used with only a factory batch calibration, in particular before the manufacturer introduced its factory multi-point calibration option in mid-2012. While it would be preferable to individually recalibrate each of these optodes, this is not always possible or practical, e.g., because the sensor is no longer accessible. To assess the quality of O₂ data obtained with such batch calibrated optodes, we compared calibration data from several multi-point laboratory calibrations with the batch calibration procedure. Similarly, (repeated) multi-point calibrations require some effort and may not be possible due to time, logistical or other constraints. We therefore looked at the accuracy of simpler recalibration approaches of multi-point calibrated optodes as well. Both assessments are summarized at the end of this section.

The key and core requirement to correct for the dynamic time response of optodes is to know the time interval between subsequent measurements (or to have at least a good estimate of the timing of each sample). Without timing information, no post-correction is possible since the dynamic time response is essentially a time series effect. To date, the Biogeochemical-Argo data system is capable to store abundant measurement timing information together with the profile data (Bittig et al., 2017). Previously, this has not been the case and the acquisition and storage of timing information has been the responsibility of the platform operator.

The key to reduce the effect of the dynamic time response itself is to enhance the flow and thus the transfer of O₂ at the interface between sensing foil and sea water. To achieve this, optodes can either be operated in a pumped water stream if feasible with respect to the energy budget and additional constraints like in air measurement capability. Or, in an unpumped mode of operation, optodes should be placed at a position on the platform with the most dynamic flow regime and hence thinnest boundary layer (compare, e.g., optode placement on a glider for Nicholson and Feen, 2017, with the standard attachment shown in Bittig et al., 2014). In any case, a reproducible and properly characterized flow regime helps to improve time response corrections (e.g., Bittig and Körtzinger, 2017).

A successful deployment comes with adequate preparation. The sensor configuration should always be kept for reference, and the treatment of the data stream anticipated before deployment (e.g., to adjust the platform's firmware to actually log and transmit timestamps for each optode sample). Raw data should be kept to allow reprocessing and to keep all information provided by the sensor. Apart from the measurement time, these data are the temperature and phase delay for Sea-Bird SBE63 optodes, whereas the temperature and the blue phase shift (BPhase or C1Phase for 3830 and 4330 models, respectively) as well as the red phase shift (C2Phase for 4330 models) should be kept for Aanderaa optodes.

Moreover, O₂ optodes should always be assumed to be out of calibration if not very recently calibrated (weeks for newly produced optodes, months for old ones). Consequently, options for reference O₂ data (e.g., by regular in-air measurement or other approaches) need to be explored before deployment.

Dissolved oxygen comes in various units, e.g., μmol O₂ kg⁻¹, μmol O₂ L⁻¹, mL_STP O₂ L⁻¹, mg O₂ L⁻¹, hPa, or % O₂ saturation, which at the end of the day all carry the same information (i.e., the amount of dissolved oxygen). This indeed is a confusing aspect of dealing with oceanic O₂ measurements and the general practice should be to always double-check the unit of a new data set, e.g., by verifying that surface O₂ saturation is within a reasonable range. However, each unit has its strength by stressing a different aspect of oxygen measurements and analysis, and it is best to be aware of the reasons for this (persistent) plurality.

Oxygen concentration can be expressed in two ways, either as number of moles of dissolved oxygen per unit mass of solution (μmol O₂ kg⁻¹; gravimetric unit) or per unit volume of solution (μmol O₂ L⁻¹, mL_STP O₂ L⁻¹, mg O₂ L⁻¹; volumetric unit). The unit μmol O₂ kg⁻¹ is the unit of choice for oceanic applications because of its independence of temperature and pressure, both of which will change the concentration when expressed in a volumetric unit even without any production or consumption of oxygen. To allow using of O₂ as a conservative tracer for ocean mixing and advection, μmol O₂ kg⁻¹ is the recommended unit for oceanic applications and used by all larger observing systems (see, e.g., documentation for GO-SHIP and Biogeochemical-Argo, Hood et al., 2010, and Thierry et al., 2016).

The standard reference method for O₂ is a wet-chemical titration analysis (e.g., Winkler, 1888; Carpenter, 1965) which essentially is a volumetric analysis, i.e., it yields the amount of O₂ in a given sample volume. Thus, the natural unit for Winkler titration is μmol O₂ L⁻¹. This holds for laboratory applications in general, and seagoing applications in particular, where measuring volumes of solutions is much more common than measuring their mass, which is impossible at sea. Moreover, O₂ concentration units per volume (e.g., mL_STP O₂ L⁻¹, mg O₂ L⁻¹) are also common for limnological applications.

Gravimetric and volumetric oxygen concentration can be converted by multiplying/dividing with the solution's density (mass per volume). For seawater, this gives about 3 % larger values for the O₂ concentration in μmol L⁻¹ than in μmol kg⁻¹, a difference that is difficult to spot but very important for applications. Therefore, care must be taken when dealing with a new data set and it is best practice to verify the O₂ unit, e.g., by confirming reasonable surface O₂ saturations or deep O₂ levels.

At interfaces like the sea surface or the optode sensing foil—water interface, oxygen data solely expressed as water-based O₂ concentration are not sensible, in particular when part of the observations are in different phases. At interfaces, the oxygen partial pressure pO₂ and a corresponding pressure unit (e.g., hPa) is the natural quantity and unit for both phases. We would discourage the use of atmospheres (atm, 101,325 Pa) but suggest to use a full power of ten of the SI unit Pascal (e.g., hPa, bar, or mbar).

Detailed conversions between the units listed here are given in the SCOR Working Group 142's recommendations on O₂ quantity conversions (Bittig et al., 2016). Converted values for 100 % O₂ saturation, 205 hPa, and 250 μmol L⁻¹ both in freshwater and at a salinity of 35 as well as at the surface and at 2,000 dbar are shown in Table S4.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.