Oxygen variance and meridional oxygen supply in the Tropical North East Atlantic oxygen minimum zone

Abstract

The distribution of the mean oceanic oxygen concentration results from a balance between ventilation and consumption. In the eastern tropical Pacific and Atlantic, this balance creates extended oxygen minimum zones (OMZ) at intermediate depth. Here, we analyze hydrographic and velocity data from shipboard and moored observations, which were taken along the 23°W meridian cutting through the Tropical North East Atlantic (TNEA) OMZ, to study the distribution and generation of oxygen variability. By applying the extended Osborn–Cox model, the respective role of mesoscale stirring and diapycnal mixing in producing enhanced oxygen variability, found at the southern and upper boundary of the OMZ, is quantified. From the well-ventilated equatorial region toward the OMZ core a northward eddy-driven oxygen flux is observed whose divergence corresponds to an oxygen supply of about 2.4 μmol kg⁻¹ year⁻¹ at the OMZ core depth. Above the OMZ core, mesoscale eddies act to redistribute low- and high-oxygen waters associated with westward and eastward currents, respectively. Here, absolute values of the local oxygen supply >10 μmol kg⁻¹ year⁻¹ are found, likely balanced by mean zonal advection. Combining our results with recent studies, a refined oxygen budget for the TNEA OMZ is derived. Eddy-driven meridional oxygen supply contributes more than 50 % of the supply required to balance the estimated oxygen consumption. The oxygen tendency in the OMZ, as given by the multidecadal oxygen decline, is maximum slightly above the OMZ core and represents a substantial imbalance of the oxygen budget reaching about 20 % of the magnitude of the eddy-driven oxygen supply.

Appendices

Appendix 1: Estimate of the characteristic eddy velocity from ship sections (parameterization of the low pass filter)

As mentioned in Sect. 3.2, the velocity variability on the mesoscale cannot be estimated from repeat ship sections via time scale analysis. Here, we propose a simple parameterization to separate the variability on the mesoscale from short term variability, such as tidal and inertial oscillations. For this purpose, we use the velocity anomalies of the 5°N, 23°W mooring data. The basic idea is to calculate the magnitude (standard deviation) of the velocity fluctuations once with ($\sigma_{Lu} \overset{\wedge}{=}u_{e}$ and $\sigma_{Lv} \overset{\wedge}{=}v_{e} ,$ representing the mesoscale velocity fluctuations) and without (σ _u and σ _v , representing the total velocity fluctuations) applying a low-pass filter L, where the cutoff frequency of the low-pass filter is chosen corresponding to a period of 10 days. Then, we do a polynomial fit of σ _u and σ _v against σ _Lu and σ _Lv to parameterize the effect of L, i.e.

$$\sigma_{Lu} = a_{0} + a_{1} \sigma_{u} + a_{2} \sigma_{u}^{2} + a_{3} \sigma_{u}^{3}$$

(19)

$$\sigma_{Lv} = a_{0} + a_{1} \sigma_{v} + a_{2} \sigma_{v}^{2} + a_{3} \sigma_{v}^{3} .$$

(20)

The parameterization of the low-pass filter is based on the following assumptions: (1) The magnitude of the low-pass filtered velocity fluctuations (σ _Lu and σ _Lv ) tends to zero, if σ _u and σ _v tend to zero. Thus, a ₀ = 0. (2) Without loss of generality we assumed that the ratio of inertial and tidal oscillations to the total velocity variability varies with the magnitude of the total velocity variability. Consequently, at least three degrees of freedom are necessary for this parameterization, where a ₀ is already defined as 0. Nevertheless, we add another degree of freedom to reduce the residual of the fit (see Sect. 4.2 for results). The application of the polynomial fit (19) and (20) on the 5°N, 23°W mooring data is shown in Fig. 5 and yielded the following values for the polynomial coefficients: a ₁ = 0.15, a ₂ = 0.11 (m s⁻¹)⁻¹, a ₃ = −5.2 × 10⁻³ (m s⁻¹)⁻².

Appendix 2: Meridional oxygen flux using the correlation of velocity and oxygen time series

The total meridional oxygen flux at a given position is defined as

$${\mathcal{F}} = \overline{{vO_{2} }}$$

(21)

where the overbar denotes the temporal average on a density surface over the recorded time series. We now use the Reynolds decomposition to separate the time series into a mean $\overline{( \cdot )}$ and an anomaly (·)′ on surfaces of potential density, i.e.

$$v(\sigma_{\theta } ,t) = \overline{v} (\sigma_{\theta } ) + v^{\prime} (\sigma_{\theta } ,t)$$

(22)

$$O_{2} (\sigma_{\theta } ,t) = \overline{{O_{2} }} \left( {\sigma_{\theta } } \right) + O_{2}^{'} \left( {\sigma_{\theta } ,t} \right)$$

(23)

where $\overline{{v^{{\prime }} }} = \overline{{O_{2}^{{\prime }} }} = 0$. Applying (21)–(23) the flux on a density surface is then given by

$${\mathcal{F}}\left( {\sigma_{\theta } } \right) = \underbrace {{\overline{v} \left( {\sigma_{\theta } } \right)\overline{{O_{2} }} \left( {\sigma_{\theta } } \right)}}_{{{\bar{\mathcal{F}}}(\sigma_{\theta } )}} + \underbrace {{\overline{{v^{\prime } \left( {\sigma_{\theta } ,t} \right)O_{2}^{\prime } \left( {\sigma_{\theta } ,t} \right)}} }}_{{{\mathcal{F}}^{'} (\sigma_{\theta } )}}$$

(24)

with the mean isopycnal oxygen flux $\overline{{\mathcal{F}}} (\sigma_{\theta } )$ and the turbulent isopycnal oxygen flux ${\mathcal{F}}^{'} (\sigma_{\theta } )$. The mean oxygen flux is highly uncertain (not shown), since the relative velocity error $\Delta v/\bar{v}$ is very large.²⁵ The mean oxygen flux due to a zonal mean flow was studied using a simple advection diffusion model in Brandt et al. (2010) and will not be considered here. Our main goal is the estimation of the eddy-driven oxygen flux and we therefore concentrate on the term ${\mathcal{F}}^{'} (\sigma_{\theta } )$.

Oxygen time series were recorded on distinct depth levels z _I (see Table 2). Due to density variability, (23) leads to gappy time series for a single density surface, which can cause large uncertainties for the results of (24). Alternatively, we define the turbulent lateral oxygen flux at the instrument depth z _I via a weighted average over density surfaces, which is given by

$$F^{{\prime }} (z_{I} ) = \frac{{\mathop \sum \nolimits_{i = 1}^{S} n_{i} {\mathcal{F}}^{{\prime }} (\sigma_{\theta i} )}}{{\mathop \sum \nolimits_{i = 1}^{S} n_{i} }},$$

(25)

where n _i is the number of data points that were measured on the ith density surface during the mooring period and $\sum\nolimits_{i = 1}^{S} {n_{i} = N}$ is the total number of data points of the time series. The time average in (24) is defined by $\overline{( \cdot )} = \sum\nolimits_{j}^{n} {( \cdot )/n}$ and (25) transforms to

$$F^{\prime } (z_{I} ) = \frac{{\mathop \sum \nolimits_{i = 1}^{S} n_{i} \left\{ {\frac{1}{{n_{i} }}\mathop \sum \nolimits_{j = 1}^{{n_{i} }} v_{j}^{{\prime }} \left( {\sigma_{\theta i} } \right)O_{2j}^{\prime } \left( {\sigma_{\theta i} } \right)} \right\}}}{{\mathop \sum \nolimits_{i = 1}^{S} n_{i} }} = \frac{{\mathop \sum \nolimits_{i = 1}^{S} \mathop \sum \nolimits_{j = 1}^{{n_{i} }} v_{j}^{\prime } \left( {\sigma_{\theta i} } \right)O_{2j}^{\prime } \left( {\sigma_{\theta i} } \right)}}{{\mathop \sum \nolimits_{i = 1}^{S} n_{i} }}$$

(26)

The double summation over indices i and j is basically a sum over the whole time series and can be written as

$$F^{{\prime }} (z_{I}) = \frac{{\mathop \sum \nolimits_{k = 1}^{N} v_{k}^{{\prime }} O_{2k}^{{\prime }} }}{N}$$

(27)

$v_{k}^{{\prime }}$ and $O_{2k}^{{\prime }}$ being the recorded time series of velocity and oxygen anomalies at the instrument depth z _I . $F^{{\prime }} (z_{I} )$ is the turbulent meridional oxygen flux at the instrument depth z _I representing a weighted average over all isopycnal surfaces that were sampled by the instrument during the mooring period. The error for the turbulent meridional oxygen flux is estimated as the standard error of an arithmetic mean value, i.e.

$$\Delta F^{{\prime }} = \frac{{F^{{\prime }} (z_{I} )}}{{\sqrt {n_{f} } }}$$

(28)

where n _f represents the degrees of freedom of the time series. We estimated n _f from the autocorrelation function of the velocity time series as follows: the number m of correlated data points in the time series was calculated by testing the autocorrelation function of the meridional velocity against 0-coherence on a 95 % confidence level and assuming the statistics of a t-distribution for the correlation coefficient. The degrees of freedom were computed with the total number of data points N divided by the number of correlated data points m

$$n_{f} = \frac{N}{m}.$$

(29)