Constraints on oceanic meridional heat transport from combined measurements of oxygen and carbon

Abstract

Despite its importance to the climate system, the ocean meridional heat transport is still poorly quantified. We identify a strong link between the northern hemisphere deficit in atmospheric potential oxygen (APO = O$_2$ + 1.1 $\times$ CO$_2$) and the asymmetry in meridional heat transport between northern and southern hemispheres. The recent aircraft observations from the HIPPO campaign reveal a northern APO deficit in the tropospheric column of $-$10.4 $\pm$ 1.0 per meg, double the value at the surface and more representative of large-scale air–sea fluxes. The global northward ocean heat transport asymmetry necessary to explain the observed APO deficit is about 0.7–1.1 PW, which corresponds to the upper range of estimates from hydrographic sections and atmospheric reanalyses.

Appendices

Appendix 1: Atmospheric aircraft observations: interpolation and uncertainties

The HIPPO campaign took place between January 2009 and September 2011 aboard the National Center for Atmospheric Research/National Science Foundations Gulfstream V research jet HIAPER and mapped the vertical and meridional distribution of atmospheric carbon cycle gases and other anthropogenic tracers including CO$_2$ and O$_2$/N$_2$ (Wofsy 2011). We used 7 of the 10 transects performed during the five HIPPO campaigns. These transects sample a similar Pacific section between 80$^\circ$N and 58$^\circ$S and cover the seasonal cycle 1–2 months apart (Fig. 2; Table 5). Atmospheric O$_2$/N$_2$ was measured in-situ by the NCAR Atmospheric Oxygen Instrument and on whole air samples collected by the NCAR/Scripps Medusa flask sampler (Bent 2014). The data file we have used is that of Wofsy et al. (2012) ($HIPPO\_all\_missions\_merge\_10s\_20121129.tbl$), but with an updated version of the APO data. The APO data in the 20121129 file included an adjustment of the flask data for thermal fractionation that used the measured Ar/N$_2$ ratios. This adjustment also affected the in situ data which are adjusted to agree with the flasks. To avoid interhemispheric gradients in Ar/N$_2$ affecting our results, we have used a version of the APO data without this adjustment, and will include this version of the data in an upcoming update to the official HIPPO data repository. Three transects were removed because they sampled different longitudes. APO was computed similarly to surface stations based on CO$_2$ concentrations and O$_2$/N$_2$ ratios at each data point (see Eq. 2). APO values were interpolated in space along this transect with a 5$^\circ$ longitude resolution and 19 vertical levels corresponding to the grid of the atmospheric transport model TM3 used in this study (see Sect. 8). We used a kriging interpolation method that computes the gaussian-weighted average based on the spatial covariance between triangulated data points, with a weighting radius spanning over 10$^\circ$ of latitude on the horizontal and 50 mb on the vertical.

Table 5 The 7 HIPPO transects used to construct the annual mean meridional transect

We computed the northern APO deficit using data interpolated to $\sim$900 mb (noted $\Delta$APO surface), which can be compared to the deficit derived from surface stations (Sect. 2.1) and data vertically integrated over the troposphere between the surface and 400 mb (noted $\Delta$APO troposphere). The northern deficit was estimated using the 7 HIPPO transects and a bi-harmonic seasonal fit with periods of 1 year and 6 months after de-trending and referencing the data to year 2009 using the time-series at the Cape Grim surface station. Annual mean values of the surface and tropospheric deficit were computed from these seasonal fits.

The uncertainty on the annual mean includes the impact of spatio-temporal sparsity in the data. The uncertainty on $\Delta$APO related to interannual variability ($\epsilon _{IA}$) was computed using a forward predictive model with an autoregressive process of order 2 (AR2). The predictive model was used to generate a 1500-year long time-series with the same mean and variance as the data. It quantifies the error made by estimating the mean from a temporally varying 3-year long time-series. It is computed as the standard deviation between the 500 means (1500/3) estimated from 3-year long segments and the mean estimated from the 1500-year long time-series. At the surface, $\epsilon _{IA}$ = $\pm$ 1.2 per meg. Integrated over the troposphere, $\epsilon _{IA}$ is assumed to be 60 % of the uncertainty at the surface. This estimate is based on the results of the atmospheric model TM3, in which the interannual variability of the northern deficit integrated vertically and meridionally is almost half of the one obtained at the surface. The uncertainty on $\Delta$APO related to the spatio-temporal undersampling of the seasonal cycle $\epsilon _{SEAS}$ is estimated by sub-sampling the APO distribution obtained with the atmospheric transport model TM3 at the time and place of HIPPO transects. $\epsilon _{SEAS}$, computed as $\pm$ the difference between the “true” mean and the mean estimated by sub-sampling, is 0.4 per meg at the surface and 0.2 per meg when integrated over the troposphere.

Appendix 2: Ocean interior inversions: computation of carbon, oxygen, nitrogen and heat air–sea fluxes

The atmospheric data are used to evaluate the fluxes of O$_2$, CO$_2$, N$_2$ and heat from a suite of ocean inverse calculations, which we perform based on the method of Gloor et al. (2001), Gruber et al. (2001) and Mikaloff Fletcher et al. (2007). These inverse calculations rely on ocean interior data from the GLobal Ocean Data Analysis Project (GLODAP) version 1 (Key et al. 2004). Ocean interior heat was computed from GLODAP potential temperature and the sea water capacity of Millero et al. (1973). N$_2$ concentrations, not available in the database, were computed following Hamme and Emerson (2004) using temperature (T) and salinity (S):

$$\begin{aligned} ln[N_2]= \,\,& {} A_0+ A_1*Ts + A_2*Ts^2 + A_3*Ts^3 \nonumber \\&+ S *(B_0+ B_1*Ts + B_2*Ts^2 )\nonumber \\ Ts=\, & {} ln \left(\frac{298. -T}{273.15+T}\right) \end{aligned}$$

(10)

with $A_0$ = 6.42931, $A_1$ = 2.92704, $A_2$  = 4.32531, $A_3$  = 4.69149, $B_0$  = $-$7.44129.10$^{-3}$, $B_1$ = $-$8.02566.10$^{-3}$ and $B_2$ = $-$1.46775.10$^{-2}$.

The inverse method relates interior tracer fields to air–sea fluxes using steady-state basis functions computed by releasing unit dye tracer at the surface of 30 oceanic regions in a ocean general circulation model (OGCM) (Mikaloff Fletcher et al. 2006) (Fig. 11). The basis function or footprint $A_i$ obtained for region i essentially gives the contribution of the air–sea flux of each surface region i to the concentration at each point in the ocean interior. The observed concentration is decomposed into contributions from each of the 30 regional sources:

$$\begin{aligned} C_{obs} = \sum _{i=1}^{30} \lambda _i A_i + \epsilon \end{aligned}$$

(11)

with $\lambda _i$ a dimensionless factor that scales the surface unit flux and $\epsilon$ the residual concentration that can not be explained by the method. Runs were carried out for 3000 years for each models, to achieve steady state and derive the basis functions $A_i$. $\lambda _i$ were obtained by minimizing the difference between $C_{obs}$ and the right hand side of equation 11 using single value decomposition (see details in, Gloor et al. 2001). Regional fluxes are then given by $F_i = \lambda _i \phi _i$, with $\phi _i$ the rigid flux pattern specified within each surface region of the OGCM to compute the basis function. We used the spatial pattern of Takahashi et al. (2002) for CO$_2$ fluxes and the heat flux pattern of Esbensen and Kushnir (1981) for heat, O$_2$ and N$_2$ fluxes.

Fig. 11

Maps of 30 regions used for the ocean interior inversions (1–30 separated by thin lines) and 21 regions after aggregation of adjacent regions within individual basins (colored). Thick dashed lines indicate the large regions used to compare inverse fluxes on Fig. 4

Basis functions ($A_i$) for the MOM models are identical to those used by Jacobson et al. (2007). The MITgcm-2.8 and MITgcm-ECCO basis functions were computed using the Transport Matrix Method (TMM), a numerical scheme for fast, “offline” simulation of passive tracers using circulations derived from ocean general circulation models as sparse “transport matrices” (TMs) (Khatiwala et al. 2005; Khatiwala 2007). For MITgcm-2.8, monthly mean TMs from an equilibrium run of the model were used to compute the basis functions, whereas for MITgcm-ECCO, monthly mean TMs representing a climatology over the 1992–2004 assimilation period were used. The TMM code and transport matrices used for these simulations are freely available from github.com/samarkhatiwala/tmm.

air–sea fluxes were estimated for the 30 regions but the result usually displayed large covariance between adjacent regions (e.g. regions 13 to 15 in the North Pacific or regions 9, 25 and 30 in the subpolar Southern Ocean) showing that these fluxes estimates are not independent. To avoid this type of underdetermination, we aggregated the 30 original fluxes into 21 regional fluxes (Fig. 11). Differences between the method used in this study and previous studies are highlighted in Table 6. Results for those 21 regions are detailed in Tables 7, 8, 9 and 10. We performed a first set of inversions without constraining the balance of the total flux. We found that this method resulted in only relatively small imbalances in the predicted fluxes (for example $-$0.1 to 0.1 PgC y$^{-1}$ for CO$_{2pi}$ and 30–50 Tmol year$^{-1}$ for O$_2$), which gives us confidence that this technique is able to capture large scale regional gradients.

Table 6 Comparison to previous ocean interior inversion studies

Table 7 Regional air–sea heat fluxes obtained with the 7 ocean interior inversions (in PW)

Table 8 Regional air–sea O$_2$ fluxes obtained with the 7 ocean interior inversions (in Tmol year$^{-1}$)

Table 9 Regional air–sea N$_2$ fluxes obtained with the 7 ocean interior inversions (in Tmol year$^{-1}$)

Table 10 Regional air–sea CO$_{2pi}$ fluxes obtained with 7 ocean interior inversions and 2009 air–sea C$_{ant}$ fluxes from Khatiwala et al. (2009, KWLA09) (in Tmol year$^{-1}$)

Ocean interior inversions incorrectly interpret the addition of carbon by rivers as an air-to-sea flux (see discussion in Gruber et al. (2009) supplementary material). At steady-state, the sum of air–sea flux and river input at global scale and hence the result of our inversion has to be balanced. We therefore performed a second set of inversions using Lagrangian multipliers to enforce the constraint that the sum of global fluxes was zero (Gloor et al. 2001). Only this second set is reported here.

Biogeochemical variables are sampled with lower coverage than temperature and salinity in the GLODAP dataset.

Appendix 3: Simulated atmospheric potential oxygen computation and uncertainties

To allow comparison with atmospheric data, we combined annual inverse model air–sea fluxes with additional fluxes as follows:

$$\begin{aligned}&F_O=F_{Oan}+F_{Cseas}+F_{Off} \end{aligned}$$

(12)

$$\begin{aligned}&F_C=F_{Cpi}+F_{Cseas}+F_{Canth}+F_{Cff} \end{aligned}$$

(13)

$$\begin{aligned}&F_N= F_{Nan}+F_{Nseas} \end{aligned}$$

(14)

The seasonal variations are those of Garcia and Keeling (2001) for O$_2$, Rödenbeck et al. (2013) for CO$_2$ and based on solubility changes expected from the seasonality of heat fluxes for N$_2$ (Keeling and Shertz 1992). The seasonality of O$_2$ was turned down by 18 % following the recent results of Bent (2014) suggesting that the amplitude reported in Garcia and Keeling (2001) was overestimated. The anthropogenic air–sea flux of CO$_2$ $F_C^{ant}$ is from Khatiwala et al. (2009, 2013), the fossil fuel $F_C^{ff}$ is taken from the Emission Database for Global Atmospheric Research (EDGAR, available at http://edgar.jrc.ec.europa.eu), and $F_O^{ff}$ is computed by scaling $F_C^{ff}$ using a constant stoichiometric ratio of $-$1.4 (Keeling 1988). To enable the comparison between model estimates and airborne data, all fluxes are referenced to year 2009 by correcting for fossil fuel using EDGAR emission database and for oceanic anthropogenic carbon uptake using Khatiwala et al. (2009, 2013).

APO was estimated using Equation 8 obtained assuming there is no changes in the total moles of air and that $(\frac{O_2}{N_2})_{reference}= \frac{X_{O2}}{X_{N2}}$ following Stephens et al. (1998). Uncertainties on resulting APO values include uncertainties on the rectifier effect, on anthropogenic carbon fluxes, on fossil fuel burning emissions and on the atmospheric circulation. The rectifier effect is the contribution to annual mean APO due to purely seasonal fluxes. We assigned a 20 % uncertainty to the seasonal rectifier effect based on the numerous studies of its dependency to both the atmospheric model used and the seasonal flux estimates (e.g., Stephens et al. 1998; Blaine 2005; Battle et al. 2006; Tohjima et al. 2012). We used the recent estimation of the uncertainty associated with fossil fuel carbon dioxide emission by Andres et al. (2014): 8.5 % (2 standard deviations). We used a conservative 20 % uncertainty on the anthropogenic air–sea flux of Khatiwala et al. (2009). The uncertainty on $\Delta$APO associated with the atmospheric circulation was estimated to $\pm$0.5 per meg, by comparing APO fields obtained using NCEP winds vs. ERA-Interim winds (Fig. 8a).

Finally, we evaluated the uncertainty related to the choice of the atmospheric transport model. We compared the APO northern deficit obtained with the TM3 model and with the transport model of the Center for Climate System Research/National Institute for Environmental Studies/Frontier Research Center for Global Change (CCSR/NIES/FRCGC) (Miyazaki et al. 2008) based on EDGAR fossil fuel emissions, observation-based seasonal fluxes of O$_2$ (Garcia and Keeling 2001), CO$_2$ (Takahashi et al. 2009) and N$_2$ (Blaine 2005). We find that the uncertainty on the northern APO deficit is about 10 % for the column-average troposphere and about 30 % at the surface. This uncertainty is included as 1-sigma in our estimate.