Understanding the annual cycle in global steric height

Authors

  • Donata Giglio,

    Corresponding author
    1. Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California, USA
    • Corresponding author: D. Giglio, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0230, USA. (dgiglio@ucsd.edu)

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  • Dean Roemmich,

    1. Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California, USA
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  • Bruce Cornuelle

    1. Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California, USA
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Abstract

[1] Steric variability in the ocean includes diabatic changes in the surface layer due to air-sea buoyancy fluxes and adiabatic changes due to advection, which are dominant in the subsurface ocean. Here the annual signal in subsurface steric height (ηbelow 200 db) is computed on a global scale using temperature and salinity profiles from Argo floats. The zonal average of Δη over a season (e.g., math formula) is compared to the wind-forced vertical advection contribution math formula both in the global ocean and in different basins. The results show agreement that extends beyond the tropics. The estimate of math formula is based on the Ekman pumping and assumes that the seasonal vertical velocity is constant over the depth range of interest. This assumption is consistent with annual isopycnal displacements inferred from Argo profiles. The contribution of horizontal advection to Δηis significant in some regions and consistent with differences between Δη and Δηw′.

1 Introduction

[2] Observations of the annual cycle in global subsurface temperature and salinity were very limited prior to the implementation of the Argo Program [Roemmich and Gilson, 2009]. Before the array was initially deployed (2000–2007), very few salinity measurements were available on a planetary scale, the data had a strong bias toward the Northern Hemisphere and summer months, and the typical maximum depth of temperature observations was 750 m. Argo provides unprecedented resolution and near-global coverage, with observations as deep as 2000 db and the first systematic sampling of subsurface salinity. Figure S1 in the supporting information illustrates, for instance, the extreme sparseness of Southern Hemisphere mid-ocean winter data in the historical archive and shows how the spatial and temporal sampling biases have been greatly reduced in Argo. The new data improve our understanding of seasonal variability in the ocean, which is dominated by air-sea exchanges of heat and freshwater in the surface layer, but which is also driven adiabatically by dynamics and in some regions extends deep into the water column. Here the focus is the subsurface ocean and in particular the relationship between the steric height seasonal cycle and wind-forced vertical advection [Gill and Niiler, 1973]. A goal is better separation of steric variability into its diabatic and adiabatic components.

[3] Gill and Niiler [1973] present the theory of large-scale seasonal variations of sea level. The steric height component is described in terms of an upper and a lower baroclinic term, to consider separately the effect of steric changes above and below 200 m. They perform a dimensional analysis of the equations for momentum and mass conservation and show that vertical advection of the mean density field by seasonal Ekman pumping velocity balances, at first order, the large-scale tendency of seasonal steric height below 200 m math formula. Their assumption regarding the seasonal vertical velocity w is a linear decay of the Ekman pumping velocity math formula (applied at z=−200 m) to zero at the bottom (z=−H), i.e., math formula. Gill and Niiler [1973] expect η to be fairly small, about 10% of the total steric height signal, but point out that a test of the theory would require measurements of this deeper steric variability, to compare with the estimate from Ekman pumping velocity. The energy in the background nonseasonal continuum tends to yield noisy observations of η, but with Argo's temporal and spatial resolution on a planetary scale, the comparison can now be achieved both globally and in different basins. This is the goal of the present study.

[4] Previous work shows that seasonal variations of the meridional overturning circulation extend as deep as 1000 m and that they are related to zonal wind stress and to the east-west slope of sea level [Kanzow et al., 2010; Liu et al., 2011]. Also, subsurface seasonal signals are observed propagating along the equator and in the tropics [Brandt and Eden, 2005; Hosoda et al., 2006; Bunge et al., 2008; Johnson, 2011], sometimes to the full depth of Argo observations in the region [Hosoda et al., 2006; Johnson, 2011]. In the present analysis, zonal averages of the data are considered and propagation is not discussed.

[5] This study is based on observations, and it describes how seasonal steric height in the subsurface ocean relates to wind-driven vertical advection. The comparison is carried out following the theory of Gill and Niiler [1973] both on a global scale and in different ocean basins, and the focus is on extra-equatorial regions, where the Ekman dynamics holds and the seasonal vertical velocity (w) can be estimated from Ekman pumping. Section 2 presents the data. Section 3 describes the results, including also a discussion of the depth dependence of w and of the role of horizontal advection. Section 4 presents a summary and conclusions.

2 Data

2.1 Argo Data

[6] Argo profiles provide temperature, salinity, and pressure data on a global scale (60°S–60°N) and as deep as 2000 db [Roemmich et al., 2009]. In this analysis, the raw Argo temperature and salinity measurements during 2005–2012 were gridded monthly on a 1°×1° grid, after quality control and adjustment of pressure bias. The gridding was done by objective mapping, with latitude-dependent decorrelation scales [Roemmich and Gilson, 2009]. In order to test how this procedure may affect the seasonal signal in lightly sampled regions, an alternate gridding method was applied to each month of the 12 month climatology (i.e., the January map combines all the January data during 2005–2012). Bin-averaged data in overlapping large-scale regions of 555 km radius yield results that are little different from the objective mapping case and are therefore not discussed further.

2.2 European Centre for Medium-Range Weather Forecasts (ECMWF) Data

[7] Zonal and meridional wind momentum flux data used in this analysis are synoptic monthly means from the European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis, ERA-Interim, for the period 2005–2012. Dee et al. [2011] describe the ERA-Interim data. Brunke et al. [2011] found that for wind stress and latent heat fluxes, ERA-Interim performed better than most other products.

3 Results

[8] Consistent with the theory of Gill and Niiler [1973], the large-scale seasonal tendency of steric height math formula, from Argo, is expected to balance, at first order, vertical advection (estimated from ERA-Interim Ekman pumping) of the Argo mean potential density field, i.e.,

display math(1)

In equation (1), ηis a basin-scale zonal average of seasonal steric height between longitudes x1 and x2; hence, it depends only on latitude, pressure, and time. ηis defined as math formula, where g is the gravitational acceleration, pref=2000 db is the reference pressure, ρ is Argo potential density, and the upper limit on p is 200 db. Here the prime symbol indicates that values are mean seasonal deviations from the time average over the complete time series (2005–2012); hence, math formula (where the bar indicates the time mean). The right-hand side of equation (1) is taken to be a basin-scale zonal average, and w is the seasonal vertical velocity based on ERA-Interim Ekman pumping (see section 3.1). The integral of this term over a season provides an estimate of the vertical advection contribution to η during that season (math formula in the following) and can be compared to how η changes from the beginning to the end of the season (Δη).

[9] Steric height is chosen for the comparison between the atmospheric forcing and the oceanic response since it is an integral quantity. Section 3.1 presents the assumption made for the depth dependence of w. Section 3.2 shows observations of the balance in equation (1), comparing Argo Δη and math formula from Ekman pumping. Section 3.3 is a discussion of the role of horizontal advection.

3.1 Depth Dependence of the Seasonal Vertical Velocity w

[10] The estimate of math formula in equation (1) requires an assumption regarding the vertical profile of w. In Gill and Niiler [1973], this assumption is a linear decay from seasonal Ekman pumping (math formula) at 200 m to zero at the ocean bottom. In the current study, instead, the depth range of interest is 200–2000 db, where Argo observations are available, and w is considered constant in pressure (math formula below 200 db), as suggested by Argo isopycnal displacement. Argo isopycnal displacement provides an estimate of the seasonal vertical velocity, i.e., math formula. This assumes that all of the seasonal density signal is caused by vertical displacement of isopycnals and it does not account for other mechanisms including surface buoyancy fluxes, horizontal advection, and mixing. Surface buoyancy fluxes play a role only in the upper ocean, but horizontal advection and mixing may be relevant also at depth. Despite these limitations, math formula still provides useful information on the depth dependence of wwhere horizontal advection and mixing are small, i.e., those regions where math formula is consistent with math formula. A comparison between math formulaand math formula during the Northern Hemisphere winter can be seen in Figure 1 (December to February average). math formula and math formula are zonally averaged in the Pacific Ocean (Figures 1a and 1b) and in the Indian Ocean (Figures 1c and 1d), and math formula is consistent with math formula (Figures 1a and 1c). Also, math formula is not very different from math formula (Figures 1a and 1c) and, in general, math formula has a large vertical scale (panels b,d in Figure 1 and section 3 in the supporting information). This is consistent with the constant vertical profile assumed for w in the present study. Similar results are found during the Northern Hemisphere summer and in the Atlantic (see Figure S3–S5 in the supporting information). While math formula clearly has a large vertical scale, the Gill and Niiler assumption that w linearly decreases with depth from the Ekman pumping velocity wEk′ (applied at z=−200 m) to zero at the bottom provides similar and equally consistent results in the depth range of interest. The same is expected for an alternate vertical structure made from the lowest baroclinic modes.

Figure 1.

Seasonal vertical velocity from Argo isopycnal displacement math formula: zonal average in the (a, b) Pacific Ocean and in the (c, d) Indian Ocean during the Northern Hemisphere winter. In Figures 1a and 1c, the green line is based on ERA-Interim wind stress Ekman pumping math formula; the red and the blue lines are math formula at 700 db and 1300 db, respectively. In Figures 1b and 1d, the color is math formula from Argo isopycnal displacement; the black contours are the temporal mean field of Argo potential density, zonally averaged in the same regions.

3.2 Argo Seasonal Steric Height and Wind-Forced Vertical Advection

[11] Figure 2 shows a comparison between the global zonal average of Argo Δη and the vertical advection contribution alone (math formula from Ekman pumping), during the Northern Hemisphere winter and summer. Δη is computed directly taking the difference between the beginning and the end of the season (i.e., η on 1 March minus η on 1 December and η on 1 September minus η on 1 June), while math formula is the time integral of the right-hand side of equation (1) from December to the end of February and from June to the end of August. Also, black-shaded values are smaller than one standard error, where the standard error computation is based on the standard deviation of Δη and math formula over the 8 years (2005–2012) of Argo having adequate global coverage (i.e., 8 independent realizations for each season). As described in Gill and Niiler [1973], Figure 2 shows that the wind-forced vertical advection contribution alone (Figures 2a and 2c) has similar spatial patterns to the total Δη from Argo (Figures 2b and 2d). The agreement is significant and extends beyond the tropics for both seasons, although Argo Δη has more structure than math formula. This may indicate the presence of strong currents, where seasonal horizontal advection could play a role and alter the balance in equation (1). Differences between Δη and math formula may, also, result from keeping the reference level at 2000 db. Variability below the Argo depth range could be estimated using the quasi-geostrophic formalism, projecting the Argo density field onto the interior barotropic and first baroclinic modes, similarly to [Wang et al., 2013], but this is beyond the scope of the present analysis. Also, while seasonal mixing is observed in the subsurface ocean both in the tropics and in the extra-tropics [Wu et al., 2011; Whalen et al., 2012], it is not addressed here. Finally, in the tropics, deep temperature variability below the thermocline is forced by seasonal Rossby waves [Hosoda et al., 2006; Johnson, 2011], but the present study describes zonal averages of Δη, globally and in each ocean basin, and propagation is not discussed. The ocean observations (i.e., Δη) do include the effect of waves but math formuladoes not account for propagation of the wind-induced signals. Since propagation is mostly zonal, the basin-wide zonal integration minimizes the fraction of signal that propagates out of the region during the season; hence, the error for not accounting for propagation in math formula.

Figure 2.

Seasonal steric height change (cm) during the Northern Hemisphere (a, b) winter and (c, d) summer: zonal average in the global ocean. Figures 2a and 2c show the contribution of vertical advection math formula. Figures 2b and 2d show Δη from Argo. Changes smaller than one standard error are shaded black.

[12] While Figure 2 is global, a similar result is found in zonal averages in the Pacific Ocean (Figures 3a and 3b), in the Indian Ocean (Figures 3c and 3d) and in the Atlantic Ocean (see Figure S6 in the supporting information), for both winter and summer seasons. Northern Hemisphere summer anomalies are of opposite sign to winter and are not shown (see Figure S7 in the supporting information). In each basin, the comparison between Δη and the vertical advection component deteriorates toward the poles (generally poleward of 50° latitude), consistent with the increase of unresolved mesoscale features at higher latitudes.

Figure 3.

Seasonal steric height change (cm) during the Northern Hemisphere winter: zonal average in the (a, b) Pacific Ocean and in the (c, d) Indian Ocean. Figures 3a and 3c show the contribution of vertical advection (Δηw′). Figures 3b and 3d show Δη from Argo. Changes smaller than one standard error are shaded black.

3.3 Horizontal Advection Contribution to Δη

[13] The zonal and meridional advection contributions to Δη (in the following, Δηu′and Δηv′) are computed during the Northern Hemisphere winter, from Argo geostrophic velocity, i.e., math formula and math formula. math formula and math formula are seasonal geostrophic velocity from Argo (i.e., referenced to 2000 db), g is the gravitational acceleration, pref=2000 db is the reference pressure, and ρis Argo potential density, as in equation (1).

[14] Figure 4 shows a comparison of math formula (in cyan), math formula (in blue), math formula (in green), and Δη (in red), spatially averaged in two different regions: 44°S–40°S in the Indian Ocean (Figure 4a) and 34°S–30°S in the Atlantic Ocean (Figure 4b). Dashed lines indicate the seasonal value plus and minus one standard error. The horizontal advection contribution is small and the error bars are relatively large, consistent with the increase of unresolved mesoscale features in the extra-tropics, but the difference between the observed Δη from Argo (in red) and the vertical advection component math formula (in green) is consistent with math formula (Figure 4a, in blue) and math formula (Figure 4b, in cyan). In general, caution is needed in asserting the relative importance of horizontal and vertical advection, since results depend on the geographical area of averaging. Unfortunately, where strong currents are present (i.e., where horizontal advection is most important), there are also mesoscale eddies that are unresolved by Argo sampling, but a longer data record will allow a more local analysis at least in some regions. Also, the effect of wave adjustment and propagation is present both in the Argo steric height and in the estimate from observed horizontal advection and has a major role in some regions [Qiu and Lukas, 1996; Chen and Qiu, 2004; Hsin and Qiu, 2012], but is not discussed here.

Figure 4.

Seasonal steric height change during the Northern Hemisphere winter: area weighted average along 20.5°E–145.5°E, 44°S–40°S in the Indian Ocean (Figure 4a) and 49.5°W–15.5°E, 34°S–30°S in the Atlantic Ocean (Figure 4b). The solid red line is Argo Δη; the advective contributions are in green (vertical advection, math formula), cyan (zonal, math formula), and blue (meridional, math formula). Dashed lines indicate error bars.

[15] Adding the surface absolute velocity anomaly from Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) altimetric data [Ducet et al., 2000] to the Argo geostrophic velocity relative to the surface (i.e. using an absolute velocity anomaly) does not yield statistically different results in the two regions of interest and it makes the estimate noisier due to mesoscale features that are present in AVISO but less so in the smoother Argo gridding.

4 Summary and Conclusions

[16] The unprecedented global coverage and accuracy of Argo temperature and salinity profiles make it possible to observe the seasonal steric height deviation (η) on global and basin scales during 2005–2012. Steric variability in the ocean includes diabatic changes in the surface layer due to air-sea buoyancy fluxes and adiabatic contributions from advection, which is most important below the surface layers. In the subsurface ocean, Argo Δη over a season agrees with vertical advection of the mean potential density field by Ekman pumping (math formula), consistent with the theory of Gill and Niiler [1973], and the agreement extends beyond the tropics. The current analysis compares zonal averages both in the global ocean and in ocean basins and describes their latitude dependence that is a primary factor in annual cycle signals and noise. Neither the role of propagation nor the role of mixing is discussed. Horizontal advection gives a significant contribution in some regions and is consistent with the differences between Δη from Argo and math formula.

[17] The depth dependence of the seasonal vertical velocity (w) is also discussed, as the expression for math formula is based on the assumption that math formula, that is, wconstant in pressure over the depth range of interest. While the estimate of w from Argo isopycnal displacement math formula is consistent with math formulaand shows a large vertical scale, the Gill and Niiler assumption that wlinearly decreases with depth from the Ekman pumping velocity math formula (applied at z=−200 m) to zero at the bottom provides similar results in the depth range of interest.

[18] As Gill and Niiler [1973] point out, although the dynamic component of the seasonal baroclinic signal is small at depth, it is useful to test the theory using observations. Moreover, this test might be regarded as a measure of Argo's ability, based on 8 years of global coarse resolution profiles, to estimate the annual cycle. Lastly, in some regions, the heat redistribution that corresponds to the dynamically driven Argo steric height variability in the subsurface ocean amounts to 10%−15% of the seasonal cycle heat gain in the upper ocean (not shown) and should not be neglected when trying to close the heat balance in the surface layer. With more Argo profiles, it will be possible to extend the analysis in this study beyond large-scale zonal averages and to assess the role of propagation in seasonal steric height on a global scale. With the current data set, averages over smaller areas yield results that are significant only in some regions.

Acknowledgments

[19] The Argo data used here were collected and were made freely available by the International Argo Program and by the national programs that contribute to it. The authors' participation in the Argo Program was supported by U.S. Argo through NOAA grant NA10OAR4320156 (SIO CIMEC). The statements, findings, conclusions, and recommendations herein are those of the authors and do not necessarily reflect the views of the National Oceanic and Atmospheric Administration or the Department of Commerce. The efforts of many international partners in planning and implementing the Argo array are gratefully acknowledged. ECMWF ERA-Interim data used in this study have been obtained from the ECMWF Data Server. The AVISO altimeter products were produced by the CLS Space Oceanography Division as part of the Environment and Climate EU ENACT project (EVK2-CT2001-00117) and with support from CNES. Valuable suggestions for this work were provided by two anonymous reviewers. The objectively mapped Argo data were provided by John Gilson.

[20] The Editor thanks two anonymous reviewers for assistance evaluating this paper.