Monitoring Atlantic overturning circulation and transport variability with GRACE-type ocean bottom pressure observations - a sensitivity study

. The Atlantic Meridional Overturning Circulation (AMOC) is a key mechanism for large-scale northward heat transport and thus plays an important role for global climate. Relatively warm water is transported northward in the upper layers of the North Atlantic Ocean, and after cooling at subpolar latitudes, sinks down and is transported back south in the deeper limb of the AMOC. The utility of in-situ ocean bottom pressure (OBP) observations to infer AMOC changes at single 5 latitudes has been characterized in recent literature using output from ocean models. We extend the analysis and examine the utility of space-based observations of time-variable gravity and the inversion for ocean bottom pressure to monitor AMOC changes and variability between 20 ◦ N and 60 ◦ N. Consistent with previous results, we ﬁnd a strong correlation between the AMOC signal and OBP variations, mainly along the western slope of the Atlantic basin. We then use synthetic OBP 10 data - smoothed and ﬁltered to resemble the resolution of the GRACE (Gravity Recovery and Climate Experiment) gravity mission, but without errors - and reconstruct geostrophic AMOC transport. Due to the coarse resolution of GRACE-like OBP ﬁelds, we ﬁnd that leakage of signal across the step slopes of the ocean basin is a signiﬁcant challenge at certain latitudes. Transport signal RMS are in a similar order of magnitude as error RMS for the reconstructed time series. However, the interannual 15 AMOC anomaly time series can be recovered from 20 years of monthly GRACE-like OBP ﬁelds with errors less than 1 Sverdrup in many locations.

western boundary (e.g., Roussenov et al. (2008), Bingham and Hughes (2008), Bingham and Hughes (2012)), but also in in sea surface height changes (e.g., Bingham and Hughes (2009b), Willis (2010), Frajka-Williams (2015)) and in sea surface temperatures (Knight et al. (2005), Zhang (2008)). The viability of using OBP along the eastern and western boundaries to calculate the basin-wide meridional geostrophic transports was first demonstrated with numerical ocean simulations (e.g., Bingham 35 and Hughes (2008), Bingham and Hughes (2009a)). More recently, Elipot et al. (2013) used bottom pressure recorder (BPR) measurements along the western boundary to monitor the AMOC. However, due to the inherent drift problems of in-situ BPR recorders, their analysis was limited to time scales shorter than one year, as well as to the specific latitude of instrument deployment. 40 In the present study, we build upon previous results (Roussenov et al. (2008), Bingham and Hughes (2008), Bingham and Hughes (2009a)) and examine the feasibility of using OBP to derive AMOC variations. While the previous works examined the relationships between OBP and AMOC variability in the North Atlantic at specific latitudes (e.g., 40 • N, 48 • N and 50 • N), we examine the entire latitude and depth range from 20 • N through 60 • N. Thereby, we specifically investigate the 45 detectability of AMOC variability using OBP inferred from time-variable gravity observations such as those provided by the GRACE satellites (Tapley et al. (2004)). The GRACE gravity observations provide complete global spatial coverage and monthly time series of ocean mass changes from 2002 until present. The challenge in using GRACE-OBP to derive AMOC variability is the relatively coarse spatial resolution as well as overall signal-to-noise levels. To estimate the effects of limited 50 spatial resolution, we use data from the ECCO2 ocean state estimate and convert the synthetic OBP fields to a GRACE-like resolution. To also capture signal contamination from nearby land hydrology variations (which are also recorded by GRACE), we evaluate the effects of terrestrial land water storage on GRACE-like OBP retrievals by combining the ocean state estimate with a land-hydrology model. Our results indicate that even though resolution along the steep basin slopes is challenging in 55 GRACE-like OBP fields, we find that the recovery of the meridional volume transports with errors less than +/-1 Sv is possible for specific regions and time scales.
Our paper is organized as follows: in Sect. 2, we briefly review the pertinent aspects of the underlying theories and relationships between OBP and AMOC transports; then we describe the ocean 60 state estimate ECCO2 and discuss the AMOC and OBP signals in the model at GRACE-like spatial resolution, including signal contamination effects from land hydrology; in Sect. 3 we present results for deriving AMOC from the model data directly compared to results for AMOC from data smoothed to a GRACE-like resolution.
2 Methods and data

Theoretical background
The Atlantic meridional overturning circulation consists of a northward flow in the upper layer of the ocean (mostly between the surface and 1000 m depth; Srokosz et al. (2012), Wunsch and Heimbach (2013)), and a return flow to the south in the deeper layer of the ocean (between approximately 1000 m to 5000 m depth). The meridional stream function ψ(y, x) is derived from meridional velocities 70 (v y ) by integration over longitudes (x) and from the surface (η) to depth (z) (Marotzke et al. (1999)), As the large-scale flows are dominated by a geostrophic balance, the meridional transport-per-unitdepth T (z), at a particular latitude (y) and depth (z), can be derived from the zonal bottom pressure 75 differences p E and p W at the eastern and western basin boundaries by taking where the constants are the Coriolis parameter f and the mean sea water density ρ 0 (Marotzke et al. (1999), Roussenov et al. (2008)). Acceleration and stress terms are neglected, as they only play a role in the Ekman layer and in the deep bottom layers. For a more rigorous derivation and justification for 80 Eq. 2 we defer to Bingham and Hughes (2008), Bingham and Hughes (2009a), and Roussenov et al. (2008), and references therein. Using the geostrophic approximation, the depth-integrated meridional transports T (z) at a particular latitude (y) can then be used to give the meridional stream function ψ at that latitude: (3)

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Equation 3 provides a method to derive the geostrophic component of the AMOC stream function (or volume transport between two layers) from ocean bottom pressure data along the boundaries of the ocean basin. Possibly intervening topography (i.e., mid-ocean ridges) should in theory be considered when evaluating Eq. 3, but Bingham and Hughes (2008) and Bingham and Hughes (2009a) demonstrated in an ocean model that for interannual time-variable transports in the North Atlantic, 90 bottom pressure variability is concentrated along the western boundary, and it is sufficient to use only the outermost eastern and western points across the basin section (if a basin-mean or depth averaged boundary pressure is removed from p W in Eq. 3, it is also possible to use only bottom pressure on the western boundary (Bingham and Hughes (2009a)). Furthermore, the dominance of the western boundary variations was recently confirmed from hydrographic in-situ data (Elipot et al. (2014)). 95 We reconfirmed this with the ocean model ECCO2 (see below for details), and thus use p E and p W only for our analyses in the North Atlantic. While knowledge of p E and p W along the boundaries is in principle sufficient to infer ψ(y, z), the actual measurement of these terms is challenging. In-situ BPRs suffer from notorious drift-problems, and thus require drift corrections that usually inhibit any inferences about longer-than-annual variations (Polster et al. (2009)). An alternative measurement of 100 OBP variations can be obtained from time-variable gravity observations from space as currently acquired by the GRACE satellites. The main challenge for OBP inferred from time-variable gravity is the limited horizontal resolution, as well as the required signal sensitivity. Due to the altitude (about 450 km) and orbit configuration of the two GRACE satellites, the horizontal spatial resolution is limited to approximately 300 km (e.g., Chambers and Bonin (2012), Landerer and Swenson (2012)).

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Much of the AMOC-related OBP signals occur along the narrow and steep western boundary slope and are thus difficult to resolve (which is also a limitation to in-situ pressure observations). In Sect. 3, we therefore quantify these resolution issues using synthetic data at GRACE-like spatial resolutions to quantify the feasibility of the OBP-AMOC approach. Also note that GRACE can only resolve OBP variations relative to a (arbitrary) time-mean. Therefore, all terms in Eqs. 1 -3 are taken to be 110 anomalies and therefore only AMOC variations can be inferred, but not its long-term average. The mean flow in the North Atlantic and the resulting OBP anomalies are illustrated in Fig. 1.   (Greatbatch (1994)). For the subsequent analysis, we removed a trend and the mean annual climatology signal from all time series (OBP, velocities), and smooth with a 15-month running mean to focus on interannual signals 125 only.

GRACE-like OBP fields: mascons and spherical harmonics
Conventional GRACE gravity field solutions are given in global spherical harmonic basis functions without any type of constraints (e.g., Chambers and Bonin (2012)). In contrast, the GRACE mascon solutions employ geophysical constraints, and provide an improved spatial localization. A best-130 fitting gravity value is estimated for each mascon cell (here: 3 • x3 • equal area cells). Importantly, the mascon solution makes the application of empirical post-processing filters (i.e.: destriping) unnecessary and thus features a better signal-to-noise ratio at smaller spatial scales.
We evaluate OBP output from the ECCO2 ocean state estimate as provided at a 0.25 • degree resolution. To create GRACE-like synthetic observations that match actual GRACE resolution, we bin-135 average the OBP fields to a 3 degree equal area grid. This grid is identical to the JPL-mascon RL05M grid (Watkins et al. (2015)). Second, the OBP data is smoothed to resemble the resolution of the  CRI, right: spherical harmonics to degree 60. Since the ECCO2 original data is not smoothed, the OBP pixels do not get affected by nearby land hydrology signals (therefore no additional plot for hydrology). Second row shows enlargements of the two mascon-resolution data sets including hydrology and details for CRI standard GRACE solutions, which are represented in spherical harmonics truncated at degree and order 60, and smoothed with a Gaussian filter with 300 km radius. This would be necessary for real GRACE data in order to reduce noise and correlated errors. This processing provides approximately 140 the resolution that is currently achieved with the GRACE satellites. However, we do not consider instrument and resulting measurement errors in the gravity field retrieval from GRACE measurements in order to focus on the issues of spatial resolution and signal leakage. The spatial smoothing and averaging of the 0.25 • OBP fields leads to significant resolution reduction in particular in highly energetic regions like the Gulf Stream, as well as in regions of steep bathymetry (Fig. 2, Fig. 3).

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Additional post-processing filters employed to reduce correlated errors in GRACE would further dampen geophysical signals (e.g., Landerer and Swenson (2012)).

From continental hydrology
In order to make the synthetic OBP observations more realistic, we add a continental hydrology sig-150 nal that we obtain from the GLDAS-NOAH hydrology model (Rodell et al. (2004)). The continental hydrology signal does not affect the OBP data on the 0.25 • ECCO2 grid. However, when the data is smoothed, the hydrology signal 'leaks' into the OBP data (Wahr et al. (1998), Chambers and Bonin (2012)), causing contamination of ocean grid points by land hydrology variations (Fig. 4). As the following analysis will show, the effects of land signal leakage tend to dominate the error budget 155 in the meridional transport and overturning calculations, in particular for the near-coastal shallower shelf areas (above approx. 1000 m). Therefore, a leakage correction (e.g., CRI (coastline resolution improvement) filter for the mascon-grid) is essential in order to employ GRACE OBP-observations: mascons that cover both land and ocean area still obtain only one value to represent the mass change within that mascon. To better distinguish where the signals originate from, a so-called coastline res-160 olution improvement (CRI) filter is employed (see Watkins et al. (2015) for details). Essentially, the CRI process separates land hydrology and ocean signals based on a-priori co-variance information from both land and ocean forward simulations. This CRI filter reduces the leakage of the continental hydrology signal into the adjacent ocean mascons significantly (Fig. 4).
Spherical harmonic GRACE solutions can be corrected for leakage as well, using an iterative ap-165 proach. However, due to large smoothing filters which need to be applied (300 km Gaussian smoothing radius) and errors in the hydrology models, these corrections may not be sufficient enough to reduce overall noise and errors in the solutions for our purposes. We therefore do not consider leakage correction for spherical harmonics further here.

Due to steep bathymetry gradients 170
Besides signal leakage from continental hydrology, leakage of the signal within the ocean between different depths must be considered. Especially along the steep basin boundary slopes, there are instances where one 3 degree mascon covers a number of different depth layers. Thus, the different OBP in these layers cannot be resolved. One possibility to make this leakage effect smaller is optimal placement in longitude of the individual mascon cells. In the JPL mascon grid, it is possible to shift 175 the mascons in longitude direction (for each mascon latitude) without influencing mascons in other latitudes. We create a synthetic data set where we position the JPL mascons optimally in order to resolve as much of the western and eastern boundary signal as possible.  Hughes (2008), Bingham and Hughes (2009a)). Even though the eastern boundary OBP contributes only a small fraction to the AMOC signal, we take the signal on the eastern boundary into account 190 rather than removing a depth-mean. By removing a mean over all depths, leakage signal from continental hydrology would contaminate the OBP data at greater depths as well as the shallower areas, and degrade the AMOC transport estimates compared to the East-West difference. Thus, we consider the eastern boundary in our calculation, even though the data on the eastern boundary reduces the signal-to-noise ratio.

Meridional transports from OBP integration
For each of the synthetic OBP data sets, meridional transport time series are computed in 1 • latitude increments and over 100 m depth intervals, and the RMS differences between reconstructed and model reference time series are computed for each depth and latitude (Fig. 5). The results for OBP without a hydrology signal (Fig. 5, top row) Fig. 5), the errors are slightly higher across all depths, and at specific latitudes, e.g., at 25 -30 • N, there are significant signal leakage errors that introduce significant transport retrieval errors. The steep topography (Fig. 2) at these latitudes causes one 3 • 205 mascon to cover depth layers from above 1000 m to below 3000 m. Very high errors (> 1.5 Sv/km) occur in the upper 100 m depth for all latitudes due to the non-geostrophic, wind-driven transport in the Ekman layer, which cannot be recovered from East-West OBP difference observations. In all following computations of the geostrophic volume transports, we therefore exclude the upper 100 m (in the OBP-derived as well as in the reference transport time series).

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While the GLDAS hydrology signal does not affect the results on the ECCO2 model grid (Fig. 5  In what follows, three different depth layers are considered in more detail: 100 m to 909 m, 909 m to 3000 m, and 3000 m to 5000 m depth, and detectability of the AMOC signal in each of these and is not considered in the following. As mentioned before, the uppermost 100 m of the ocean are also excluded, because the Ekman circulation and related transports cannot be recovered from OBP gradients. Over interannual periods, the net water volume transported northward should equal the water volume transported back south (e.g., Srokosz et al. (2012), or Kanzow et al. (2007) for 10-day timescales). Thus, it should be sufficient to observe either the northward or the southward transport 250 in order to reconstruct the interannual AMOC transport variations, as long as the depth of maximum overturning circulation is known. Since we do not know the correct depth of maximum overturning for each latitude and time, we make an assumption of a constant depth, which introduces only a small error.

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In what follows, three different depth layers are considered in more detail: 100 m to 909 m, 909 m to 3000 m, and 3000 m to 5000 m depth, and detectability of the AMOC signal in each of these three layers from GRACE-like OBP resolutions is assessed. The first layer covers the northward transport (down to the maximum of the mean AMOC, Fig. 6), the second layer covers steep ocean basin slopes for most latitudes (Fig. 2), and the third layer covers deeper transport, where the bathymetry 260 is less steep (Fig. 2), and therefore can be expected to be more favorable for GRACE-like resolutions.  (Fig. 2, Fig. 4). When the data is smoothed, the OBP values cannot be attributed to the 275 correct depth as the depth interval for one 3 • smoothing interval becomes very large. Between 45 • N and 60 • N, the depth gradient for a 3 • longitude interval becomes much smaller, i.e., more than one three degree pixel is needed to cover the depth gradient from 909 m to 3000 m. Thus, OBP at individual depth layers can be better resolved and the transport reconstruction is more accurate, leading to smaller error RMS. For the upper transport, RMS errors are high (0.5 Sv to 2 Sv) for spherical  errors RMS for the original ECCO2 resolution is mostly just below the signal RMS. Even though error RMS for mascons are higher, the results in the upper and deeper layers achieve smaller error RMS than signal RMS for selected latitudes. As mentioned before, the overturning transport signal is on the edge of detectability in GRACE gravity data, but we show in this study that it is possible with CRI improved mascons for selected latitudes. In conclusion, Fig. 7 Fig. 8).

Summary and outlook
Our model studies have shown that even though signal leakage (from hydrology and across different depths layers) is a challenge at GRACE-like resolutions, the AMOC anomaly time series can be this leads to an error of about 2 Sv from spherical harmonics. However, we note that mascon data errors are estimated to be about 30% smaller than this in the current study region (see Watkins et al. (2015)). The AMOC retrieval is rather sensitive to the bathymetry profile, and therefore the quality of the signal recovery is very latitude dependent (Fig. 7, errors vary with latitude and depth layer from 0.05 Sv to 5 Sv). Furthermore, error RMS levels are in the same order of magnitude as signal 370 RMS levels (Fig. 7); they are smaller only for selected depths and latitudes. However, in the deeper layers of the ocean (where the bathymetry gradients are less steep than in shallower layers), OBP measurements at GRACE-like resolutions lead to errors below 1 Sv, while they are up to 3 Sv for the other two layers (Fig. 7). Thus, the deep layer appears to be the most suitable target to retrieve ocean transports from OBP observations at GRACE-like resolutions. Since the AMOC is not very coherent