An ocean state estimate constrained by most available data is explored to assess characteristics of variability in deep steric height—a mostly unobserved quantity, yet important for understanding the relation between sea level, heat content and other ocean climate parameters. Results are based on monthly-averaged steric height anomalies, vertically integrated over the “unobserved” deep ocean (below ∼1700 m). Excluding linear trends, variability in deep steric height is typically 10–20% of that in the upper ocean, with larger values seen in extensive regions. Enhanced deep variability, at monthly to interannual time scales, occurs in areas of strong eddy energy. Deep signals are mostly thermosteric in nature, with halosteric contributions tightly correlated and generally compensating in the Atlantic and Indian oceans and adding in the Pacific. Potential inference of deep signals from knowledge of the upper ocean is hampered by poor correlations, and regressions based on upper ocean steric height fail to represent the estimated deep variability. Monthly sampling at ∼2° scales would allow for best determination of deep variability and long term trends.
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 The need to accurately observe long-term climate signals in the deep ocean has been recently recognized [e.g.,Garzoli et al., 2010]. Present in situ measurements provided by the Argo system focus on the upper ocean and provide no data below depths varying from ∼1000 to 2000 meters [e.g., von Schuckmann et al., 2009]. Other available data, mostly from repeat hydrographic sections [e.g., Purkey and Johnson, 2010], are extremely thin in time and space and insufficient to provide comprehensive temporal and spatial characteristics of variability in temperature and salinity over the deep ocean. Yet knowledge of properties over the full water column is important for the interpretation of variability in sea level, heat storage and freshwater content, both at regional and global scales.
 Most accurate deep variability estimates are based on differences between high-quality hydrographic sections taken years or decades apart, which are then typically interpreted in terms of decadal changes in heat content, steric height, etc. [e.g.,Purkey and Johnson, 2010]. Any long-term changes are of course superposed on unresolved variability at interannual and shorter periods. Estimated uncertainties from these unresolved fluctuations can overwhelm the instrumental errors and render insignificant any long-term changes inferred from the sparse time sampling [Purkey and Johnson, 2010].
 To overcome poor in situ data coverage, one can attempt to infer deep signals from denser upper ocean observations assuming good vertical correlations [Sutton and Roemmich, 2011], but such assumptions remain largely untested. Combinations of sea level observations from altimetry, upper ocean hydrographic data, and bottom pressure values derived from satellite gravity missions can in principle provide a window on the deep density field, but accuracies of the different systems remain a limiting factor [Llovel et al., 2010]. Apart from data analyses, the importance of decadal trends in the deep ocean have been explored using model simulations [Song and Colberg, 2011] and model-data synthesis efforts [Wunsch et al., 2007], but an investigation of the deep variability across the full range of time scales has not been attempted, to our knowledge.
 At a time when the design and deployment of deep observing systems are actively being considered [Garzoli et al., 2010], an assessment of the expected space and time variability at depths below the Argo range seems warranted. We describe an attempt to quantify deep steric height (ζρ) variability—a quantity involved in the analysis and interpretation of sea level and heat content fluctuations—using a state estimate produced under the “Estimating the Circulation and Climate of the Ocean” (ECCO) consortium [Menemenlis et al., 2008; Wunsch et al., 2009]. The ECCO estimates provide dynamical interpolation in time and space of the mostly data-void deep ocean, using information from other measurements to help constrain the deep properties, while maintaining full consistency of all fields with the model dynamics and thermodynamics. Focus is onζρvariability at monthly to interannual time scales, including effects from eddies, and how those signals can affect the attribution of regional sea level variability and the determination of deep long-term climate signals. Although the analyzed deep fields can be affected by the lack of direct data constraints at depth and the imperfect knowledge of topography, subgrid scale parameterizations, etc., the inferredζρ variability provides a baseline for observing system design and basic guidance on the accuracies needed for both measuring any deep ζρ signals and constraining state estimates such as produced by ECCO.
2. Deep ζρ Analysis
 For the basic calculations, we use the eddy-permitting estimates produced by ECCO2 and constrained to available altimetry, in situ hydrography, and other observations using a Green's function method [Menemenlis et al., 2008]. Solutions are based on a coupled ocean-sea ice model run on a global 1/4° horizontal grid, with 50 vertical levels, and have been used to explore several scientific topics [e.g.,Menemenlis et al., 2008; Fu, 2009]. Full details on ECCO2 estimates, their overall quality, and examples of science applications are given in the cited references. Here, ECCO2 estimates of temperature θ and salinity S fields are used to calculate ζρ, as well as thermosteric and halosteric components, denoted ζθ and ζS, respectively. Focus is on depths below ∼1700 m (layers 36–50). Monthly time series are available over the period 1993–2006. Sub-monthly sampling was not archived, but the effects of those relatively short time scales onζρ are expected to be small, particularly outside the tropics [Vinogradova et al., 2007; Bingham and Hughes, 2008]. Lack of data prevents a direct assessment of the estimated deep ζρ variability, but basic statistics and spectral characteristics of sea level variability in ECCO2 compare well with those in altimeter data [Fu, 2009; C. Wortham, A four-dimensional spectral description of oceanic variability, PhD dissertation, manuscript in preparation, 2012]. In particular, magnitude and range of variability are very similar, although western boundary regions can show different patterns and weaker eddy energy in the ECCO2 estimates [Fu, 2009, see Figure 10]. To the extent that ζρ relates linearly to sea level, our estimates of deep variability are thus expected to lie within realistic bounds, but details of the spatial patterns should be treated with caution.
 Given the tendency for model-basedθ and S fields to exhibit long term drift, the realism of linear trends is hard to judge. Thus, trends are removed from the estimates and not discussed further here. Trends can still influence other time scales, however, as full separability is not possible in a nonlinear system. The variability in deep ζρ is quantified in Figure 1 based on the standard deviation σof the detrended monthly time series from 1°-averaged ECCO2 fields. The mean seasonal cycle, computed by averaging all available values for each month (January,…, December), and the residual non-seasonal variability are examined separately. Although the seasonal cycle tends to dominate variability in the upper ocean, its contributions to deepζρ variability are relatively weak, with σ values rarely surpassing 1 cm (Figure 1a). Enhanced deep ζρ seasonal variability is found in tropical areas with the strongest sea level seasonal cycle (e.g., Arabian Sea, tropical North Pacific), and also in regions of larger horizontal density gradients (e.g., along western boundary currents and the Antarctic Circumpolar Current). By comparison, σ values for residual nonseasonal series can be >2 cm and are higher than that of the seasonal series over much of the oceans (Figure 1b). Average σ is ∼6 mm, compared to ∼2 mm for the seasonal case.
 Regions known to have strong eddy variability show prominently as places of enhanced deep nonseasonal ζρ fluctuations. A considerable part of this energy is associated with interannual fluctuations. Values of σ based on nonseasonal time series smoothed over 6 months are shown in Figure 1c. The diminished values, relative to Figure 1b, represent the effect of subannual variations removed by the time smoothing. The average σ decreases to ∼5 mm, compared to ∼6 mm in Figure 1b. Thus, a significant part of the deep variability is of interannual nature. Moreover, substantial areas with σ> 1 cm remain in much of the eddy-filled regions, when only periods >1 year are considered.
 Ultimately, the importance of deep ζρ variability relates to how it compares to the more energetic upper ocean. The ratio of deep to upper ocean σ values of ζρ, shown in Figure 1d for the case of residual nonseasonal variability, averages to ∼0.2. Over much of the ocean the ratio is 0.1–0.2, but at many regions (e.g., in the Southern Ocean) ratios > 0.5 can occur. A similar ratio for the mean seasonal cycle (not shown) reveals a comparatively weaker impact of deep seasonal ζρ variability, and for the remainder of the paper we concentrate on the analysis of nonseasonal fluctuations at monthly to interannual scales.
 The influence of eddies inferred from Figure 1 has been seen in many hydrographic surveys [e.g., Purkey and Johnson, 2010] and raises questions about the spatial scales present in the deep ζρ fields. Figure 2 shows σ values calculated with no smoothing applied to the 1/4° ECCO2 fields and with smoothing over 2° (cf. 1° smoothing in Figure 1b). Differences between 1/4° and 1° cases are minor, while at 2° the effects of eddies are still clearly seen. Smoothing over 4° (not shown) leads to much weaker amplitudes, particularly in eddy regions (average σ ∼ 3 mm vs. 6 mm for 1° case). Results thus indicate approximate spatial decorrelation scales ∼2°, similar to inferences based on hydrographic sections [cf. Purkey and Johnson, 2010], and point to the need to sample at these scales to avoid spatial aliasing, particularly in regions of strong eddy energy.
 The breakdown of deep ζρ variability in terms of ζθ and ζS is shown in Figure 3. Similar to shallower depths, θ effects are much more effective in producing deep ζρ variability. Values of σ for ζθ are a factor of 3 or more larger than ζS, on average. However, the relative magnitudes of ζθ and ζS vary with region (e.g., their effects are similar in the Kuroshio region but ζθ dominates over much of the Southern Ocean). From Figures 3a, 3b, and 1b, ζθ and ζS seem to be compensating in the North Atlantic and adding up in the North Pacific. Indeed the correlation between ζθ and ζS (Figure 3c) reveals a striking basin-scale pattern of coefficients <0 in the Atlantic, Indian and Southern Ocean (mostly south of the main ACC flows) and >0 in the Pacific, extending to parts of the South Indian Ocean. Results can be understood from the general characteristics of deepθ and S fields. As can be seen, for example, in the water mass analysis of Worthington , θ and S values tend to be correlated in the Atlantic and Indian basins and anticorrelated in the Pacific. Any processes involved in ζρ changes, such as vertical advection and heaving isopycnal motions, should thus lead to the observed correlations for ζθ and ζS, given the opposite effects of θ and S on density.
 From the observational perspective, an important question is whether deep ζρ changes can be inferred from upper ocean data, provided for example by Argo floats, as discussed by Sutton and Roemmich  for decadal trends. For such inference to be possible, the upper and deep ocean ζρ signals need to be well correlated. Figure 4a shows the correlation coefficients between deep and upper ζρ fluctuations. Although positive over most of the mid and high latitudes, correlations are far from perfect and rather poor in the tropics. Many factors may contribute to the weaker correlations at low latitudes, including the shallower vertical stratification, higher baroclinicity of the flows and stronger lateral advection effects compared to higher latitudes. As a stricter test, we also performed regression analysis of deep ζρ on upper ζρ series and calculated σ of the regression residuals, normalized by the σ of the deep ζρ series. These ratios, shown in Figure 4b, typically range ∼0.5–1, indicating that regression analyses based on upper ocean ζρ leave substantial residuals, which can be nearly as large as the deep ζρ signals in many regions.
3. Summary and Discussion
 Fully 3-dimensional ECCO estimates of the time-varying ocean state, produced using advanced models and data-constraining methods that enforce dynamically-consistent solutions, allow a more comprehensive assessment of deep variability than is possible from the extremely sparse observations. Variability in deep (<1700 m)ζρ at nonseasonal (monthly to interannual) time scales ranges from a few mm to >2 cm, and its neglect can measurably affect the interpretation of sea level changes (Figure 1). Effects of eddies and short spatial scales are important, even at interannual periods (Figures 1 and 2). The weak correlations and poor performance of regression analysis in Figure 4 suggest that inference of deep ζρ signals from upper ocean observations will be difficult in many regions.
 These findings stress the importance of routinely measuring deep ocean properties. In principle, deep ζρ variability could be inferred from satellite altimetry and upper ocean θ and S data, if bottom pressure variability is negligible. However, bottom pressure variability (not shown) is comparable in magnitude to that of deep ζρ, at the time scales of interest here. For proper sampling of the deep variability, maintaining monthly observations at scales ∼2° would be desirable (Figures 1 and 2). From the dominance of ζθ variations and the pattern of strong correlations between ζθ and ζS (Figure 3), observations of θ might allow for determination of S signals. In this regard acoustic thermometry [Munk and Forbes, 1989; Dushaw et al., 2010], which is mostly sensitive to changes in θ, is an interesting possibility. Space-based bottom pressure estimates at accuracies of ∼1 mm, not yet attained with GRACE but possible for future gravity missions [Wiese et al., 2009], would also be useful to constrain changes in deep ζρ, if similar accuracies can be delivered by satellite altimetry and upper ocean θ and S data. A thorough discussion of observing platforms, required sampling and accuracies is warranted but beyond our scope here.
 The problem of trend determination is crucial to detecting long-term climate signals. Standard errors in deepζρ or ζθ trend estimates can be inferred from the residual variability in Figures 1b or 3a. Without accounting for full auto-covariance properties of residuals, for the 14-year series considered, typical standard errors would be a few mm/yr but spatially dependent and considerably larger in western boundary and Southern Ocean regions. A crude conversion in terms of heat flux is 1 mm/yr ≈ 1 W/m2. For context, basin-averaged decadal (abyssal)ζθ trends in the work by Purkey and Johnson  are considerably <1 mm/yr (in fact many are not statistically significant, cf. Figure 8). The implied uncertainties of a few mm/yr from Figures 1b and 3aput stringent detectability thresholds on regional decadal trends. The statistics can improve if longer (multi-decadal) records are considered, or if large-scale averages are examined, but better sampling is needed than just a few high-resolution hydrographic sections, as in the past. Tradeoffs between spatial and temporal sampling (e.g., spatially-dense repeat hydrography every few years vs. coarser Argo-type data every month) need to be considered and ECCO estimates such as analyzed here could provide guidance on these issues.
 The analysis presented here is intended as mainly defining a baseline for future studies. A more complete characterization of the deep oceanic variability, extending to different variables and separate depth levels, is possible using the ECCO estimates, and a full spectral description is in the making (C. Wortham, manuscript in preparation, 2012). Analysis of other state estimates and model simulations would be useful for comparison. Going forward, the synergies between state estimates and data will need to continue to be exploited, with estimates providing guidance on observational requirements and new data yielding further constraints and consistency checks on the estimates.
 Calculations and figures were done by D. Spiegel. Discussions with C. Wunsch, P. Heimbach, and C. Wortham and comments from 2 anonymous referees are acknowledged. Support for this work was provided by the National Oceanographic Partnership Program (NNX08AV89G), NSF (OCE-0961507) and NASA (NNH08CE34C).
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.