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How is the ocean filled?

2011; American Geophysical Union; Volume: 38; Issue: 6 Linguagem: Inglês

10.1029/2011gl046769

1944-8007

Geoffrey Gebbie, Peter Huybers,

Meteorological Phenomena and Simulations

Geophysical Research LettersVolume 38, Issue 6 OceansFree Access How is the ocean filled? Geoffrey Gebbie, Geoffrey Gebbie [email protected] Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, USASearch for more papers by this authorPeter Huybers, Peter Huybers Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USASearch for more papers by this author Geoffrey Gebbie, Geoffrey Gebbie [email protected] Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, USASearch for more papers by this authorPeter Huybers, Peter Huybers Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USASearch for more papers by this author First published: 23 March 2011 https://doi.org/10.1029/2011GL046769Citations: 45AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract [1] The ocean surface rapidly exchanges heat, freshwater, and gases with the atmosphere, but once water sinks into the ocean interior, the inherited properties of seawater are closely conserved. Previous water-mass decompositions have described the oceanic interior as being filled by just a few different property combinations, or water masses. Here we apply a new inversion technique to climatological tracer distributions to find the pathways by which the ocean is filled from over 10,000 surface regions, based on the discretization of the ocean surface at 2° by 2° resolution. The volume of water originating from each surface location is quantified in a global framework, and can be summarized by the estimate that 15% of the surface area fills 85% of the ocean interior volume. Ranked from largest to smallest, the volume contributions scaled by surface area follow a power-law distribution with an exponent of −1.09 ± 0.03 that appears indicative of the advective-diffusive filling characteristics of the ocean circulation, as demonstrated using a simple model. This work quantifies the connection between the surface and interior ocean, allowing insight into ocean composition, atmosphere-ocean interaction, and the transient response of the ocean to a changing climate. 1. Introduction [2] Traditionally, a handful of water masses having distinct hydrographic properties are called upon to describe the composition of the ocean [e.g., Wüst, 1935; Warren, 1981], where each water mass is defined by a characteristic set of temperature, salinity, and other hydrographic properties. The oceanic volume occupied by each water mass is typically estimated by inverting hydrographic measurements [e.g., Tomczak, 1981; Mackas et al., 1987; Tomczak and Large, 1989], but the results have proven sensitive to the number and definition of the water masses. For example, Broecker et al. [1998] used one hydrographic property to distinguish between North Atlantic Deep Water and Antarctic Bottom Water, finding that they contributed equally to filling the deep Pacific. More recently, Johnson [2008] decomposed the subthermocline world ocean into seven water masses and found that Antarctic Bottom Water fills two to three times more of the deep Pacific than North Atlantic Deep Water. Another answer might be obtained if more water masses were included, but traditional inverse approaches are limited to distinguishing only as many water masses as there are distinct water properties, and there is little prospect of obtaining enough well-measured global tracers to resolve this issue using previous methods. 2. Method [3] To circumvent this methodological roadblock, we extend and apply a recently developed inverse technique [Gebbie and Huybers, 2010], referred to as Total Matrix Intercomparison (TMI). Like other water mass decompositions [e.g., Tomczak, 1999], TMI is based upon inverting tracer conservation equations, but it is unique to this class of methods in that it also accounts for the geography interconnecting the tracer observations in a more complete way. More specifically, TMI diagnoses the pathways that connect each interior box to every surface region of a discretized ocean by following trails of similar water properties, where directionality is determined using the telltale signs of nutrient remineralization. Instead of solving for water masses that are defined by water properties, we seek a solution in terms of water origins, where we distinguish waters last in contact with a specific surface region of the ocean. TMI yields an estimate of the interior ocean volume filled from every surface gridbox resolved in a given dataset, thus permitting a more detailed quantification than previously available from observations. [4] Each surface box is a source of water with a particular set of property values, and as such, can be considered a “water type” as defined by Tomczak and Large [1989]. Many surface boxes have similar properties, and thus, interior ocean waters cannot be distinguished by these relatively minor differences. The crucial additional step in this study is to identify waters by their surface origin, and to trace the constituents of each interior water back to the surface location from which they originated. The degree to which waters from adjacent locations can be distinguished is addressed later. [5] The information content in TMI is encapsulated in the pathways matrix, A, derived fully by Gebbie and Huybers [2010] and reviewed here. To obtain the matrix, we first solve for the mass contribution made to each box by each of its immediate neighbors using the same form as a traditional water-mass decomposition. In steady state, the tracer concentration in each box must satisfy, co = m1c1 + m2c2 + … + q, where the m's give the fractional mass contribution and q represents internal sources for nonconservative tracers, related by stoichiometric ratios of 1:15.5:-170 for phosphate, nitrate, and oxygen concentrations [Anderson and Sarmiento, 1994]. Each box has up to six neighbors and a biological source term, giving seven unknowns constrained by the six observed tracers and mass conservation. For ease of notation, the mi and q unknown terms are combined in the vector, x. Using a weighted, tapered, non-negative least squares method [Lawson and Hanson, 1974], we solve the matrix equation at each location: Ex + n = y, where E is a square matrix, n is noise, and y is the observations. The weighting accounts for data accuracy, and the non-negativity constraint enforces mass contributions and nonconservative sources to be zero or greater. The local information is aggregated into a single matrix equation, Ac = d, where A contains the m's from the local inversion, c is any tracer distribution, and d provides the surface boundary conditions and interior source terms. The global matrix A is square, full rank, and encapsulates the influence of any ocean grid box on any other. [6] The principles underlying TMI are straightforward, but several complexities must be dealt with. To account for the effects of the seasonal cycle, we apply TMI to observations that represent late wintertime conditions by requiring that the ocean be well-mixed above the seasonally-maximum mixed-layer depth, as this depth is most indicative of the properties transmitted into the ocean interior [Stommel, 1979]. Longer-term variations due to natural ocean-atmosphere variability and anthropogenic changes [Johnson and Orsi, 1997; Curry and Mauritzen, 2005] are treated by allowing uncertainty in the surface tracer concentrations that are explicitly solved for. In the rare ( 1250. One could also fit the 100 most important points with a power law with a shallower slope closer to p = 1, although it does not have the statistical significance of our first fit. Repeating the analysis at 4° × 4° resolution results in a similar distribution once differences in surface area are accounted for (see Figure S3 in auxiliary material), reflecting the scale invariance associated with power-law processes. Figure 3Open in figure viewerPowerPoint The distribution of volume contributions from 11,113 surface sites. (top) The distribution of equivalent thickness ordered from largest to smallest (red dots) with the best-fit power law (black line). If the x-axis is replaced by the cumulative fraction of ocean area, the plot is not visibly changed. (middle) A rank-size diagram of the same form as the top panel, but for an idealized advection-diffusion model of an overturning circulation. (bottom) The overturning streamfunction (black lines) of the idealized model with the fraction of water originating from the left-most five surface gridpoints (background color). [13] Some further insight into the controls upon the equivalent thickness distribution can be obtained from a simple tracer model containing an advective two-dimensional overturning cell and horizontal diffusion. The model produces a power-law scaling in equivalent thickness similar to that of the observations (Figures 3, middle and 3, bottom). The power-law slope is a function of the model's Peclet number; for example, decreasing the rate of advection relative to diffusion increases the breadth of surface sources entrained in downwelling fluid and gives a flatter distribution of dn. Entrainment of diffusively mixed ambient fluid is expected from dynamical studies of ocean convection [Jones and Marshall, 1993] and gravity currents [Hughes and Griffiths, 2006]. Even if the advective velocity field indicates a small sinking region, it is possible to have a wide range of contributing surface regions. 5. Discussion and Conclusions [14] The interpretation of the ocean as being filled by just a handful of sinking regions [Stommel and Arons, 1960; Stommel, 1962] was an idealized construct, and there is observational evidence for at least a few tens of waters that fill the ocean [e.g., Gordon, 1974; Talley and Raymer, 1982; McCartney and Talley, 1982; Hanawa and Talley, 2001; Yashayaev and Clarke, 2008]. Nonetheless, numerical tools for dealing with more than ten water masses have been lacking, essentially requiring observational studies to assume just a few surface regions contribute to filling the interior [e.g., Stuiver et al., 1983; Matsumoto, 2007]. Here we quantify how the ocean is filled at 2° resolution through the inversion of most of the available ocean tracer data. Prior to this work, only numerical models [Haine and Hall, 2002; Primeau, 2005] or data assimilation products [e.g., Schlitzer, 2007] could provide a picture of how the ocean is filled at this resolution. [15] Furthermore, we find that the volume filled by each surface box generally follows a power-law distribution, when ranked from highest to lowest. The shallow slope of the power law, which we suggest is set by the ratio of advective and diffusive processes, indicates that the ocean is filled from a broad number of surface locations. Specifically, 15% of the ocean surface fills 85% of the interior. Nonetheless, it is possible to describe much of the variability in interior property distributions using small numbers of property combinations due to regional homogeneities. The power-law scaling of ocean filling is rather simple given the various controls upon water formation, including brine rejection in polar regions, gravitational instability of deep water formation in subpolar regions, and wind-induced subduction in the subtropics. It will be useful to explore the degree to which this power law holds in the presence of changes in ocean energetics, stratification, and bathymetry. The more detailed quantification of the relationship between surface properties and the interior composition of the ocean should also facilitate study of how variations in interior water-mass properties [e.g., Johnson et al., 2007] relate to surface climate. Acknowledgments [16] GG and PH were funded by NSF award 0645936. GG was also supported by the J. Lamar Worzel Assistant Scientist Fund and the Penzance Endowed Fund in Support of Assistant Scientists. PH was also supported by NSF award OCE-0960787. We thank Carl Wunsch, Andrew Rhines, Luke Skinner, and two anonymous reviewers for constructive comments. We also thank Bruce Warren for his feedback and dedicate this work to him. [17] The Editor thanks two anonymous reviewers for their assistance in evaluating this paper. Supporting Information Auxiliary material for this article contains a description of the mathematical underpinnings of the calculations made in the main text. Auxiliary material files may require downloading to a local drive depending on platform, browser, configuration, and size. To open auxiliary materials in a browser, click on the label. To download, Right-click and select “Save Target As…” (PC) or CTRL-click and select “Download Link to Disk” (Mac). Additional file information is provided in the readme.txt. Filename Description grl27903-sup-0001-readme.txtplain text document, 1.1 KB readme.txt grl27903-sup-0002-txts01.pdfPDF document, 645.3 KB Text S1. Description of the mathematical underpinnings of the calculations made in the main text with three figures. grl27903-sup-0003-t01.txtplain text document, 1.1 KB Tab-delimited Table 1. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article. References Anderson, L. A., and J. L. 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