Global General Circulation of the Ocean Estimated by the ECCO-Consortium

. Following on the heels of the World Ocean Circulation Experiment, the Estimating the Circulation and Climate of the Ocean (ECCO) consortium has been directed at making the best possible estimates of ocean circulation and its role in climate. ECCO is combining state-of-the-art ocean general circulation models with the nearly complete global ocean data sets for 1992 to present. Solutions are now available that adequately fit almost all types of ocean observations and that are, simultaneously, consistent with the model. These solutions are being applied to understanding ocean variability, biological cycles, coastal physics, geodesy, and many other areas.

conceivable that oceanographers would be able to determine with useful accuracy the entire three-dimensional ocean circulation and its variability over a period of five to 10 years, and that this ability would lay the foundation for understanding the behavior of the entire ocean over decades to come. It was also believed that oceanic general circulation models (GCMs) inevitably would become more capable and realistic, and that without a greatly enhanced observational capability, they would become essentially untestable.
Because the observational technologies were so disparate, and because the coverage by any one type of sensor was likely to be very spatially and temporally inhomogeneous, a true global picture of the ocean would be possible only by combining the diverse data sets into a unified whole through the use of a GCM.
The meteorological methodology called "data assimilation" appeared to be applicable to the oceanographic problem, suggesting in a rough way the technical feasibility of what could be done. But, as described below, the analogy is significantly misleading.
By the time the major WOCE field components had concluded operations in the mid to late 1990s (see Figure 1), planning had begun for a program that would synthesize WOCE data; that program ultimately became ECCO. It was clear then that adequate computer power was going to be a major issue, but computers and ancillary equipment (e.g., storage devices) were still roughly following Moore's Law, and a reasonable expectation was that calculations that were very difficult in 1998 would likely be relatively easy in 2008. That expectation has generally been fulfilled, at least for calculations approaching eddypermitting horizontal resolutions.

iNTroduCTioN
The consortium that came to be called Estimating the Circulation and Climate of the Ocean (ECCO), and its various subcomponents, supported by the National Oceanographic Partnership Program (NOPP), had its origins in the World Ocean Circulation Experiment (WOCE). That experiment, conceived around 1980, was intended to depict the ocean as a major element of the global climate system with high fidelity. Some of the roots of WOCE are described in Siedler et al. (2001) and Wunsch (2006a).
By 1980, it was clear that growing concerns about climate change, in particular the ongoing rise in atmospheric CO 2 , meant that it was necessary to greatly improve understanding of the ocean's behavior worldwide.
Developments in a large number of technologies (e.g., satellites, floats, drifters, chemical tracers) made it −1 0 1 2 3 4 5 6 7 8 9 10 11 12 figure 1. The distribution of conductivity-temperature-depth (CTd) data used in the eCCo-Godae estimates, superimposed upon the time-averaged 800-m temperature as estimated through the optimization procedure described in the text. Table 1 lists the WoCe-era and later data used by the project.

aN ouTliNe of eCCo
Oceanographers have, generally speaking, two knowledge reservoirs: (1) theory (the fluid is described by the Navier-Stokes equations plus a few supplementary statements such as the equation of state), and (2) observations.
The ECCO challenge is to combine these two knowledge reservoirs, taking advantage of their complementarity, in such a way that ocean circulation could be consistently described and understood.
The ECCO problem is one of interpolation: fit a model to a data set during a finite time interval, 0 ≤ t ≤ T, over the entire three-dimensional volume of the ocean. The word "fit" requires definition. Let y i be any data point at time t i at location in latitude and longitude φ i , λ i and depth d i , and let ỹ i be the value at that time and place that the model calculates (commonly, the model, which in our case is on a grid, is interpolated to the data's nearest time and geographical location). Almost universally, ỹ i ≠ y i -that is, the model does not agree with the data. But data are always imperfect (noisy) and models are also imperfect (the reason why they are called models rather than reality). So, how far apart should one permit the difference ỹ i -y i to be before proclaiming that the model needs modifying to render it consistent with the data?
An infinite number of ways exist to measure misfit. The ECCO choice is the most nearly conventional one and is δ i the expected misfit and is the sum of estimated variance of the noise in y i and the estimated square of the model error.
In an ideal situation, all δ i would have values not far from one-meaning that the model and data agreed within one or two standard deviations of the expected errors in data and models. Typically, δ i 2 >> 1, and one then seeks to minimize the "cost" or "misfit" or "objective" function summed over all data types and times and locations:  . schematic of the time evolution of one component of a model state vector when using pure filtering methods. at time t 1 , the model is integrated from the starting condition shown by the red "x" labeled "a" until time t 2 , where the estimated state is the black "x" denoted "b." at time t 2 (the analysis time), a high-quality observation with small relative error is available (the triangle denoted "o"). because the observation is of high quality, the analysis step forces the model to jump from state value "b" to new estimated state value "c." The computation continues forward in time from this new starting condition. The changes from "b" to "c" at analysis times do not satisfy the model equations, an issue of no concern in forecasting, but central to understanding climate evolution. a smoothing step, such as employed in the rTs algorithm, produces the dashed blue curve by using data at all times following t 1 , t 2 , and which then satisfies the underlying model equations.  hydrography By "hydrography" we mean temperature and salinity data however they are observed. As used in ECCO, data are gathered primarily with conductivitytemperature-depth (CTD) sensors, expendable bathythermographs (XBTs), and Argo profilers, as well as the elephant seal described separately below. Figure 1 shows the distribution of CTD data used in the interval 1992-2007.
Compilations of the historical data into climatologies are now familiar.
ECCO-GODAE uses the so-called WOCE climatology of Gouretski and Koltermann (2004) Figure 3 shows the available coverage.

The eCCo models
The main, but not the only, GCM used in ECCO-GODAE has been an evolving version of the MIT model described by Marshall et al. (1997) and Adcroft et al. (2002). Giering (Giering and Kaminski, 1998; see also Marotzke et al., 1999;Heimbach et al., 2005)  The first ECCO results were the nearglobal 5 adjoint solutions described by Stammer et al. (2002) and run over the interval 1992-1997 on a 2° x 2° horizontal grid, and a near-global analysis of shorter duration (1997)(1998)(1999)(2000) with enhanced tropical resolution (0.3°) run by Lee and Fukumori (2003).
A series of Kalman filters and RTS smoothers have also been devised for this higher-resolution model following is normally omitted in studies using only a single data type (updated from .

Biological Applications
Understanding of the sustenance and evolution of biological communities depends directly upon having accurate physical flow and mixing fields.
Stephenie Dutkiewicz of MIT and here, the contribution to sea level trends from thermal effects over the entire water column is calculated from one of the eCCo-Godae solutions . Where the black and dashed blue lines coincide, changes are dominated by the upper 800 m, but where they differ, as in the southern ocean and in mid latitudes, the much deeper layers of the ocean contribute significantly and must be accounted for.  Figure 7 shows their regional mean surface topography estimate.

Earth Rotation and Geodesy
Estimates of oceanic mass and velocity fields produced by ECCO have been used to interpret geodetic measurements of Earth's orientation in space and its variable gravity field, and to highlight the major role of ocean angular momentum variability in explaining observed polar motion (e.g., Gross et al., 2005;Ponte et al., 2001Ponte et al., , 2007a Figures 8 and 9 show two representative results.

Sensitivity Analysis
In addition to their use in optimization problems, model adjoints are Among numerous examples, some already mentioned, the MITgcm adjoint has been employed in identifying causal factors in oceanic variability (e.g., Fukumori et al., 2007), studying pathways of circulation , and exploring observing system design (Köhl and Stammer, 2004).

Budgets
One of the unique characteristics in many of the ECCO estimates is their physically consistent closure of modeled property budgets. Kim et al. (2004Kim et al. ( , 2007

Paleoclimate
Understanding how the ocean adjusts to major injection of tracers at the sea surface is one of the major goals of paleoceanographic studies. One of the ECCO-GODAE solutions was used by Wunsch and Heimbach (2008) figure 7. five-year mean sea surface height from a regional ocean model simulation using eCCo-Godae open ocean boundary conditions. The coastal model is roms (regional ocean modeling system) and the atmospheric forcing is CoamPs (Coupled ocean atmosphere mesoscale Prediction system). Contour interval is 2 cm. Courtesy C. Edwards. See Veneziani et al., 2008 size. But, when a system is integrated over years and decades, even compara- . seasonal averages (three months) of volume transport contours (m 3 s -1 ) through time as a function of depth at 27°N in the North atlantic ocean. There are shifts on the longest observed time scales, but no simple trends. From Wunsch and Heimbach, 2006 6 it is possible that much more intense eddy motions than seen in the southern ocean state estimate could render ineffective the line-search algorithm used in eCCo-Godae. although we have not yet seen such behavior, its possibility remains. alternative optimization methods, not dependent upon the local derivatives of the lagrange multiplier method, can then be used. achieving the goal of global-scale, eddyresolving state estimation . Figure 11 shows an example of the type of solution that is becoming possible. This particular solution is only partly adjusted to fit the observations and it has been run only over a limited time duration. As computer power and numerical methods improve, it will eventually become the central product.  (Follows et al., 2007) to incorporate full biogeochemical cycles. In another application, for her MIT PhD thesis, Holly Dail is determining ocean circulation during the last glacial maximum, and an effort is ongoing to generate an ECCOlike system for continental ice sheets (Heimbach and Bugnion, in press).