Proxies indicate that the Last Glacial Maximum (LGM) Atlantic Ocean was marked by increased meridional and zonal near sea surface temperature gradients relative to today. Using a least squares fit of a full general circulation and sea ice model to upper-ocean proxy data with specified error estimates, a seasonally varying reconstruction is sought of the Atlantic Ocean state that is consistent with both the known dynamics and the data. With reasonable uncertainty assumptions for the observations and the adjustable (control) variables, a consistent LGM ocean state is found, one not radically different from the modern one. Inferred changes include a strengthening of the easterly and westerly winds, leading to strengthened subtropical and subpolar gyres, and increased upwelling favorable winds off the coast of Africa, leading to particularly cold SSTs in those regions.

4. Testing with the modern circulation Section: Choose Top of page Abstract 1.Introduction 2.Background 3.Dynamical reconstructio... 4.Testing with the modern... << 5.Application to Last Gla... 6.Discussion REFERENCES CITING ARTICLES The modern circulation, which is much better observed and understood than that of the LGM, is used to test model adequacy and to understand the shortcomings. An existing modern state estimate made using the same Lagrange multiplier machinery, OCCA (Forget 2010), for the time-varying global ocean state over 2004–06, is used as a reference. This estimate is preferred over climatology as a target because it is demonstrably consistent with ocean physics and with a wide variety of observations and because the atlas includes self-consistent, gridded estimates of temperature, salinity, and velocity. A mean annual cycle of ocean conditions is obtained by computing monthly-mean OCCA conditions across 2004–06; this estimate will be referred to as OCCA hereafter, recognizing that it is an average of the full version. We ask a simple question: can the dominant ocean properties of OCCA be reproduced with a reduced model and using the dynamical reconstruction approach? OCCA came from a direct fit to observations and the present test becomes instead a fit to the time-averaged OCCA. Note that the model configuration used here is a simplified, and regionally restricted, version of the one used in OCCA and is not expected to fully mimic the OCCA ocean state. Bathymetry, grid resolution, and vertical levels in our model configuration are identical to those of Forget (2010). The 2006 National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis product (an updated version of Kalnay et al. 1996) is used to drive the model. Daily mean atmospheric forcing is used, under the assumption that the diurnal cycle is not of first-order importance in setting the large-scale properties of the Atlantic Ocean. The model is started from OCCA temperatures and salinities, and OCCA properties are used to prescribe southern boundary conditions. To search for solutions close to the actual modern climate state, relatively small uncertainty assumptions are used for the control variables (see Table 2). The model is constrained by OCCA temperatures and salinities at all grid points, with assumed uncertainties on OCCA properties given by the hydrographic uncertainties of Forget and Wunsch (2007). Among many differences between OCCA and the present setup, the use here of a much longer estimate length and of a repeating seasonal cycle make reproducing OCCA properties a challenge. Table 2. Prior uncertainties for atmospheric controls in modern and LGM dynamical reconstructions. Image of typeset table An initial ocean circulation estimate is required before proceeding with improving the fit of the model to OCCA; this prior estimate was generated by running the forward model with the above-defined prior estimates of atmospheric forcing and initial and boundary conditions (i.e., control variables are zero). The estimate was then iteratively improved. After 20 iterations, total cost J [Eq. (4)] was reduced by 82%. While the prior estimate had a poor fit to OCCA [J data = 5.0; see Eq. (3)], after 21 iterations the estimated ocean state was consistent (J data = 0.9). This fit to OCCA is sufficient to proceed, and the iteration 21 estimate, which will hereafter be referred to as Mod_DR [for modern dynamical reconstruction (DR)], is briefly analyzed with a focus on the differences between the estimates [see Dail (2012) for more extensive analyses]. Compared to OCCA, Mod_DR is consistently warmer in the near-surface ocean (see Fig. 3). Because mixed layer physics are parameterized here with Gaspar et al. (1990), while OCCA used that of Large et al. (1994), some change is expected. Near-surface equatorial conditions are not well reproduced. This region is likely particularly sensitive to the choice of internal model parameters, which differ in the two models. Other models also have difficulty in this region: PMIP2 preindustrial simulations are consistently 2°–4°C warmer than the modern in the eastern equatorial Atlantic (Otto-Bliesner et al. 2009). Finally, at 720 m, large-scale biases are not present, but some difficulty in reproducing water mass properties is apparent in the Mediterranean outflow region and in the Labrador Sea. These are both regions of water mass formation, a process that is highly sensitive to model numerics that vary between OCCA and the current approach. The OCCA estimate is itself not “truth” and, overall, our inference is that modern upper-ocean temperatures and salinities are relatively well represented by the dynamical reconstruction approach.



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6. Discussion Section: Choose Top of page Abstract 1.Introduction 2.Background 3.Dynamical reconstructio... 4.Testing with the modern... 5.Application to Last Gla... 6.Discussion << REFERENCES CITING ARTICLES A dynamical reconstruction (state estimate) of the LGM Atlantic Ocean has been obtained. The estimate is based on the MARGO near–sea surface temperature proxy records, a full general circulation and sea ice model, uncertainties in the data, and uncertainties in the prior estimates of the model atmospheric forcing and initial conditions. As with studies of the modern circulation, numerical solution of the constrained least squares problem using Lagrange multipliers proves to be useful in practice. The resulting solution, including estimates of the meteorological forcing, contrasts with published LGM forward modeling efforts, which have not succeeded in providing a close fit to proxy estimates of LGM NSSTs. As in any estimation problem, no claim is made that LGM_DR is correct—only that it exactly satisfies known adjusted model equations and is generally consistent with the observations insofar as that is possible. Disagreements among the four MARGO NSST compilations used here are sometimes large, especially north of 40°N, and the uncertainty assignments suggested as a first estimate on site-specific proxies in MARGO Project Members (2009) are insufficient to permit reconciliation of these datasets. However, if uncertainties are doubled on dinocyst data everywhere and on alkenone data north of 40°N, it is possible to identify an ocean state, LGM_DR, that agrees relatively well with MARGO NSST estimates. Previously, it was unknown how closely a numerical model could reproduce observed LGM NSSTs. An important inference is that moderate changes from the modern atmosphere are sufficient to reproduce LGM NSSTs—wholesale reorganizations are not required. As compared to the modern atmosphere, required changes include increases in the strength of easterly and westerly winds, increases in upwelling favorable winds in the eastern equatorial zone and along the western African coast, 4°C or more of cooling of air temperatures in the eastern subpolar gyre and eastern equatorial zone, and large-scale increases in net surface freshwater flux out of the Atlantic. LGM_DR is also marked by several key differences from the modern ocean state: strong decreases in NSST in the eastern equatorial Atlantic and eastern subpolar gyre, a significant eastward shift of the core of the subpolar gyre, increased upper-ocean transports in the subpolar and subtropical gyres, increased zonality of the North Atlantic current, and increased sea ice extent, especially in winter. These inferred changes are a baseline solution for further study, and we note that much larger differences might have existed—only that they do not appear to be required by the model physics or the MARGO NSST data. A number of limitations of the current study are important. Among them are the assumptions that, to first order, the LGM Atlantic Ocean can be represented with a fixed seasonal cycle and that interannual variability can be neglected. Longer-term variability is surely present, but the database used does not depict it. A 10-yr state estimate has been used here under the assumption that upper-ocean conditions are largely controlled by atmospheric forcing and that the upper-ocean properties are reasonably close to equilibrium with atmospheric forcing after that time. This assumption can be tested by studying the sensitivity of estimated conditions to state estimate duration and to the choice of initial conditions in the ocean. Modern atmospheric conditions have been used here as an a priori estimate of atmospheric forcing. In principle, the dynamical reconstruction approach can be applied to a coupled ocean–atmosphere–sea ice model, although such approaches, for technical reasons, have not yet been rendered practical even in the modern world. Meteorological fields from coupled model simulations of the LGM could be used as priors to evaluate the sensitivity of the estimated conditions to these choices. More generally, uncertainty quantification for both ordinary models as well as adjoint-based state estimates is needed but has been problematic for technical reasons. Recent progress in this area on simplified problems is encouraging (Kalmikov 2013), although it is not yet applicable to full problems such as the current one. The distribution of LGM NSST data is sparse and uneven, and the proxies show substantial disagreements with each other. Known key aspects of the ocean state, such as salinity, are largely unconstrained by available LGM data. Continued proxy development is key to improving future state estimates, even as more elaborate models could be used. A first step has been taken down the road toward a critical objective—the ability to find dynamically consistent estimates of the glacial ocean that are also consistent with diverse proxy records. Discussions will be published elsewhere of the implied full water column circulation. We anticipate that this approach will prove useful in a variety of studies, including the use of a higher-resolution global model, the inclusion of additional oceanic data types, the consideration of data constraints on paleoatmospheric properties, and application of the method for defining future sampling strategies.

Acknowledgments Olivier Marchal, Jake Gebbie, and Claire Waelbroeck provided helpful reviews on an earlier version of this manuscript; suggestions from three anonymous reviewers also improved the manuscript. Gaël Forget, Matt Mazloff, Patrick Heimbach, and Jean-Michel Campin provided much appreciated technical assistance with state estimation. The work of the MARGO Project participants, and those who collected the records compiled in MARGO, make studies such as this one possible. We also thank the participants of the PMIP project for making their simulation results available. NASA and NCAR computational resources were used for all simulations reported in this study. This work was funded by a National Defense Science and Engineering Graduate Fellowship and National Science Foundation Awards OCE-0645936 and OCE-1060735.