letters to nature NATURE | VOL 408 | 23 NOVEMBER 2000 | www.nature.com 453 of 3D periodic mesostructured materials without assuming any structural models. The resolution for the structure is primarily limited by the quality of the HREM images, which depends on the long-range mesoscale ordering. Therefore, although further pro- gress may give better resolution, we expect no future change to the present conclusions about the structures of SBA-1, SBA-6 and SBA- 16, because the validity of the solutions does not depend on the resolution. This is a characteristic of our method that makes it different from other approaches. We also suggest that the results presented here provide a quantitative topological description of ordered mesostructured composites, and that such descriptions are essential in understanding the properties and possible applications of the composites. The resolution of periodically ordered, 3D arrangements of bimodal (meso-micro) pores in SBA-1 and SBA- 6 makes it possible to consider the detailed characterization of the range of complicated porous phases that are now synthetically achievable. M Methods Synthesis of SBA-6 3.75 g of tetraethoxysilane (TEOS) was added with magnetic stirring to a clear solution containing 0.5 g of the gemini surfactant 18B4-3���1 (N,N,N,N9N9-pentamethyl-N9- [4-(4-octadecyloxyphenoxy)-butyl]-propane-1,3-diammonium dibromide, C18H37OC6H4OC4H8N(CH3)2C3H6N(CH3)3Br2), 45.4 g of doubly distilled water, and 3.69 g of benzyltrimethylammonium hydroxide at room temperature. Stirring was continued for 20 h after the addition of TEOS at room temperature. The reaction gel mixture was heated for 2 d at 80 8C without stirring. The precipitate was filtered and dried in air at room temperature. Determination of properties Ar adsorption and desorption isotherms were measured at 87 K. Pore volumes (cm3 g-1) for SBA-1, SBA-6 and SBA-16 are 0.6, 0.86 and 0.45, respectively, and the ratios of the pore volume to unit cell are respectively 0.57, 0.65 and 0.47. The surface-area/pore-volume ratio (2.26 �� 109 m-1) for SBA-1 is nearly three times that of SBA-6 (7.93 �� 108 m-1). The silica wall densities determined with an AccPyc 1300 helium pycnometer are also substantially different for SBA-1 (2.00 g cm-3) and SBA-6 (2.20 g cm-3). Received 23 May accepted 6 October 2000. 1. Zhao, D. et al. Triblock copolymer syntheses of mesoporous silica with periodic 50 to 300 Angstrom �� pores. Science 279, 548���552 (1998). 2. Zhao, D., Huo, Q., Feng, J., Chmelka, B. F. & Stucky, G. D. Nonionic triblock and star diblock copolymer and oligomeric surfactant syntheses of highly ordered, hydrothermally stable, mesoporous silica structures. J. Am. Chem. Soc. 120, 6024���6036 (1998). 3. Alfredsson, V. & Anderson, M. W. Structure of MCM-48 revealed by transmission electron microscopy. Chem. Mater. 8, 1141���1146 (1996). 4. Monnier, A. et al. Cooperative formation of inorganic-organic interfaces in the synthesis of silicate mesostructures. Science 261, 1299���1303 (1993). 5. Schacht, S., Janicke, M. & Schuth, �� F. Modeling X-ray patterns and TEM images of MCM-41. Microporous Mesoporous Mater. 22, 485���493 (1998). 6. Huo, Q. et al. Generalized syntheses of periodic surfactant/inorganic composite materials. Nature 368, 317���321 (1994). 7. Huo, Q. et al. Organization of organic molecules with inorganic molecular species into nanocom- posite biphase arrays. Chem. Mater. 6, 1176���1191 (1994). 8. Auvray, X. et al. X-ray diffraction and freeze-fracture electron microscopy study of the cubic phase in the cetylpyridinium chloride formamide and cetyltrimethylammonium chloride formamide systems. Langmuir 9, 444���448 (1993). 9. Charvolin, J. & Sadoc, J. F. Periodic systems of frustrated fluid films and ������micellar������ cubic structures in liquid crystals. J. Phys. France 49, 521���526 (1988). 10. Ryoo, R., Kim, J. M. & Ko, C. H. in Studies in Surface Science and Catalysis Vol. 117 (eds Bonneviot, L., Beland, �� F., Danumah, C., Giasson, S. & Kaliaguine, S.) 151���158 (Elsevier, Amsterdam, 1998). 11. Nakanishi, K. Pore structure control of silica gels based on phase separation. J. Porous Mater. 4, 67���112 (1997). 12. Geis, H. Studies on clathrasils. III. Crystal structure of melanophlogite, a natural clathrate compound of silica. Z. Kristallogr. 164, 247���257 (1983). Supplementary Information is available on Nature���s World-Wide Web site (http://www.nature.com) or as paper copy from the London editorial office of Nature. Acknowledgements This work was supported in part by CREST, Japan Science and Technology Corporation (O.T.), by the National Research Laboratory Program of Korea (R.R.), and by the National Science Foundation (G.D.S.) and the Army Research Office (G.D.S.). O.T. thanks S. Andersson for encouragement and support. Y.S. thanks the Japan Society for the Promotion of Science. Correspondence and requests for materials should be addressed to O.M. (e-mail: terasaki@msp.phys.tohoku.ac.jp) or R.R. (e-mail: r.ryoo@mail.kaist.ac.kr). ................................................................. Improved estimates of global ocean circulation,heattransportandmixing from hydrographic data Alexandre Ganachaud* & Carl Wunsch MIT 54-1517, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA .............................................................................................................................................. Through its ability to transport large amounts of heat, fresh water and nutrients, the ocean is an essential regulator of climate1,2. The pathways and mechanisms of this transport and its stability are critical issues in understanding the present state of climate and the possibilities of future changes. Recently, global high-quality hydrographic data have been gathered in the World Ocean Circulation Experiment (WOCE), to obtain an accurate picture of the present circulation. Here we combine the new data from high-resolution trans-oceanic sections and current meters with climatological wind fields, biogeochemical balances and improved a priori error estimates in an inverse model, to improve estimates of the global circulation and heat fluxes. Our solution resolves globally vertical mixing across surfaces of equal density, with coefficients in the range ��3���12�� 3 10 2 4 m2 s 2 1. Net deep- water production rates amount to ��15 6 12�� 3 106 m3 s2 1 in the North Atlantic Ocean and ��21 6 6�� 3 106 m3 s2 1 in the Southern Ocean. Our estimates provide a new reference state for future climate studies with rigorous estimates of the uncertainties. Obtaining a consistent picture of the oceanic circulation requires adjusting thousands of parameters consistently with a priori error estimates. We present here our best estimate from selected hydro- graphic data (Fig. 1), which will improve with the appearance of new data. Mass flux is the most basic element of the circulation and Fig. 2 shows the best-estimate coast-to-coast integrated water mass transports for selected density classes. A volume of 15 6 2 Sv (1 sverdrup �� 1 3 106 m3 s2 1) of North Atlantic Deep Water (NADW) is produced in the northern North Atlantic Ocean and moves southward, entraining Antarctic Bottom Water (AABW) from below, and Antarctic Intermediate Water (AAIW) from above. As a result, the NADW is increased to 23 6 3 Sv as it exits the South Atlantic at 308 S. In the Southern Ocean, a total of 21 6 6 Sv of bottom water is formed from lower Circumpolar Deep Water (CDW)���which corresponds approximately to the lower NADW density range. Bottom water inflows (NADW �� AABW mixture) to the Atlantic, Indian and Pacific oceans are 6 6 1:3 Sv, 11 6 4 Sv and 7 6 2 Sv, respectively. In the Indian and Pacific oceans, most of this water returns southward at deep and intermediate levels. These net values are the sums of large, strongly spatially varying, flows of opposing sign, and thus over- simplify the actual circulation a detailed description of the circula- tion within each ocean basin will be published elsewhere3,4. Our standard model estimate of the inflow in the South Pacific Ocean is in the lower range of previously published values, but it depends directly upon the weight given to the ������PO������ phosphate���oxygen combination (see Methods4,5) conservation constraints relative to mass conservation3. The deep inflow to the North Pacific Ocean is also weaker than previously found5, as a consequence of our consideration of heat and salt conservation in the northern parts of those basins. No definition of bottom-water formation can be completely unambiguous because of the entrainment of ambient fluid during the sinking process. In our Southern Ocean definition, the bottom- * Pressent address: Laboratoire de Physique des Oceans, �� IFREMER, 29280 Plouzane, �� France. �� 2000 Macmillan Magazines Ltd

letters to nature NATURE | VOL 408 | 23 NOVEMBER 2000 | www.nature.com 455 Diffusivities could not be resolved in the Southern Ocean, where many neutral surfaces outcrop. The improved inverse model method has produced the first near-global, resolved estimates of the dianeutral transfers. The overall results are inconsistent with recent suggestions that the ocean mixes primarily at near-surface outcrops of the neutral surfaces, that is, primarily in the Southern Ocean12. Strong abyssal mixing is required by the observed geos- trophically balanced circulation, and its absence is incompatible with the observed property distributions. Figure 1 shows the heat (actually, enthalpy) transports, across each hydrographic section (arrows) along with the residuals reflect- ing atmospheric heat exchanges (boxes). Residuals are accurately determined at middle and high latitudes, but are more uncertain at lower latitudes (for example, in the Atlantic Ocean) owing to an enhancement of the geostrophic noise there3. Nevertheless, the total heating over the tropical Atlantic and Pacific oceans are well- determined, respectively 0:7 6 0:2 PW (1 PW �� 1015 W) and 1:6 6 0:4 PW. No significant heat transfers are found in the Indian Ocean because of the large, uncertain, warm water inflow from the Pacific Ocean. This large warm water flux is the main heat escape from the Pacific Ocean, resulting in a northward heat flux in the South Pacific. In the southern Pacific sector, significant heating is found, in contrast with the sparse in situ observations13, but in qualitative agreement with the recent re-analysis of the European Centre for Medium Range Weather Forecasts14. Figure 3 shows the globally integrated heat fluxes compared to independent estimates. Most of the cooling occurs in the Northern Hemisphere, at a rate of 2 1:7 6 0:2 PW, in balance with the 2:3 6 0:4 PW heating in the tropical band and the 2 0:7 6 0:3 PW cooling in the Southern Ocean. Changes in the oceanic heat transport can have a large impact on atmospheric temperature gradients15,16 and thus on climate. Pre- vious estimates of the ocean���atmosphere heat exchanges that are based upon purely ocean surface observations are highly uncertain17,18. Analyses from numerical weather prediction centres provide oceanic surface fluxes that are often used as boundary conditions for driving ocean models, but associated uncertainty estimates are not provided. Heuristic calculations suggest uncer- tainties in their estimates of at least 60.6 PW for the meridional oceanic heat transport at most latitudes19. The present inversion indicates uncertainties that depend on latitude, with a high accuracy of globally integrated heat transfers (Fig. 3). Similar budgets, to be 60��W 0��W 60��W 120��W 180��W 120��W 50��S 25��S 0�� 25��N 50��N 15�� 2 14�� 2 12�� 2 3�� 1 16�� 2 13�� 2 4�� 2 (Entire Atlantic) 10�� 2.5 16�� 3 6�� 1.3 23�� 3 140�� 6 21�� 6 8�� 9 157�� 10 9�� 3 7�� 2 19�� 5 5.5�� 2 2.5�� 4 0.5�� 4 1 �� 3 1.5�� 1 16�� 5 8�� 4 3�� 5 27�� 6 14�� 6 11�� 5 28.11��n 27.72��n28.11 ��n27.72 Global circulation summary standard solution (Sv) (Entire Southern) Figure 2 Zonally integrated layer mass transports. The estimated water transports are indicated for the different density classes bounded by neutral surfaces (gn, in kg m-3) and across selected hydrographic sections. Neutral surfaces are close to surfaces of constant density, but are chosen so that movement along them minimizes the work done against gravity. The colour of the upwelling or down-welling arrows indicates the layer from which the water is coming. A flux of 0.8 Sv from the Pacific to the Atlantic Ocean through the Bering Strait was taken into account, although it is much smaller than the uncertainties on the net transports. In the Southern Ocean, the bottom water formation takes place mostly in the Weddell Sea, while the upwelling distribution is uncertain. In the Indian Ocean, most of the upwelling takes place north of 78 S. The South Pacific transports are given at 178 S because of the more complicated structure at 328 S (ref. 3). Note the increase in the Southern Ocean transport south of Australia owing to the recirculation of Indonesian throughflow water. Table 1 Basin-averaged dianeutral velocities and diffusivities w p (10-6 m s-1) k p (10-4 m2 s-1) ............................................................................................................................................................................. Atlantic bottom 0:5 6 0:2 9 6 4 Indian bottom 0:6 6 0:3 12 6 7 Pacific bottom 0:4 6 0:1 9 6 2 Southern bottom 2 0:25 6 0:1 ��� Atlantic deep 0:1 6 0:05 3 6 1:5 Indian deep 0:3 6 0:15 4 6 2 Pacific deep 0:1 6 0:03 4 6 1 Southern deep 0:1 6 0:1 ��� ............................................................................................................................................................................. The average is calculated on neutral surfaces from gn �� 28:1 kg m2 3 to the bottom (generally 3,800 decibars (or metres) to the bottom) for the ���bottom layers��� and from gn �� 27:96 to gn �� 28:07 for the ���deep layers��� (generally 2,000 m to 3,500 m). �� 2000 Macmillan Magazines Ltd