R EPORTS about 1.Љ2, the true spectral resolution is around 9. P. Møller and P. Jakobsen, Astron. Astrophys. 228, 299 16. S. G. Djorgovski et al., GCN Circular 216 (1999). 8 Å, consistent with the measured width of the (1990). 17. J. Hjorth et al., Science 283, 2073 (1999). 18. We thank the NOT director for continued support to our spectral features. The average line profile, con- 10. M. Pettini, D. L. King, L. J. Smith, R. W. Hunstead, Astrophys. J. 478, 536 (1997); M. Pettini, L. J. Smith, GRB programme. This research was supported by the Danish structed from the Fe II lines above 6000 Å, D. L. King, R. W. Hunstead, ibid. 486, 665 (1997). Natural Science Research Council (SNF), the Icelandic Coun- cil of Science and the University of Iceland Research Fund. appears unresolved. This implies that the ab- 11. J. S. Bloom et al., in preparation, preprint available at The Nordic Optical Telescope is operated on the island of La sorbing clouds have a velocity dispersion of http://www.lanl.gov/abs/astro-ph/9902182. Ϫ Palma jointly by Denmark, Finland, Iceland, Norway, and less than 100 km s 1 in the rest frame. 12. A. S. Fruchter et al., in preparation, preprint available Sweden in the Spanish Observatorio del Roque de los at http://www.lanl.gov/abs/astro-ph/9902236. Muchachos of the Instituto de Astrofı´sica de Canarias. The The observed BATSE gamma-ray fluence of 13. S. Holland and J. Hjorth, Astron. Astrophys., in press, Ϯ ϫ –4 –2 data presented here have been taken using ALFOSC, which GRB 990123 is 5.09 0.02 10 erg cm for preprint also available at http://www.lanl.gov/abs/ is owned by the Instituto de Astrofı´sica de Andalucı´a (IAA) energies above 20 keV (14). In Table 2 we give astro-ph/9903175. and operated at the Nordic Optical Telescope under agree- the luminosity distance and the inferred isotropic 14. R. M. Kippen, GCN Circular 224 (1999). ment between IAA and the Astronomical Observatory of the ϭ 15. See Thermonuclear Supernovae, P. Ruiz-Lapuente, R. University of Copenhagen. energy output in various cosmologies for z Canal, J. Isern, Eds. (Kluwer Academic, Dordrecht, 1.600. A lower limit to the isotropic energy Netherlands, 1997). 23 February 1999; accepted 9 March 1999 release in gamma-rays alone is obtained in an ⍀ ⍀ ϭ Einstein-de Sitter Universe with ( 0 ⌳) (1,0). For a upper limit to the Hubble constant of H Ͻ 80 km s–1 Mpc–1 we find a lower limit of A Simple Predictive Model for 0 0.5 times the rest mass of a neutron star (1.4 MJ ϭ 2.5 ϫ 1054 erg) or ϳ2.5 times its binding the Structure of the Oceanic energy. For a set of currently observationally ⍀ ⍀ ϭ favored cosmological parameters ( 0 ⌳) ϭ Ϫ1 Ϫ1 Pycnocline (0.2, 0.8) and H0 65 km s Mpc we derive an energy release in gamma-rays equivalent to Anand Gnanadesikan 1.8 neutron stars. This is 45 times larger than the total energy emitted in all wavelengths by the A simple theory for the large-scale oceanic circulation is developed, relating most luminous Type II supernova, including pycnocline depth, Northern Hemisphere sinking, and low-latitude upwelling to neutrino emission (15). pycnocline diffusivity and Southern Ocean winds and eddies. The results show on October 14, 2016 If the GRB 990123 is located at z Ͼ 1.6 our that Southern Ocean processes help maintain the global ocean structure and upper limit on z translates into an upper limit on that pycnocline diffusion controls low-latitude upwelling. ϫ 55 Ͼ the energy release of 1.3 10 erg for H0 50 –1 –1 ⍀ ⍀ ϭ km s Mpc and ( 0 ⌳) (0.2, 0.8). More- The main oceanic pycnocline delineates the sphere (NH) leads to the conversion of light over, if the z ϭ 1.6 absorption system is associ- boundary between light, low-latitude sur- water to dense water, which flows southward at ated with the main mass component along the face waters and dense, abyssal waters a rate Tn. Some portion of this flux upwells line of sight to GRB 990123, the upper limit on whose properties are set in the high lati- within the Southern Ocean, where precipitation z leads to a required lensing surface mass density tudes (Fig. 1A). The physical properties at causes it to become lighter. This light water is of a factor of about three to four times that in work in the pycnocline and the flows driven then exported to the north at a rate Ts. That normal galaxy lenses. This effectively rules out by the pressure gradients associated with portion of the NH sinking flux that is not bal- the possibility that GRB 990123 was lensed the pycnocline affect the transport of heat, anced by upwelling within the Southern Ocean (multiply imaged) (16) by this mass. salt, and nutrients through the ocean. Here upwells through the low-latitude pycnocline at a http://science.sciencemag.org/

Any of the above numbers indicates a huge I examine the relative importance of sever- rate Tu. I have ignored deep flows associated isotropic energy release which is difficult to al key processes in setting the structure of with the Antarctic Bottom Water (AABW), as- reconcile with current physical theories. In the the pycnocline. These are (i) vertical diffu- suming that they have little direct effect on the absence of lensing one resolution of this energy sion within the pycnocline, (ii) upwelling pycnocline as they are returned at mid-depth (3). problem is that the gamma-ray emission from through the pycnocline in low latitudes, Instead I focus on the effect of Northern and GRB 990123 was not isotropic. This interpre- (iii) the conversion of light to dense water Southern Hemisphere mode waters on the lower tation is consistent with polarimetric observa- associated with the formation of North At- pycnocline. Downloaded from tions (17) and is supported by the breaks ob- lantic Deep Water, (iv) Southern Ocean These fluxes can be connected to the depth served in the light curve (5, 8, 12) which sug- winds, and (v) Southern Ocean eddies. Pre- of the pycnocline, reducing the equations gov- gest that the optical afterglow may have been vious scaling theories of the pycnocline (1) erning the large-scale oceanic circulation to a beamed. have only included the first three processes. single cubic equation in the pycnocline depth D.

The western Atlantic Ocean contains a bowl The first step is to derive an expression for Tn, of waters lighter than 1027.5 kg mϪ3 ϳ1000 m the NH sinking flux. It is common to assume References and Notes deep, with some upward deflection at the equa- that this flow is proportional to the density dif- 1. G. J. Fishman and C. A. Meegan, Annu. Rev. Astron. Astrophys. 33, 415 (1995). tor (2). A tongue of fresh Antarctic Intermediate ference between the light and dense water ⌬␳ 2. M. R. Metzger et al., Nature 387, 879 (1997); S. R. Water (AAIW) penetrates northward from the (4). Because northward flow of AAIW and the Kulkarni et al., ibid. 393, 35 (1998); S. G. Djorgovski Southern Ocean and a tongue of salty North southward flow of NADW are essentially pres- et al., Astrophys, J. 507, L25 (1998). 3. J. Heise, in preparation. Atlantic Deep Water (NADW) moves south- sure-driven, there is a level of no motion be- 4. S. C. Odewahn, J. S. Bloom, S. R. Kulkarni, GCN Circular ward. In the conceptual framework I propose tween the two flows at which the velocities and 201 (1999); IAU Circular 7094 (1999). (Fig. 1C), surface cooling in the Northern Hemi- hence the pressure gradients are negligible. The 5. S. R. Kulkarni et al., Nature, in press, preprint mass of water above the level of no motion is also available at http://www.lanl.gov/abs/astro- ph/9902272. thus the same at all latitudes. Because the warm 6. C. W. Akerlof and T. A. McKay, GCN Circular 205 National Oceanic and Atmospheric Administration waters in low latitudes are less dense, they take (1999); IAU Circular 7100 (1999); Nature, in press. (NOAA) Geophysical Fluid Dynamics Laboratory and up more volume and the surface height is higher 7. A more comprehensive analysis of the absorption Atmospheric and Oceanic Sciences Program, Prince- system will be presented in a paper in preparation. ton University, Post Office Box CN710, Princeton, NJ at the equator than in high latitudes. This surface 8. A. J. Castro-Tirado et al., Science 283, 2069 (1999). 08544, USA. E-mail: [email protected] height difference will cause a pressure differ-

www.sciencemag.org SCIENCE VOL 283 26 MARCH 1999 2077 R EPORTS ence ⌬p within the water column Fig. 1. (A) Average po- tential density refer- ⌬p ϳ ⌬␳gD/␳ ϭ gЈD (1) enced to 1000 m in the ␳ Atlantic Ocean. (B) Av- Ј erage salinity in the where D is the depth of the light water and g western Atlantic ocean. is the reduced gravity. According to classical (C) Schematic of the boundary layer theory (5) this pressure dif- flows which the simple ference will produce a frictional flow near the theoretical model pre- eastern or western boundary (4, 6) sented here assumes are responsible for the p A V density and salinityץ 2v 1ץ ϭ 3 h .structure 2 ץ ␳ 2 ץ Ah x y Lm CgЈD ϭ 1/3␤2/3 ϭ Ah V n (2) Ly where V is the north-south velocity within the ϭ ␤ 1/3 boundary layer, Lm (Ah/ ) is the width n of the frictional boundary layer Ly is the north-south distance over which the gradient in layer depth occurs, ␤ is the north-south

gradient of the Coriolis parameter, Ah is the eddy viscosity, and C is a constant that incor- porates effects of geometry and boundary layer structure. The volume flux driven by such a circulation is then CgЈD2

ϭ ϭ ϫ ϫ on October 14, 2016 Tn n V D Lm (3) ␤L Ϫ y must be balanced by a downward diffusive between 100 and 3000 m2 s 1 (10). If it is The final expression is independent of the flux of heat by means of turbulent mixing. large, a considerable amount of light water can eddy viscosity. These fluxes can be related to the depth of the be exported to the Southern Ocean within the ϭ The Southern Hemisphere (SH) is governed thermocline (9), D Kv A/Tu where Kv is the near-surface layer. For other parameters held by different dynamics. Between 55°S and 63°S vertical diffusion coefficient and A is the fixed, larger values of AI would imply a thinner (Drake Passage latitudes) there is open water all surface area of the low-latitude box. The pycnocline and weaker NH sinking. If Kv is around the globe above depths of about upwelling is the difference between Tn and Ts nonvanishing (but small), the low-latitude up- 2000 m. Here, frictional boundary currents are welling will be correlated with A . CgЈ I absent in the surface ocean. Instead, the princi- T D ϭ (T Ϫ T )D 3 K A ϭ D3 For the data used to construct Fig. 1 we u n s v Ln Јϭ Ϫ2 n ϭ s ϭ pal flows are a northward mass flux (the Ekman y can estimate g 0.01 m s , Ly Ly transport) driven by the winds (7) and a return ␶ 1500 km, and a pycnocline depth of 570 m AI Lx Lx flow of light water associated with mesocale ϩ D2 Ϫ D (5) (11). Given that ␤ϭ2 ϫ 10Ϫ11 mϪ1 sϪ1, L http://science.sciencemag.org/ Ls ␳f x eddies. The net transport to the north is com- y ϭ 25,000 km, and A ϭ 2.44 ϫ 1014 m2,in pensated by a deep pressure-driven flow of This equation represents the following two order to generate the observed overturning of dense water along the flanks of submarine ridg- important balances: around 17 Sv (12), C ϭ 0.16 (within about ϭ 2 es (3). Suppose the eddy component can be 1) If Ts 0, the quadratic and linear terms 20%). A reasonable value of AI is 1000 m represented by the parameterization of Gent and are zero and the effect of Southern Ocean pro- sϪ1 (10). The dependence of the pycnocline

McWilliams (8), so that the eddy-induced trans- cesses is neglected. Then the low-latitude up- depth, NH sinking, and overturning ratio Ts/

Downloaded from ץ ץ ϭ port velocity goes as veddy AI S/ z, where welling (constant term) balances the NH sink- Tn on SH wind stress and Kv can then be ϳ s S D/Ly is the slope of the upper layer in the ing (cubic term). In this regime, the pyc- calculated from Eq. 5 (Fig. 2). Ј 1/3 north-south direction and AI is a diffusion co- nocline depth goes as (Kv/g ) and the NH The observed pycnocline depth can be pro- 2/3 Ј1/3 efficient. Such a flow will act to reduce the sinking goes as Kv g . This is the scaling duced with low values of Southern Ocean wind north-south slope of the upper layer. The me- previously found (1) that has a strong depen- stress and high values of vertical diffusion (0.6 ridional mass transport then is given by dence on vertical diffusivity. In this regime, the cm2 sϪ1). This result agrees with models of the magnitude of the NH sinking depends solely on ocean circulation in simple closed basins. How- ␶ T ϭ ͩ Ϫ v ϫ Dͪ ϫ L processes within the NH and pycnocline. ever, such high values of vertical diffusion do s ␳f eddy x 2) When the vertical diffusivity Kv and not agree with observations (13); values of 0.1 horizontal diffusivity A are vanishingly to 0.15 cm2 sϪ1 seem to be more realistic. Such ␶ I AID ϭ ͩ Ϫ ͪ ϫ small, the constant and quadratic terms in Eq. high values of Kv are also associated with large ␳ s Lx (4) f Ly 5 vanish. In this case, all the water that sinks amounts of equatorial upwelling, which Togg- where ␶ is the wind stress in the Southern in the north is supplied from the Southern weiler and Samuels (14) concluded was incon-

Ocean, f is the Coriolis parameter, and Lx is Ocean so that there is a tight linkage between sistent with the observed radiocarbon field. The the circumference of the earth in Drake Pas- NH sinking (cubic term) and SH Ekman mismatch between the high values of Kv seem- sage latitudes. transport (linear term). ingly required by the numerical models and low

The difference between Tn and Ts must Southern Ocean eddies can substantially al- values observed in the oceanic thermocline is upwell through the low-latitude pycnocline. ter either scenario. The horizontal eddy ex- often colloquially referred to as the “missing

In order to maintain the pycnocline structure, change coefficient AI has not been directly mea- mixing problem” (15). the upward advective flux of dense water sured, although it has been estimated as being The deeper thermocline can be produced

2078 26 MARCH 1999 VOL 283 SCIENCE www.sciencemag.org R EPORTS

4. H. M. Stommel [Tellus 13, 224 (1961)] was the first to use this approximation. See D. G. Wright and T. Stocker, J. Phys. Oceanogr. 21, 1713 (1991); R. X. Huang, J. R. Luyten, H. M. Stommel, ibid. 22, 231 (1992); and S. M. Griffies and E. Tziperman, J. Climate 8, 2440 (1995) for more recent examples. 5. W. Munk, J. Meteorol. 7, 79 (1950). 6. D. G. Wright, T. F. Stocker, and D. Mercer [ J. Phys. Oceanogr. 28, 791 (1998)] provide a comprehensive discussion of this issue in zonally averaged climate models. T. M. C. Hughes and A. Weaver [ibid. 24, 619 (1994)] provide evidence for a relation between me- ridional pressure gradient and overturning strength in a GCM. An alternative explanation to the frictional explanation is to suppose that some portion of the eastward geostrophic transport associated with the pressure gradient is converted to overturning, as sup- Fig. 2. Solutions to Eq. 5 as a function of Southern Ocean wind stress and vertical diffusivity within posed by Bryan [in (1)]. the pycnocline. Results from a general circulation model are superimposed as x symbols. (A) 7. The flow will be off to the left of the wind stress, because the Coriolis force acting on this velocity will Pycnocline depth (in meters). (B) NH sinking Tn (in Sverdrups). (C) Overturning ratio Ts/Tn. This quantity represents the fraction of NH sinking supplied from the south. Negative values mean that balance the surface stress; see J. F. Price, R. A. Weller, there is net sinking in both NH and SH which is supplied from low-latitude upwelling. R. R. Schudlich, Science 238, 1534 (1987) for obser- vations of such flow. 8. P. R. Gent and J. C. McWilliams, J. Phys. Oceanogr. 20, 150 (1990); P. Gent, J. Willebrand, T. J. McDougall, J. C. McWilliams, ibid. 26, 463 (1995); and G. Danaba- soglu, J. C. McWilliams, P. R. Gent, Science 264, 1123 (1994) document the effect of this parameterization on the global temperature and salinity structure. 9. W. Munk, Deep-Sea Res. 13, 707 (1966). 10. D. Olbers and J. Wenzel [in Ocean Circulation Models: Combining Data and Dynamics, D. Anderson and J. Willebrand, Eds. (Kluwer, Dordrecht, Netherlands, 1989), pp. 99–140] estimate values for AI between 2 Ϫ1

100 and 1000 m s . These values are substantially on October 14, 2016 lower than the 2000 to 3000 m2 sϪ1 estimated by G. Holloway [Nature 323, 243 (1986)] from observed sea surface height variability. J. Ledwell, A. Watson, and C. S. Law [ J. Geophys. Res. 103, 21499 (1998)] ϳ 2 Ϫ1 also found large values of AI ( 1000 m s )inthe Fig. 3. Dependence of the (A) pycnocline depth (in meters) and (B) NH sinking and (C) equatorial relatively quiet subtropical gyre. 11. The pycnocline depth z␴ is computed by defining upwelling (in Sverdrups) on AI and Kv. Contours are from solving Eq. 5 with the coefficients as given in the text given a Southern Ocean wind stress of 0.12 Pa; x symbols are from a general circulation model. 0 0 ␴ ϭ ͵ ⌬␴ ͵ ⌬␴ z 2 zdz/ 2 dz zϭϪH zϭϪH ⌬␴ ϭ␴ Ϫ␴ ␴ without resorting to high levels of diffusion if model even though the simple model was in- where H is the depth, 2 2(z) 2(max), and 2 Southern Ocean processes are taken into account tentionally not tuned to match the GCM. Both is the potential density referenced to 2000 m. Pyc- nocline depths are computed from 50°W to 70°W (Fig. 2). As the Southern Ocean wind stress predict that as the SH winds increase, so do the and 40°S to 40°N in the Atlantic Basin. http://science.sciencemag.org/ increases to more realistic values (0.1 to 0.2 Pa) depth of the pycnocline, magnitude of the NH 12. See, for example, W. J. Schmitz and M. S. McCartney, the pycnocline depth, and thus the NH sinking, sinking, and the portion of this sinking flux Rev. Geophys. 33, 151 (1993). switches over to being primarily dependent on supplied from the SH (14, 17). The theory does 13. J. Ledwell, A. Watson, C. S. Law, Nature 364, 701 (1993). the SH winds and is relatively insensitive to the reasonably well quantitatively. For example, it 14. J. R. Toggweiler and B. Samuels, in The Global Carbon vertical diffusion. The low-latitude upwelling is explains the rough magnitude of the range in Cycle, M. Heimann, Ed. (Springer-Verlag, Berlin, very strongly dependent on the vertical diffusion pycnocline depth versus A (ϳ250 m) as well as 1993), pp. 303–331. I 15. W. Munk and C. Wunsch [Deep-Sea Res. Part I Ocean- and weakly dependent on the Southern Ocean the rough magnitude of the change in low- ogr. Res. Pap. 45, 1977 (1998)] discuss this issue in

ϳ Downloaded from winds. For the parameter values that are thought latitude upwelling versus Kv ( 20 Sv). It also detail. to govern the ocean at present (wind stresses of predicts the rough magnitude of the increase in 16. The model used here is the GFDL Modular Ocean Model 0.1 to 0.2 Pa, vertical diffusivity of 0.1 to 0.15 thermocline depth with increases in Southern Version 3.0 documented in R. C. Pacanowski and S. M. Ϫ Griffies, GFDL Tech. Rep. 3 (Geophysical Fluid Dynamics cm2 s 1), the model predicts that most of the NH Ocean winds (ϳ500 m). Analysis showed that Laboratory, Princeton, NJ, 1998). The grid spacing and sinking is supplied from the Southern Ocean. the value of C that provided the best fit to the bottom topography for this model are identical to those used in Toggweiler and Samuels (17). The surface winds The solution is dependent on the parame- model (0.1) was smaller than that chosen from are taken from S. Hellermann and M. Rosenstein, J. terization of Southern Ocean eddies. As AI the data (0.16). Although the model predicts a Phys. Oceanogr. 13, 1093 (1982). Surface salinities are increases, the pycnocline depth decreases and systematically lower NH sinking (and hence restored toward the climatological observations of Levi- the low-latitude upwelling increases (Fig. 3). overturning ratio) than the simple theory, the tus (2), whereas surface temperatures are restored to- ward the data set that was used to drive the Atmo- When AI is very large, almost all of the NH rough magnitude of the changes in sinking and spheric Model Intercomparison Project (AMIP) runs as described in W. L. Gates, Bull. Am. Meteorol. Soc. 73, sinking goes into low-latitude upwelling, so overturning ratio with respect to wind stress, AI, that the overturning ratio is small. When A is and K are reasonable. 1962 (1992). I v 17. J. R. Toggweiler and B. Samuels, J. Phys. Oceanogr. small most of the NH sinking does not upwell 28, 1832 (1998). in low latitudes, and so the overturning ratio References and Notes 18. This work was supported by the Carbon Modeling is large. This highlights the importance of 1. F. Bryan, J. Phys. Oceanogr. 17, 970 (1987); R. A. Consortium, NOAA grant NA56GP0439, and by the DeSzoeke, ibid. 25, 918 (1995). Geophysical Fluid Dynamics Lab. I thank A. Gnan- understanding the dynamical effects of eddies 2. S. Levitus, A Climatological Atlas of the World Ocean adesikan and T. Hughes for extensive help with the in the Circumpolar Current. (NOAA Prof. Pap. 13, U.S. Government Printing Of- text and model runs, and H. Bjornsson, R. Toggweiler, Results from a general circulation model fice, Washington, DC, 1992). K. Bryan, and R. Hallberg for useful discussions. This 3. See A. Macdonald and C. Wunsch, Nature 382, 436 paper is dedicated to the memory of Tertia Hughes. (GCM) (16) (symbols in Figs. 2 and 3) show a (1996); C. Wunsch, D. Hu, B. Grant, J. Phys. Oceanogr. strong resemblance to the simple predictive 13, 725 (1983). 30 December 1998; accepted 26 February 1999

www.sciencemag.org SCIENCE VOL 283 26 MARCH 1999 2079 A Simple Predictive Model for the Structure of the Oceanic Pycnocline Anand Gnanadesikan (March 26, 1999) Science 283 (5410), 2077-2079. [doi: 10.1126/science.283.5410.2077]

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