Ocean Science www.ocean-sci.net 1812-0784 1812-0792 5 2 2009 10.5194/os-5-155-2009 http://www.ocean-sci.net/5/155/2009/ http://www.ocean-sci.net/5/155/2009/os-5-155-2009.html http://www.ocean-sci.net/5/155/2009/os-5-155-2009.pdf 155 172 2009-05-28 A new method for forming approximately neutral surfaces A. Klocker andreas.klocker@csiro.au T. J. McDougall D. R. Jackett CSIRO Marine and Atmospheric Research, Castray Esplanade, TAS 7000, Australia Antarctic Climate and Ecosystems Cooperative Research Center, University of Tasmania, Private Bag 80, <br> TAS 7001, Australia Institute of Antarctic and Southern Ocean Studies, University of Tasmania, Private Bag 77, TAS 7001, Australia Centre for Australian Climate and Weather Research, Castray Esplanade, TAS 7000, Australia We introduce a simple algorithm to improve existing density surfaces to ensure that the resulting surfaces are as close to neutral as possible. This means the slopes at any point on the surfaces are close to neutral tangent planes – the directions along which layered stirring and mixing occurs – minimizing the fictitious diapycnal diffusivity. Inverse techniques and layered models have been used for decades to understand ocean circulation. The most-used density surfaces are potential density or neutral density surfaces. Both these density surfaces and all others produce a fictitious diapycnal diffusivity to some degree due to the helical nature of neutral trajectories – with the magnitude of this artificial diffusivity in some cases being larger than the values measured in the ocean. Here we show how this error can be reduced by up to four orders of magnitude and therefore becomes insignificant compared to measured values, thus providing surfaces which would produce more accurate results when used for inverse techniques. de~Szoeke, R A., Springer, S R., and Oxilia, D M.: Orthobaric Density: A Thermodynamic Variable for Ocean Circulation Studies, J. Phys. Oceanogr., 30, 2830–2852, 2000. Eden, C. and Willebrand, J.: Neutral density revisited, Deep Sea Research II, 46, 33–54, 1999. Gouretski, V V. and Koltermann, K P.: WOCE global hydrographic climatology, Tech. rep., Bundesamtes für Seeschifffahrt und Hydrographie, 35, 1–52, 2004. Jackett, D R. and McDougall, T J.: A Neutral Density Variable for the World's Oceans, J. Phys. Oceanogr., 27, 237–263, 1997. Jackett, D R., McDougall, T J., and LeSommer, J.: A new and improved neutral density variable for the world's oceans, in preparation, 2009. Klocker, A. and McDougall, T J.: Quantifying the ill-defined nature of neutral surfaces, J. Phys. Oceanogr., submitted, 2009. Levitus, S.: Climatological Atlas of the World Ocean, NOAA Prof. Paper No 13, Govt. Printing office, Washington~DC, USA, 173~pp., 1982. Matlab: MATLAB – The Langugage of Technical Computing, the Math Works Inc., www.mathworks.com, 2007. McDougall, T J.: Neutral surfaces, J. Phys. Oceanogr., 17, 1950–1964, 1987. McDougall, T J.: Neutral-Surface Potential Vorticity, Prog. Oceanogr., 20, 185–221, 1988. McDougall, T J.: Potential Enthalpy: A Conservative Oceanic Variable for Evaluating Heat Content and Heat Fluxes, J. Phys. Oceanogr., 33, 945–963, 2003. McDougall, T J. and Jackett, D R.: On the helical nature of neutral trajectories in the ocean, Prog. Oceanogr., 20, 153–183, 1988. McDougall, T J. and Jackett, D R.: An Assessment of Orthobaric Density in the Global Ocean, J. Phys. Oceanogr., 35, 2054–2075, 2005a. McDougall, T J. and Jackett, D R.: The material derivative of neutral density, J. Mar. Res., 63, 159–185, 2005b. McDougall, T. J. and Jackett, D. R.: Neutral surfaces and the equation of state, Encyclopaedia of Ocean Sciences, 2nd edn., edited by: Steele, J. H., Turekian, K. H., and Thorpe, S. A., Elsevier, 4097-4103, 2009 Montgomery, R B.: A suggested method for representing gradient flow in isentropic surfaces, Bull. Amer. Meteor. Soc., 18, 210–212, 1937. Paige, C C. and Saunders, M A.: LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Softw., 8, 43–47, 1982. Polzin, K L., Toole, J M., Ledwell, R W., and Schmitt, R W.: Spatial Variability of Turbulent Mixing in the Abyssal Ocean, Science, 276, 93–96, 1997. Veronis, G.: The role of models in tracer studies, in: Numerical Models of Ocean Circulation, National Academy of Science, 133–146, 1975.