Auxiliary material for Paper 2011GL046769 How is the ocean filled? Geoffrey Gebbie Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts, USA Peter Huybers Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USA Gebbie, G., and P. Huybers (2011), How is the ocean filled?, Geophys. Res. Lett., 38, L06604, doi:10.1029/2011GL046769. Introduction The auxiliary material consists of one PDF file with text and figures. This material describes the mathematical underpinnings of the calculations made in the main text. There are a total of 3 figures in the PDF file. 1. 2011gl046769-txts01.pdf Text S1. Description of the mathematical underpinnings of the calculations made in the main text with three figures. Contents 1. The steady-state circulation 2. Estimating tracer distributions 3. Diagnosing water-mass pathways 4. Adjoint method for the surface origination map 5. The distribution of water masses and its sensitivity to spatial resolution 6. References 7. Figures