1 Supplementary material Organic carbon burial efficiencies in sediments: The power law of mineralization revisited Sergei Katsev 1* and Sean A. Crowe 2 1 Large Lakes Observatory and Department of Physics, University of Minnesota Duluth, 2205 East 5 th St., Duluth, Minnesota 55812, USA 2 Departments of Microbiology and Immunology, and Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, BC V6T1Z4, Canada *Corresponding author: skatsev@d.umn.edu 1. Calculation of remaining carbon fraction by integration of mineralization power law The power law of organic matter reactivity k as a function of time t k(t) = bt -a , (1) where b and a are constants defines the rate of organic carbon mineralization R: R  dC dt  k (t )C . (2) Equation 2 can be integrated to obtain the fraction of organic material that remains unmineralized after a given amount of time. For aβ1, separation of variables and integration of dC dt bt  a C (3) yields C  C 0 exp bt 1a 1  a ｧ ｩ ｨ ｷ ｹ ｸ (4) where C 0 is the initial concentration at time t=0. For a special case of a=1, integration of Eq. (3) results in