Box model for the global surface warming response to carbon emissions: solving for heat and carbon exchange between the atmosphere and the ocean over 1000 years since the pre-industrial era

(1) University of Liverpool Department of Earth, Ocean and Ecological Sciences; (2) University of Southampton School of Ocean and Earth Science

This box model for global surface warming response comprises three homogeneous layers: a well-mixed atmosphere, an ocean mixed layer, and an ocean interior, all assumed to have the same horizontal area. The model solves for the heat and carbon exchange between these layers, including physical and chemical transfers, but ignoring biological transfers, and sediment and weathering interactions. The model is forced from an equilibrium by carbon emitted into the atmosphere with a constant rate of 20 PgC/y for 100 years and integrated for 1000 years (from 1861 to 2861). The increase in the atmospheric CO2 is assumed to drive a radiative forcing, which then is assumed to drive a global-mean radiative response together with a planetary heat uptake. Ocean ventilation is represented by the ocean interior taking up the heat and carbon properties of the mixed layer on an e-folding time scale of 200 years. The model initialisation parameters include a climate feedback parameter, thickness of mixed layer, thickness of ocean interior, time scale for ventilation of ocean interior, and pre-industrial values for atmospheric CO2. The box model MATLAB script is provided alongside two MATLAB functions, one for the partitioning of dissolved inorganic carbon, and one for setting the initial values for dissolved inorganic carbon when starting from equilibrium. The funding for this model was provided by the Natural Environment Research Council (NERC) grant NE/N009789/1. The model was built by Dr Anna Katavouta, University of Liverpool, other contributors were Professor Ric Williams (Lead Principal Investigator), University of Liverpool, Dr Philip Goodwin (Co-Investigator), University of Southampton, and Dr Vassil Roussenov, University of Liverpool.