The purpose of this paper is to derive an analytical impulse response function (IRF), for the carbon cycle between atmosphere and sea. The analysis is starting from the Box-Diffusion model (BDM) given by Oeschger et al. The BDM is also the underlying model for the “sum of exponentials –IRF” presently used in many papers to describe the atmosphere/sea carbon cycle.
10 to 100 years is a relevant time scale when discussing the effect of anthropogenic emissions onthe atmospheric carbon dioxide. We show that on this time scale there is an analytical IRF. Our view is that this analytical IRF is a better representation of the physics in the system than the presently used “sum of exponentials” IRF.
Another important conclusion is that there is only one characteristic time constant. All physics in the BDM can thus be represented with one characteristic time and an analytical IRF. With the values used in the BDM the characteristic time will be in the interval 80 – 145 years. This value is strongly dependent on assumed values of Revelle factor and eddy diffusion constant.