A box diffusion model to study the carbon dioxide exchange in nature

Abstract

Phenomena related to the natural carbon cycle as the 14C distribution between atmosphere and ocean and the atmospheric response to the input of fossil fuel CO2 and of 14C produced in nuclear weapon tests have been quantitatively discussed by other authors using box models. However the exchange coefficients derived from the natural 14C distribution do not agree with those valid to describe the short‐term phenomena. A model consisting of a well mixed atmospheric box coupled to a long‐term biosphere, of an ocean surface box and a diffusive deep ocean is discussed. The dynamic parameters were derived from the preindustrial 14C distribution in atmosphere and ocean. A consistent description of phenomena with completely different characteristic times is possible, because in the box diffusion model the flux from mixed layer to deep sea increases for decreasing time constants of the perturbations. This is in contrary to box models where it is essentially independent of the time constants if they are smaller than a few hundred years. Due to this fact our model is valid for predictions of the atmospheric CO2 response to the various possible future CO2 input time functions.

The ocean carbon sink – impacts, vulnerabilities and challenges

“…There is a considerable uncertainty about the gas transfer velocity of CO 2 and other gases across the air-water interface (Carpenter et al, 2012;Garbe et al, 2014). While the global ocean carbon sink estimates may not too strongly depend on this choice (otherwise projections with simple two box models for the global ocean would not have worked at all; Oeschger et al, 1975), the projected local CO 2 concentration in ocean surface waters is highly influenced by the chosen gas transfer velocity values, also for appropriate regional validation of ocean models. The co-limitation of biological production by various factors is an established concept; however, crucial details are not uniformly established, such as the potential variation of carbon to nitrogen ratios in biogenic matter under different environmental conditions (Riebesell et al, 2007;Jiang et al, 2013).…”

The Bern Simple Climate Model (BernSCM) v1.0: an extensible and fully documented open-source re-implementation of the Bern reduced-form model for global carbon cycle–climate simulations

“…Another application of simple models (e.g., Boucher and Reddy, 2008;Bruckner et al, 2003;Enting et al, 1994;Good et al, 2011;Hooss et al, 2001;Huntingford et al, 2010;Oeschger et al, 1975;Raupach, 2013;Siegenthaler and Oeschger, 1984;Smith et al, 2017;Tanaka et al, 2007;Urban and Keller, 2010;Wigley and Raper, 1992) is to compare, analyze, or emulate more complex models (Geoffroy et al, 2012a, b;Meinshausen et al, 2011;Raper et al, 2001; Thompson and Randerson, 1999). Simple models also play a significant role in previous assessments of the Intergovernmental Panel on Climate Change (e.g., Harvey et al, 1997).…”

“…SCMs have been used since the pioneering days of computational climate science to analyze the planetary heat balance (Budyko, 1969;Sellers, 1969) and to clarify the role of the ocean and land compartments in the climate response to anthropogenic forcing through carbon and heat uptake (e.g., Oeschger et al, 1975;Siegenthaler and Oeschger, 1984;Hansen et al, 1984). Due to their modest computational demands, SCMs enabled pioneering research using the limited computational resources of the time and continue to play a useful role in the hierarchy of climate models today.…”

“…The uptake of excess, anthropogenic carbon from the atmosphere is described as a purely physicochemical process . As in pioneering modeling approaches with box-type (Oeschger et al, 1975;Revelle and Suess, 1957) and general ocean circulation models (Maier-Reimer and Hasselmann, 1987;Sarmiento et al, 1992), modification of the natural carbon cycle through potential changes in circulation and the marine biological cycle (Heinze et al, 2015) are not explicitly considered. While such modifications and their potential socioeconomic consequences are vividly discussed in the literature , associated climate-CO 2 feedbacks are likely of secondary importance.…”

Monitoring and interpreting the ocean uptake of atmospheric CO 2

“…Later modelling efforts [3,4] were 'box model' descriptions calibrated using the observed distribution of 14 C in the oceans, as measured by the Geochemical Ocean Sections (GEOSECS) campaigns of the early 1970s. At that period, it was not known whether the terrestrial biosphere was taking up CO 2 or was at a steady state: it seemed possible that the anthropogenic carbon budget was a simple balance between fossil-fuel emission, ocean uptake and accumulation in the atmosphere.…”