Donohue J G, Florio B J, Fowler A C
MACSI, University of Limerick, Limerick, Ireland.
Department of Education, East Perth, WA Australia.
GEM. 2023;14(1):12. doi: 10.1007/s13137-023-00221-0. Epub 2023 May 30.
We analyse a model of the phosphorus cycle in the ocean given by Slomp and Van Cappellen (Biogeosciences 4:155-171, 2007. 10.5194/bg-4-155-2007). This model contains four distinct oceanic boxes and includes relevant parts of the water, carbon and oxygen cycles. We show that the model can essentially be solved analytically, and its behaviour completely understood without recourse to numerical methods. In particular, we show that, in the model, the carbon and phosphorus concentrations in the different ocean reservoirs are all slaved to the concentration of soluble reactive phosphorus in the deep ocean, which relaxes to an equilibrium on a time scale of 180,000 y, and we show that the deep ocean is either oxic or anoxic, depending on a critical parameter which we can determine explicitly. Finally, we examine how the value of this critical parameter depends on the physical parameters contained in the model. The presented methodology is based on tools from applied mathematics and can be used to reduce the complexity of other large, biogeochemical models.
The online version contains supplementary material available at 10.1007/s13137-023-00221-0.
我们分析了由斯隆普和范卡佩伦给出的海洋磷循环模型（《生物地球科学》4：155 - 171，2007。10.5194/bg - 4 - 155 - 2007）。该模型包含四个不同的海洋区域，并纳入了水、碳和氧循环的相关部分。我们表明该模型基本上可以通过解析方法求解，并且无需借助数值方法就能完全理解其行为。特别是，我们表明在该模型中，不同海洋储库中的碳和磷浓度都取决于深海中可溶性活性磷的浓度，其在18万年的时间尺度上弛豫到平衡状态，并且我们表明深海是有氧的还是缺氧的，取决于一个我们可以明确确定的关键参数。最后，我们研究这个关键参数的值如何取决于模型中包含的物理参数。所提出的方法基于应用数学工具，可用于降低其他大型生物地球化学模型的复杂性。
在线版本包含可在10.1007/s13137 - 023 - 00221 - 0获取的补充材料。
