Water, carbon, climate and life on Earth | 水、碳、气候与地球生命

📚 Water, carbon, climate and life on Earth | 水、碳、气候与地球生命

Water, carbon, climate and life on Earth form an interconnected system that can be studied through the lens of A-Level Mathematics. By using differential equations, statistical methods and optimisation techniques, we can model the flows, reservoirs and feedbacks that keep our planet habitable.

水、碳、气候与地球生命构成一个相互关联的系统，可以通过 A-Level 数学的视角来研究。利用微分方程、统计方法和最优化技术，我们可以模拟维持地球宜居性的流动、储库和反馈过程。

1. The Earth as a coupled system | 地球作为一个耦合系统

The Earth is not a collection of independent parts but a coupled system in which the hydrosphere, atmosphere, biosphere and geosphere exchange energy and matter. In mathematical terms, a coupled system is described by a set of simultaneous differential equations, where the rate of change of one variable depends on the current values of the others.

地球并不是独立部分的集合，而是一个耦合系统，其中水圈、大气圈、生物圈和岩石圈交换能量与物质。用数学术语来说，耦合系统由一组联立微分方程描述，其中一个变量的变化率取决于其他变量的当前值。

For example, if C(t) represents atmospheric carbon and T(t) represents global temperature, a simple coupled model might be written as dC/dt = F(T) − kC and dT/dt = G(C) − λT. Solving such systems allows us to predict how changes in one component, such as a rise in CO₂, will propagate through the whole Earth system.

例如，若 C(t) 表示大气碳含量，T(t) 表示全球温度，一个简单的耦合模型可以写作 dC/dt = F(T) − kC 和 dT/dt = G(C) − λT。求解这类方程组使我们能够预测某一组分的变化（如 CO₂ 上升）如何在整个地球系统中传播。

2. Modelling the water cycle with differential equations | 用微分方程模拟水循环

The water cycle can be modelled by treating reservoirs such as oceans, glaciers, lakes and soil moisture as interconnected boxes. A basic mass-balance equation for a reservoir of volume V is dV/dt = I(t) − O(t), where I(t) is the total inflow and O(t) is the total outflow at time t.

水循环可以通过将海洋、冰川、湖泊和土壤水分等储库视为相互连接的箱体来建模。储库体积 V 的基本质量平衡方程为 dV/dt = I(t) − O(t)，其中 I(t) 是时间 t 时的总流入量，O(t) 是总流出量。

Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com

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