📚 Quick Reference Handbook of Formulas and Theorems for Year 12 AQA Geography | Year 12 AQA 地理：公式定理速查手册
This handbook compiles the key equations, indices, and quantitative relationships that Year 12 AQA Geography students need to apply across both physical and human topics. Mastering these formulas supports precise analysis of hydrological budgets, carbon cycles, coastal processes, population change, and urban inequality.
本手册汇编了 Year 12 AQA 地理课程中学生需要掌握的核心公式、指数和定量关系，涵盖自然地理和人文地理主题。熟练掌握这些公式有助于精准分析水文收支、碳循环、海岸过程、人口变动与城市不平等。
1. The Water Balance Equation | 水分平衡方程
The water balance equation is the foundational budget for any drainage basin. It links inputs, outputs, and changes in storage over a defined time period.
水分平衡方程是任何流域的基本收支关系。它将给定时段内的输入、输出及储存量变化联系在一起。
P = Q + E + ΔS
where P is precipitation (mm), Q is total runoff (mm), E is evapotranspiration (mm), and ΔS is the change in water stored in the soil, groundwater, lakes, and channel network. When the basin gains water, ΔS is positive.
其中 P 为降水量（毫米），Q 为总径流量（毫米），E 为蒸散发量（毫米），ΔS 为土壤、地下水、湖泊及河网中储存水量的变化。当流域获得净水量时，ΔS 为正。
- P: all forms of atmospheric water input, mainly rainfall and snowmelt.
- Q: surface runoff + interflow + baseflow.
- E: total evaporation from water surfaces and transpiration from plants.
- P：所有形式的大气降水输入，主要为降雨和融雪。
- Q：地表径流 + 壤中流 + 基流。
- E：水面蒸发与植物蒸腾之和。
If precipitation exceeds runoff plus evapotranspiration, the catchment stores the surplus (ΔS > 0); the opposite indicates a deficit that depletes existing stores.
若降水量大于径流和蒸散发之和，流域储存盈余水分（ΔS > 0）；反之则出现亏缺，消耗原有储存。
2. Runoff Coefficient and Runoff Depth | 径流系数与径流深度
The runoff coefficient reveals what fraction of precipitation becomes immediate surface runoff. It helps compare the flashiness of different catchments.
径流系数揭示了多少比例的降水转化为即时地表径流，有助于比较不同流域的暴涨特性。
C = Qs / P
where C is the runoff coefficient (dimensionless), Qs is surface runoff depth (mm), and P is total precipitation depth (mm) for the same event or period.
其中 C 为径流系数（无量纲），Qs 为地表径流深度（毫米），P 为同一事件或时段的降水量（毫米）。
Urban catchments with extensive impermeable surfaces can have C values approaching 0.9, whereas forested basins with deep soils often record C < 0.2. Runoff depth alone, derived from hydrograph separation, is also used to compare absolute runoff volumes.
具有大面积不透水地面的城市流域，C 值可接近 0.9，而具有深厚土壤的森林流域常记录到 C < 0.2。仅从流量过程线分割得出的径流深度也可用于比较绝对径流量。
3. Rational Method for Peak Discharge | 峰值流量推理公式
The Rational Method provides a simplified estimate of the peak discharge generated by a uniform rainstorm over a small catchment. It appears frequently in flood-risk assessments.
推理公式提供了一场均匀降雨在小流域产生的峰值流量的简化估算，常见于洪水风险评估中。
Q = C × I × A
where Q is peak discharge (m³ s⁻¹), C is the dimensionless runoff coefficient, I is rainfall intensity (mm h⁻¹), and A is catchment area (km² or ha). Appropriate unit conversion factors must be applied to keep the result in m³ s⁻¹.
其中 Q 为峰值流量（立方米/秒），C 为无量纲径流系数，I 为降雨强度（毫米/小时），A 为集水面积（平方公里或公顷）。须使用适当的单位换算系数使结果保持为 m³ s⁻¹。
The method assumes that the rainfall duration equals the catchment’s time of concentration, meaning the entire area contributes runoff simultaneously at the outlet.
该方法假设降雨历时等于流域的汇流时间，即整个集水区同时向出口断面贡献径流。
4. River Discharge Equation | 河道流量方程
At-a-section river discharge is computed by multiplying cross-sectional area by mean velocity. This principle underpins all current-meter gauging.
断面流量通过横截面积乘以平均流速计算。所有流速仪测流均基于此原理。
Q = A × v̅
where Q is discharge (m³ s⁻¹), A is wetted cross-sectional area (m²), and v̅ is the mean stream velocity (m s⁻¹). In practice, velocity is measured at multiple verticals and depth intervals to obtain a representative mean.
其中 Q 为流量（m³ s⁻¹），A 为过水横截面积（m²），v̅ 为平均流速（m s⁻¹）。实际操作中通常在多条垂线、多个深度上测量流速以获取代表性平均值。
As discharge increases during a storm, both area and velocity rise, causing the stage–discharge relationship (rating curve) to steepen. Reliable discharge estimates are essential for constructing flood hydrographs.
暴雨期间流量增大时，面积和流速均上升，致使水位–流量关系（率定曲线）变陡。可靠的流量估算是绘制洪水过程线的基础。
5. Infiltration Capacity | 下渗能力
Infiltration capacity is the maximum rate at which water can enter the soil surface. It declines during a storm as the soil wets up and surface pores seal.
下渗能力是水分进入土壤表层的最大速率，随降雨持续，土壤湿润和表层孔隙堵塞而下降。
f(t) = fc + (f0 − fc) e−kt
where f(t) is infiltration capacity at time t (mm h⁻¹), f0 is the initial infiltration rate, fc is the steady-state minimum rate, and k is a decay constant determined by soil texture and structure. This Horton-type equation describes the exponential decline.
其中 f(t) 为 t 时刻的下渗能力（毫米/小时），f0 为初始下渗率，fc 为稳定最小速率，k 为由土壤质地和结构决定的衰减常数。该霍顿型方程描述了指数衰减过程。
When rainfall intensity exceeds infiltration capacity, overland flow (Hortonian overland flow) begins. Coarse sands maintain high fc, while clays often exhibit low terminal rates, increasing flood risk.
当降雨强度超过下渗能力时，产生超渗地表径流（霍顿坡面流）。粗砂土保持高 fc，而黏土通常终值速率低，增加洪水风险。
6. Net Primary Productivity | 净初级生产力
NPP is the rate at which plants accumulate biomass after subtracting respiratory losses. It is a cornerstone of the carbon cycle topic.
NPP 是植物在扣除呼吸消耗后积累生物量的速率，是碳循环主题的核心概念。
NPP = GPP − R
where GPP is gross primary productivity (kg C m⁻² yr⁻¹) and R is autotrophic respiration (kg C m⁻² yr⁻¹). NPP represents the energy and carbon available to the rest of the ecosystem.
其中 GPP 为总初级生产力，R 为自养呼吸所消耗的碳。NPP 表示可供生态系统中其他营养级利用的能量和碳。
Typical NPP values range from <0.1 kg C m⁻² yr⁻¹ in extreme deserts to >2.0 kg C m⁻² yr⁻¹ in tropical rainforests. Changes in NPP caused by deforestation or climate shifts have cascading effects on carbon storage.
典型的 NPP 值从极端沙漠的不足 0.1 kg C m⁻² yr⁻¹ 到热带雨林的超过 2.0 kg C m⁻² yr⁻¹。森林砍伐或气候变化引起的 NPP 变化会对碳储存产生连锁影响。
7. Carbon Stock Estimation | 碳储量估算
Estimating the carbon stored in vegetation, soils, and oceans underpins global carbon budget assessments. For forests, a simple proportional rule links biomass to carbon content.
估算植被、土壤和海洋中的碳储量是全球碳收支评估的基础。对于森林，一条简单的比例法则将生物量与碳含量联系起来。
Cstock = Biomass × CF
where Cstock is carbon stored (kg or t), Biomass is dry organic matter (kg or t), and CF is the carbon fraction — typically assumed to be 0.45–0.50 for wood. For soil organic carbon, bulk density, depth, and carbon concentration are combined multiplicatively.
其中 Cstock 为储存碳量，Biomass 为干有机质重量，CF 为碳含量分数——对于木材通常取 0.45–0.50。对于土壤有机碳，则将容重、深度和碳浓度相乘。
Applying these relationships allows students to compare carbon pools in temperate, boreal, and tropical biomes, and to quantify the impact of land-use change on CO₂ emissions.
运用这些关系可让学生比较温带、北方和热带生物群系的碳库大小，并量化土地利用变化对 CO₂ 排放的影响。
8. Wave Energy per Unit Area | 单位面积波浪能
Wave energy is a key driver of coastal erosion, sediment transport, and landform development. The energy contained in a deep-water wave depends on wave height.
波浪能是海岸侵蚀、泥沙搬运和地貌发育的关键驱动力。深水波所含的能量取决于波高。
E = (ρ g H²) / 8
where E is energy per unit sea-surface area (J m⁻²), ρ is seawater density (~1025 kg m⁻³), g is gravity (9.81 m s⁻²), and H is significant wave height (m). Broken waves dissipate this energy on the shoreface.
其中 E 为单位海面面积的波浪能（焦耳/平方米），ρ 为海水密度（约 1025 kg m⁻³），g 为重力加速度，H 为有效波高（米）。破碎波将这部分能量耗散于滨面。
y × wave group speed). Higher-energy coastlines typically experience faster cliff retreat.
海岸管理决策（如海堤和防波堤设计）依赖波浪功率（能量 × 波群速度）的估算。高能海岸通常经历更快的崖壁后退。
9. Sediment Grain Size: Phi Scale | 沉积物粒径：Φ尺度
The Udden–Wentworth phi scale converts raw grain diameters into a symmetrical scale suitable for statistical analysis and cumulative frequency plots of coastal and fluvial sediments.
乌登–温特沃斯Φ尺度将实际颗粒直径转换为适合统计分析以及海岸/河流沉积物累积频率曲线绘图的对称尺度。
Φ = −log₂(D)
nsionless). Coarse sand of 0.5 mm corresponds to Φ = 1; fine sand of 0.125 mm gives Φ = 3.
其中 D 为颗粒直径（毫米），Φ 为 phi 值（无量纲）。0.5 毫米的粗砂对应 Φ = 1；0.125 毫米的细砂对应 Φ = 3。
Graphical measures such as median (MdΦ), mean, sorting, skewness, and kurtosis are derived from cumulative curves. Well-sorted beach sands exhibit low sorting values (narrow phi range), while glacial tills are poorly sorted.
诸如中值 (MdΦ)、平均、分选、偏度和峰度等图形统计量从累积曲线得出。分选良好的海滩砂呈现低分选值（窄 Φ 范围），而冰碛物则分选很差。
10. Population Growth and Doubling Time | 人口增长与翻倍时间
Simple demographic metrics enable students to compare natural change and migration across countries and over time. The annual population growth rate integrates natural increase and net migration.
简单的人口统计学指标使学生能够比较不同国家、不同时期的自然变动和迁移。年人口增长率综合了自然增长和净迁移。
rpop = ((CBR − CDR) / 1000) × 100 + Net migration rate (%)
where CBR and CDR are crude birth and death rates per 1000 people. When the migration component is zero or negligible, the natural growth rate alone can be used.
其中 CBR 和 CDR 分别为千分出生率和死亡率。当迁移成分为零或可忽略时，可仅用自然增长率。
Doubling Time (years) = 70 / (growth rate %)
This 'rule of 70' approximates how long it takes for a population to double at a constant annual growth rate. A 2% growth rate implies a doubling time of about 35 years, highlighting enormous future pressure on resources.
这个“70法则”近似给出了以恒定年增长率人口翻倍所需的时间。2% 的增长率意味着翻倍时间约为 35 年，凸显未来巨大的资源压力。
11. Location Quotient | 区位商
Location Quotient (LQ) measures the concentration of a particular economic activity in a region relative to a larger reference area, revealing specialisation and economic bases.
区位商 (LQ) 衡量某一地区特定经济活动相对于更大参照区域的集中程度，揭示专业化与经济基础。
LQ = (Eir / Er) / (Ein / En)
where Eir is employment in industry i in the region, Er is total regional employment, Ein is national employment in industry i, and En is total national employment.
其中 Eir 为某地区 i 行业的就业人数，Er 为该地区总就业，Ein 为全国 i 行业就业，En 为全国总就业。
An LQ > 1 indicates a higher-than-average concentration, suggesting that the region exports that good or service (a basic sector). LQ is used in changing places and contemporary urban environments to analyse functional specialisation and deindustrialisation.
区位商 > 1 表示集中度高于平均水平，意味着该地区输出该产品或服务（基础部门）。在“变化的地域”和“当代城市环境”中，区位商用于分析功能专业化和去工业化过程。
12. Gini Coefficient | 基尼系数
The Gini coefficient quantifies inequality in a distribution, most commonly applied to income or wealth within a population. It ranges from 0 (perfect equality) to 1 (total inequality).
基尼系数量化了分布中的不平等程度，最常用于人口内部收入或财富的不平等。取值 0（完全平等）到 1（完全不平等）。
G = A / (A + B)
where A is the area between the Lorenz curve and the line of perfect equality, and B is the area under the Lorenz curve. In AQA Geography, students interpret plotted Lorenz curves to compare spatial and social inequality in urban areas.
其中 A 为洛伦兹曲线与绝对平等线之间的面积，B 为洛伦兹曲线下方的面积。在 AQA 地理中，学生通过解读绘制的洛伦兹曲线来比较城市内部的空间与社会不平等。
Higher Gini values are associated with greater socio-economic polarisation, which has implications for service provision, housing, and quality of life. The coefficient is a powerful tool in the Changing Places unit.
较高的基尼值与更强的社会经济极化相关，并对服务供给、住房和生活质量产生影响。该系数是“变化的地域”单元的有力工具。
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