📚 A-Level AQA Geography: Formula and Theorem Quick Reference Handbook | A-Level AQA 地理：公式定理速查手册
This quick reference handbook brings together the essential formulas, laws, and theoretical relationships that underpin the AQA A-level Geography specification. From water balance and fluvial discharge to population dynamics and spatial interaction models, each entry is presented with a concise English explanation followed immediately by its Chinese equivalent. Statistical techniques required for fieldwork, such as Spearman’s rank correlation and chi-squared test, are also included with their calculation steps. Use this guide to consolidate your revision, tackle numerical questions confidently, and make explicit links between physical and human geography concepts.
这本速查手册汇集了支撑AQA A-Level地理课程的基本公式、定律和理论关系。从水量平衡、河流流量到人口动态和空间相互作用模型，每个条目都以简洁的英文解释和紧随其后的中文对应呈现。实地考察所需的统计技术，例如斯皮尔曼等级相关和卡方检验，也包含在内并附有计算步骤。使用本指南巩固复习，自信地应对数字类题目，并在自然地理与人文地理概念之间建立清晰的联系。
1. Water Balance Equation | 水量平衡方程
The water balance equation describes how precipitation (P) is partitioned into runoff (Q), evapotranspiration (E), and changes in storage (ΔS) within a drainage basin. It is a fundamental concept for understanding flood response, soil moisture budgets, and the impact of climate variability.
水量平衡方程描述了流域内降水量（P）如何被分配为径流（Q）、蒸发蒸腾（E）和储水量变化（ΔS）。它是理解洪水响应、土壤水分收支以及气候变率影响的基本概念。
P = Q + E ± ΔS
In a temperate mid-latitude catchment, accumulating winter precipitation may result in a positive ΔS as groundwater and soil moisture increase, whereas in late summer high evapotranspiration can produce a negative ΔS even with moderate rainfall events.
在温带中纬度集水区，冬季积累的降水可能导致ΔS为正值，即地下水和土壤水分增加；而在夏末，即使有中等降水事件，高蒸发蒸腾量也可能导致ΔS为负值。
2. Fluvial Discharge and Sediment Transport | 河流流量与沉积物搬运
River discharge (Q) is the volume of water passing a channel cross-section per unit time. It is determined by multiplying the cross-sectional area (A) by the mean flow velocity (V).
河流流量（Q）是单位时间内通过河道横截面的水量。它由横截面积（A）乘以平均流速（V）决定。
Q = A × V
Discharge is measured in cubic metres per second (m³ s⁻¹) and is the primary variable used for rating curves and flood frequency analysis. As discharge increases downstream, a river’s competence and capacity to transport sediment typically rise, but relationships are threshold-dependent.
流量以立方米每秒（m³ s⁻¹）为单位，是用于水位-流量关系曲线和洪水频率分析的主要变量。随着下游流量的增加，河流搬运沉积物的能力和容量通常都会上升，但这些关系取决于阈值。
The Hjulström curve illustrates the critical erosion velocity and deposition velocity for different particle sizes. For cohesive clays, erosion requires relatively high velocities, while fine sand is entrained at lower velocities. Once suspended, silt and clay settle only when flow is almost still.
尤尔斯特伦曲线说明了不同粒径颗粒的临界侵蚀流速和沉积流速。对于粘性粘土，侵蚀需要较高的流速，而细砂在较低流速下就能被搬运。一旦悬浮，粉砂和粘土只有在水流几乎静止时才会沉积。
Grain size in fluvial and coastal sediments is often expressed using the phi (φ) scale, a logarithmic transformation of particle diameter (D) in millimetres:
河流和海岸沉积物中的颗粒大小常使用φ标度表示，这是以毫米为单位的颗粒直径（D）的对数变换：
φ = −log₂ (D)
3. Carbon Cycle and Ecosystem Productivity | 碳循环与生态系统生产力
Net primary productivity (NPP) quantifies the rate at which plants store carbon after accounting for respiratory losses (R). Gross primary productivity (GPP) is the total carbon fixed by photosynthesis.
净初级生产力（NPP）量化了植物在扣除呼吸消耗（R）后储存碳的速率。总初级生产力（GPP）是光合作用固定的总碳量。
NPP = GPP − R
High NPP values are typical of tropical rainforests and other ecosystems with ample solar radiation, moisture, and nutrient availability, whereas deserts and polar regions exhibit low NPP. In carbon cycle studies, net ecosystem exchange (NEE) adjusts NPP for heterotrophic respiration, indicating whether an ecosystem is a net carbon sink or source.
高的NPP值通常出现在热带雨林及其他具有充足太阳辐射、水分和养分可利用性的生态系统中，而沙漠和极地地区的NPP较低。在碳循环研究中，净生态系统交换量（NEE）在NPP基础上调整了异养呼吸，指示生态系统是净碳汇还是碳源。
4. Coastal Wave Energy | 海岸波浪能量
The energy carried by a wave is proportional to the square of its height (H). Destructive storm waves with large wave heights can mobilise large quantities of beach material, while constructive waves with lower heights and longer wavelengths tend to build up the beach face.
波浪携带的能量与其波高（H）的平方成正比。具有较大波高的破坏性风暴波浪能够搬运大量滩涂物质，而波高较小、波长较长的建设性波浪则倾向于堆积滩面。
E ∝ H²
Though a simplified proportionality, it captures why a doubling of wave height roughly quadruples the energy available for erosion, sediment entrainment, and cliff undercutting along high-energy coastlines.
尽管这是一个简化的比例关系，但它解释了为什么波高加倍会导致可供侵蚀、沉积物夹带和悬崖掏蚀的能量大约增加为四倍，这在高能量海岸线表现得尤为明显。
5. Population Change Formulas | 人口变化公式
Population change over a given period is the result of natural increase and net migration.
特定时期内的人口变化是自然增长和净迁移共同作用的结果。
Population Change = (Births − Deaths) + (Immigration − Emigration)
The crude birth rate (CBR) and crude death rate (CDR) are expressed per 1000 population per year. The rate of natural increase (RNI) as a percentage is then:
粗出生率（CBR）和粗死亡率（CDR）以每年每千人为单位表示。自然增长率（RNI）的百分比形式为：
RNI (%) = (CBR − CDR) / 10
Doubling time, the number of years required for a population to double at its current growth rate, is approximated by the ‘rule of 70’.
翻倍时间，即一个人口在当前的增长率下翻一番所需的年数，可通过“70法则”近似得到。
Doubling Time ≈ 70 / Growth Rate (%)
6. Demographic Dependency Ratio | 人口依赖比率
The dependency ratio provides a measure of the proportion of the population that is economically dependent on the working-age group. It is widely used to assess the demographic pressure on the productive sector.
依赖比率衡量了在经济上依赖于劳动年龄组的人口比例，广泛用于评估生产性部门面临的人口压力。
Dependency Ratio = [(P₀₋₁₄ + P₆₅₊) / P₁₅₋₆₄] × 100
A high dependency ratio, often seen in countries with youthful populations or rapidly ageing societies, can place strain on education, healthcare, and pension systems. Conversely, a low dependency ratio may provide a ‘demographic dividend’ if suitable employment opportunities exist.
高依赖比率常见于年轻型人口或快速老龄化的社会，可能给教育、医疗和养老金体系带来压力。反之，如果存在适当的就业机会，低依赖比率则可能带来“人口红利”。
7. Gravity Model of Spatial Interaction | 空间相互作用的重力模型
The gravity model predicts the interaction between two places based on their population sizes and the distance separating them. Larger populations generate more movement, while greater distance reduces the likelihood of interaction.
重力模型根据两个地点的人口规模和它们之间的距离来预测相互作用。较大的人口规模会产生更多流动，而较大的距离则会降低相互作用的可能性。
Interaction ∝ (PA × PB) / DAB2
In retail geography and migration studies, the exponent on distance may be calibrated empirically; a squared distance term is often used as a generalisation. The model explains why most commuting and shopping trips are concentrated between large urban centres that are relatively close together.
在零售地理学和移民研究中，距离的指数可以通过实证校准；通常用距离的平方项作为一种概括。该模型解释了为什么大多数通勤和购物出行集中在相对接近的大城市中心之间。
8. Location Quotient (LQ) and Economic Base | 区位商与经济基础
The location quotient compares the concentration of a particular industry in a local area with the national average, identifying sectors of specialisation.
区位商将某个行业在局部区域的集中度与全国平均水平进行比较，以识别专业化部门。
LQ = (ei,local / elocal) / (Ei,national / Enational)
An LQ greater than 1 indicates that the local area has a higher share of employment in that sector than the nation, pointing to an export-oriented activity that forms part of the economic base. LQ analysis is commonly used by planners to understand regional economic structure and vulnerability.
LQ大于1表明该局部区域在该部门的就业份额高于全国水平，指向一个属于经济基础部分的出口导向型活动。规划人员常用LQ分析来理解区域经济结构和脆弱性。
9. Inequality Measurement: Gini Coefficient | 不平等度量：基尼系数
The Gini coefficient quantifies income or wealth inequality within a population, derived from the Lorenz curve that plots the cumulative share of total income received by the cumulative share of households.
基尼系数量化了人口内部收入或财富的不平等程度，基于洛伦兹曲线得出，该曲线描绘了累计家庭百分比与累计收入百分比之间的关系。
A Gini coefficient of 0 represents perfect equality, while a value of 1 represents maximum inequality. The coefficient is calculated as the area between the line of equality and the Lorenz curve divided by the total area under the line of equality.
基尼系数为0表示绝对平等，为1表示极端不平等。系数的计算方法是平等线与洛伦兹曲线之间的面积除以平等线下的总面积。
Comparing Gini coefficients across countries helps geographers evaluate the spatial impacts of globalisation, trade liberalisation, and social policies on uneven development and quality of life.
比较各国的基尼系数有助于地理学家评估全球化、贸易自由化和社会政策对发展不平衡和生活质量的空间影响。
10. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s rank correlation (ρ) is a non-parametric test used to assess the strength and direction of a monotonic relationship between two ranked variables. It is frequently employed in geography fieldwork, for example to test whether pebble size varies with increasing distance down a beach.
斯皮尔曼等级相关系数（ρ）是一种非参数检验，用于评估两个排序变量之间单调关系的强度和方向。它经常用于地理实地考察，例如检验海滩上卵石大小是否随距离增加而变化。
ρ = 1 − [ 6Σd² / (n(n² − 1)) ]
where d is the difference between the ranks of each pair and n is the number of pairs. A ρ value close to +1 or −1 indicates a strong positive or negative correlation. Significance is determined by comparing the calculated value with critical values for the given sample size.
其中d是每对数据的秩次差值，n为样本对数。ρ值接近+1或−1表示强正相关或强负相关。其显著性通过将计算值与相应样本量的临界值进行比较来确定。
11. Chi-squared Test (χ²) | 卡方检验
The chi-squared test evaluates whether there is a significant difference between observed frequencies (O) and expected frequencies (E) in categorical data. Geographers use it to investigate distributions, such as the occurrence of landslide scars across different rock types or variations in agricultural land use.
卡方检验评估分类数据中观察频次（O）与期望频次（E）之间是否存在显著差异。地理学家利用它来研究分布，例如不同岩石类型中滑坡疤痕的发生情况或农业土地利用的差异。
χ² = Σ[ (O − E)² / E ]
A higher χ² value indicates a larger departure from the expected distribution. Degrees of freedom are calculated as (number of rows − 1) × (number of columns − 1). The result is then checked against a chi-squared distribution table to assess statistical significance, often at the 0.05 level.
χ²值越高，表明与期望分布的偏离越大。自由度的计算公式为（行数−1）×（列数−1）。然后将结果与卡方分布表进行比较，通常在0.05水平上评估统计显著性。
12. Nearest Neighbour Index | 最近邻指数
The nearest neighbour index (Rₙ) measures the spatial pattern of point data, distinguishing between clustered, random, and regular distributions. It is frequently applied to the geography of settlements, retail outlets, or disease incidence points.
最近邻指数（Rₙ）度量点数据的空间格局，区分聚集分布、随机分布和规则分布。它常被用于聚落地理、零售店或疾病发生点的分析。
Rₙ = D̄ₒ / D̄ₑ
D̄ₒ is the observed mean nearest neighbour distance (Σd / n), and D̄ₑ is the expected mean distance for a random distribution of the same point density, given by D̄ₑ = 1 / (2√(n / A)), where A is the area. An Rₙ value significantly less than 1 suggests clustering, close to 1 indicates a random pattern, and values approaching the maximum (around 2.15) indicate uniform spacing.
D̄ₒ为观察到的平均最近邻距离（Σd / n），D̄ₑ为在相同点密度下随机分布的期望平均距离，计算公式为D̄ₑ = 1 / (2√(n / A))，其中A为面积。Rₙ值显著小于1表示聚集分布；接近1表示随机分布；接近最大值（约2.15）则表示均匀间隔。
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