Year 13 WJEC Geography: Formula & Theorem Quick Reference | Year 13 WJEC 地理：公式定理速查手册

📚 Year 13 WJEC Geography: Formula & Theorem Quick Reference | Year 13 WJEC 地理：公式定理速查手册

In Year 13 WJEC Geography, a firm grasp of essential formulas, indices, and theorems is crucial for interpreting data, tackling fieldwork questions, and writing high-mark exam responses. This quick reference handbook brings together the core equations from both physical and human geography – covering hydrology, demographics, spatial interaction, climate change, statistical tests, and more. Use it alongside your class notes to speed up revision and deepen your quantitative understanding.

在 Year 13 WJEC 地理中，牢固掌握关键的公式、指标和定理对于解读数据、应对实地考察题目以及在考试中拿下高分至关重要。这本速查手册汇集了自然地理与人文地理的核心方程，涵盖水文学、人口统计、空间相互作用、气候变化、统计检验等多个领域。配合课堂笔记使用，可以帮助你加快复习节奏、加深定量分析的理解。

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1. Hydrological and Fluvial Formulas | 水文与河流公式

River discharge is the foundation of fluvial studies. It quantifies the volume of water moving through a channel and links directly to flood risk, erosion, and sediment transport.

河流流量是河流研究的基础。它可以量化通过河道的水量，并与洪水风险、侵蚀和泥沙搬运直接相关。

Q = A × V

Discharge (Q) is the product of cross-sectional area (A) in square metres and mean velocity (V) in metres per second. The result is in cubic metres per second (m³/s, also called cumecs).

流量(Q)是横截面积(A, 单位 m²)与平均流速(V, 单位 m/s)的乘积，单位为立方米每秒(m³/s，也称 cumecs)。

Hydraulic radius: R = A / P

For estimating channel efficiency, the hydraulic radius (R) is calculated by dividing the cross-sectional area (A) by the wetted perimeter (P). A higher R indicates a more efficient channel shape with less friction.

估算河道效率时，水力半径(R)通过横截面积(A)除以湿周(P)求得。R 值越大表明河道形态效率越高，摩擦阻力越小。

Velocity–discharge relationship: V ∝ Q

In many WJEC scenarios, you will relate changes in velocity and discharge to the Bradshaw model, which describes downstream trends in channel variables.

在许多 WJEC 情境题中，流速和流量的变化会与 Bradshaw 模型相联系，该模型描述了河道变量沿下游的变化趋势。

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2. Runoff, Water Balance and the Drainage Basin | 径流、水平衡与流域

Water balance equations help to explain how a drainage basin stores and transfers water, forming the basis for flood hydrograph interpretation.

水平衡方程有助于解释流域如何储存和传输水分，是理解洪水过程线的基础。

P = Q + E ± ΔS

Precipitation (P) is partitioned into runoff (Q), evapotranspiration (E), and the change in storage (ΔS) within the basin. This is a fundamental continuity equation for the water cycle.

降水量(P)被分为径流(Q)、蒸散发(E)和流域蓄水量的变化(ΔS)。这是水循环中一个基本的连续性方程。

Runoff coefficient = total runoff ÷ total precipitation

The runoff coefficient expresses the proportion of rainfall that becomes immediate runoff. Impermeable surfaces in urban catchments push this value towards 1.

径流系数表示降雨转化为即时径流的比例。城市流域的不透水表面会使该系数趋近于 1。

Storm hydrograph: Lag time = peak rainfall – peak discharge

Lag time is a key measure of basin response. A short lag time indicates a flashy regime, often associated with steep slopes, intense rainfall, and urbanisation.

滞时是衡量流域响应的重要指标。较短的滞时表明流态陡涨陡落，通常与陡坡、强降雨和城市化有关。

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3. Coastal and Glacial Process Equations | 海岸与冰川作用公式

Quantitative concepts in coastal and glacial systems tend to focus on energy, mass balance, and sediment budgets, helping students link processes to landforms.

海岸与冰川系统中的量化概念多集中在能量、物质平衡和沉积物收支上，帮助学生将过程与地形联系起来。

Wave energy: E = ⅛ × ρ × g × H² × T

Wave energy (E) per unit area depends on water density (ρ ≈ 1025 kg/m³ for seawater), gravity (g = 9.81 m/s²), wave height (H) squared, and wave period (T). Larger, longer-period waves carry substantially more energy for erosion and longshore drift.

单位面积波能(E)取决于水体密度(ρ，海水约 1025 kg/m³)、重力加速度(g=9.81 m/s²)、波高(H)的平方和波周期(T)。高大、长周期的波浪携带的能量要大得多，对侵蚀和沿岸漂沙作用更强。

Longshore drift transport rate: Q₁ ∝ H_b² × C_b × sin(2α_b)

Although full calculation is beyond WJEC, the principle shows that the volume of longshore drift increases with breaker height (H_b), wave speed (C_b), and the angle of wave approach (α_b).

尽管完整计算超出 WJEC 要求，但这一原理表明沿岸漂沙量随破碎波高(H_b)、波速(C_b)和波浪入射角(α_b)的增加而增大。

Glacial mass balance: B = Σ accumulation – Σ ablation

Net mass balance (B) is the difference between total accumulation (snowfall, avalanches) and total ablation (melting, calving). A negative mass balance signals glacier retreat and links directly to climate change case studies.

净物质平衡(B)是总积累量(降雪、雪崩)与总消融量(融化、崩解)的差值。负平衡意味着冰川退缩，与气候变化案例有直接联系。

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4. Demographic Rates and Population Growth | 人口比率与人口增长

Demographic formulas are essential for analysing population structures, projecting future growth, and evaluating development in WJEC Changing Places themes.

人口统计公式对于分析人口结构、预测未来增长以及在 WJEC “变化的地方” 主题中评估发展至关重要。

Rate of natural increase (per 1000) = CBR – CDR

The crude birth rate (CBR) minus the crude death rate (CDR) gives the natural change per 1000 population. The percentage RNI is then (CBR – CDR) / 10.

粗出生率(CBR)减去粗死亡率(CDR)得出每千人的自然变化。以百分比表示的自然增长率则为 (CBR–CDR) / 10。

Doubling time (years) ≈ 70 ÷ annual growth rate (%)

The rule of 70 provides a quick estimate of how long it takes a population to double at a constant growth rate. A 2% growth rate gives a doubling time of about 35 years.

“70 法则” 可以快速估计在恒定增长率下人口翻倍所需时长。2% 的增长率对应约 35 年的翻倍时间。

Population density = total population ÷ land area

Expressed in persons per km², this measure underpins discussions of overpopulation and urban sprawl. Always check whether the area includes only habitable land.

以人/km² 表示，这一指标是探讨人口过剩和城市蔓延的基础。务必确认面积是否仅包含宜居土地。

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5. Migration and Population Change | 迁移与人口变化

Migration equations quantify the movement of people and allow analysis of net migration’s contribution to population change alongside natural increase.

迁移方程可以量化人口流动，并分析净迁移在人口变化中的贡献，与自然增长并列。

Net migration rate (per 1000) = (immigration – emigration) ÷ total population × 1000

A positive value indicates net in-migration; a negative value shows net out-migration. This can be combined with RNI to calculate total population growth rate.

正值表示净迁入，负值表示净迁出。该指标可与自然增长率结合，计算总人口增长率。

Population growth rate (%) = (CBR – CDR)/10 + (net migration rate/1000)×0.1

In WJEC data-response questions, use this to compare the relative importance of natural change and migration in a country’s demographic story.

在 WJEC 数据应答题中，可以利用该公式比较自然变化和迁移在一个国家人口动态中的相对重要性。

Migration efficiency = (in-migration – out-migration) ÷ (in-migration + out-migration)

This index ranges from -1 (all out-migration) to +1 (all in-migration) and describes the effectiveness of a migration stream.

该指数取值从 -1(全部迁出)到 +1(全部迁入)，用于刻画迁移流的有效性。

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6. Development and Inequality Measures | 发展与不平等指标

Composite indices and income-distribution measures are central to WJEC Global Governance and Development topics. Knowing how they are computed is vital for evaluation.

综合指数和收入分配衡量指标是 WJEC 全球治理与发展专题的核心。了解它们的计算方法对于评估分析至关重要。

Human Development Index (HDI) = (I_health × I_education × I_income)¹⁄³

HDI is the geometric mean of normalised indices for life expectancy (I_health), mean and expected years of schooling (I_education), and GNI per capita (I_income). Values range from 0 to 1.

HDI 是对预期寿命(I_健康)、平均与预期受教育年限(I_教育)和人均 GNI(I_收入)的标准化指数的几何平均数，取值范围在 0 到 1 之间。

Gini coefficient = A / (A + B)

Derived from the Lorenz curve, A is the area between the line of perfect equality and the curve, B is the area below the curve. A higher Gini (0–1) indicates greater income inequality.

基尼系数得自洛伦兹曲线，A 是完全平等线与曲线之间的面积，B 是曲线下方的面积。基尼系数越高(0–1)，表明收入分配越不平等。

Gender Inequality Index (GII): calculated from reproductive health, empowerment, and labour market participation

GII ranges from 0 (equality) to 1 (maximum inequality). Remember the three dimensions: maternal mortality ratio, adolescent birth rate, share of parliamentary seats, educational attainment, and labour force participation.

性别不平等指数取值 0(平等)到 1(最大不平等)。需记住三个维度：生殖健康、赋权和劳动力市场参与，包括孕产妇死亡率、青少年生育率、议会席次比例、受教育程度和劳动参与率。

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7. Spatial Interaction and Gravity Models | 空间相互作用与重力模型

Spatial interaction models predict flows of people, goods, and information between places. They are directly applicable to settlement and retail case studies in WJEC.

空间相互作用模型可以预测地方之间的人流、货流和信息流，直接适用于 WJEC 的聚落与零售业案例研究。

Gravity model: I_ij = k × (P_i × P_j) / d_ijᵇ

Interaction (I_ij) between place i and place j is proportional to the product of their populations (P_i, P_j) and inversely proportional to the distance (d_ij) raised to the exponent b (friction of distance). k is a constant.

地点 i 与 j 之间的相互作用(I_ij)与两地人口乘积(P_i × P_j)成正比，与距离(d_ij)的 b 次方成反比(b 为距离摩擦系数)，k 为常数。

Reilly’s law of retail gravitation: breaking point D_b = d_ab / (1 + √(P_a / P_b))

This defines the boundary between the trade areas of two centres a (larger) and b (smaller). D_b is the distance from the larger centre to the breaking point.

该定律界定了两中心 a(较大)和 b(较小)之间商圈的边界。D_b 表示从较大中心到断裂点的距离。

Distance-decay principle: interaction ∝ 1/d² or e⁻ᵏᵈ

All interaction weakens with distance; the decay function can be power-based or exponential. This underpins the concept of the “friction of distance” in both human and physical geography.

一切相互作用随距离衰减；衰减函数可以是幂律型或指数型。这支撑着人文与自然地理中“距离摩擦”的概念。

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8. Central Place Theory and Urban Models | 中心地理论与城市模型

Christaller’s central place theory provides spatial principles for the distribution, size, and spacing of settlements. The associated formulas clarify threshold and range.

克里斯塔勒的中心地理论为聚落的分布、规模和间距提供了空间原则。相关公式可以阐明门槛人口和商品范围。

Threshold population = minimum demand needed to support a service

Threshold is the number of consumers required for a shop, school, or hospital to be economically viable. It varies with service type and consumer income.

门槛人口是指使商店、学校或医院等设施经济上可行所需的最低消费者数量，随服务类型和消费者收入而异。

Range of a good = maximum distance consumers are willing to travel

The upper limit of the market area. If range exceeds threshold, the service survives. In exams, you may be asked to calculate range using map scales and travel time.

商品范围是消费者愿意出行的最大距离，即市场区的上限。若范围大于门槛，服务便能存活。考试中可能会要求利用地图比例尺和出行时间估算范围。

K-value (Christaller): K = 3 (marketing principle), K = 4 (transport principle), K = 7 (administrative principle)

These nested hierarchy multipliers define how many lower-order settlements are served by a higher-order centre under different organising principles.

这些嵌套层级乘数决定了在不同组织原则下，一个高等级中心服务多少个低等级聚落。

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9. Climate Forcing and Energy Balance | 气候强迫与能量平衡

Climate-related formulas in WJEC Geography link greenhouse gas concentrations to radiative forcing and global temperature change. They are essential for 20-mark evaluative essays.

WJEC 地理中与气候相关的公式将温室气体浓度与辐射强迫和全球温度变化联系起来，是撰写 20 分评估性论文的基础。

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