Year 12 WJEC Geography: Formula & Theorem Quick Reference Handbook | 公式定理速查手册

📚 Year 12 WJEC Geography: Formula & Theorem Quick Reference Handbook | 公式定理速查手册

This handbook collects the essential quantitative relationships, models, and statistical tools that appear across the Year 12 WJEC Geography specification. Use it alongside your fieldwork, Changing Landscapes, and Changing Places topics to reinforce your understanding of the numbers behind the processes.

本手册汇集了 Year 12 WJEC 地理课程中出现的核心数量关系、模型与统计工具。结合野外调查、变化的地貌和变化的地点等主题使用，可以帮助你强化对过程背后数字关系的理解。

1. Discharge and Continuity Equation | 流量与连续性方程

Discharge (Q) is the volume of water flowing through a channel cross-section per unit of time. It is a fundamental measure in both river and coastal flooding studies.

流量 (Q) 是单位时间内通过河道断面的水体体积，是研究河流与海岸洪水的基本量。

Q = A × V

where A is cross-sectional area (m²) and V is mean flow velocity (m/s). The equation assumes continuity of mass, meaning discharge stays constant if no water is added or lost.

式中 A 为横截面积 (m²)，V 为平均流速 (m/s)。方程基于质量连续性，若没有水量增减，流量保持不变。

• Units: Discharge is expressed in cubic metres per second (m³ s⁻¹).
• 单位：流量以立方米每秒 (m³ s⁻¹) 表示。

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2. Hydraulic Radius and Manning's Equation | 水力半径与曼宁公式

When studying river channels, the hydraulic radius (R) helps describe flow efficiency. It is the ratio of the cross-sectional area of flow to the wetted perimeter.

研究河道时，水力半径 (R) 用于描述水流效率，为过流断面面积与湿周的比值。

R = A / P

where P is the wetted perimeter (m). A larger hydraulic radius generally means less friction and more efficient flow. Manning's equation then links this to velocity.

式中 P 为湿周 (m)。水力半径越大，通常意味着摩擦越小，水流效率越高。曼宁公式将该值与流速联系起来。

V = (1/n) × R^2/3 × S^1/2

Here n is Manning's roughness coefficient (higher values indicate rougher beds), and S is the channel slope or energy gradient. This equation is vital for flood modelling.

其中 n 为曼宁粗糙系数 (数值越大河床越粗糙)，S 为河道坡度或能坡。该方程对洪水模拟至关重要。

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3. Stream Gradient and Drainage Density | 河道比降与河网密度

These two measures describe the steepness of a channel and the extent of the drainage network in a basin. They help explain runoff response and erosion potential.

这两个量度描述河道陡峭程度和流域内河网发育程度，有助于解释产流响应与侵蚀潜力。

Gradient = Vertical Drop / Horizontal Distance

Usually expressed as a ratio or percentage. A steep gradient leads to higher velocity and more erosive power.

通常以比降或百分比表示。陡峭的比降会导致流速更快、侵蚀力更强。

Drainage Density (D_d) = ΣL / A

where ΣL is the total length of all stream channels in the basin (km) and A is the basin area (km²). High drainage density indicates rapid water evacuation and flashy hydrographs.

式中 ΣL 为流域内所有河道的总长度 (km)，A 为流域面积 (km²)。高河网密度意味着排水迅速、洪水过程线陡涨。

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4. Demographic Formulas | 人口统计公式

Population change is driven by births, deaths, and migration. The following standard equations are central to the Changing Places topic.

人口变化由出生、死亡和迁移驱动。以下标准方程是“变化的地点”主题的核心。

Crude Birth Rate (CBR) = (B / P) × 1000

year, P is total mid-year population. Similarly, Crude Death Rate (CDR) = (D / P) × 1000.

B 为一年内活产数，P 为年中总人口。类似地，粗死亡率 (CDR) = (D / P) × 1000。

Natural Increase Rate (%) = (CBR - CDR) / 10

ion. For net migration rate: (I - E) / P × 1000, where I is immigrants and E is emigrants.

由此得出不考虑迁移时的人口变动百分比。净迁移率：(I - E) / P × 1000，I 为迁入，E 为迁出。

Population Doubling Time (years) ≈ 70 / Growth Rate (%)

The 'rule of 70' is a quick estimate of how long it takes a population to double at a constant growth rate.

'70法则' 用于快速估算在恒定增长率下人口翻一番所需的时间。

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5. Population Density and Dependency Ratio | 人口密度与抚养比

Pressure on resources and services is often measured through density and age-structure indicators.

资源与服务压力通常通过密度和年龄结构指标来衡量。

Population Density = Total Population / Land Area (km²)

Agricultural density and physiological density may also be used, but the basic density gives a broad indication of human concentration.

亦可使用农业密度与生理密度，但基本密度可给出人文集聚的概略指示。

Dependency Ratio = [(Population 0–14 + 65+) / Working-age (15–64)] × 100

A higher ratio signals a greater economic burden on the productive population. Ageing populations in HICs push this ratio upwards.

比值越高，表明生产性人口负担越重。高收入国家人口老龄化使该比值上升。

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6. Gravity Model and Spatial Interaction | 重力模型与空间相互作用

The gravity model estimates the interaction between two places based on their population sizes and the distance between them. It is widely used in migration and retail studies.

重力模型根据两地的人口规模和距离估算其相互作用强度，广泛应用于迁移与零售研究。

I_ij = k × (P_i × P_j) / (D_ij)²

where I_ij is the interaction between places i and j, P is population, D is distance, and k is a constant. The distance exponent can vary, but 2 is typical for decay with the square of distance.

式中 I_ij 为 i 地与 j 地间相互作用，P 为人口，D 为距离，k 为常数。距离指数可变，但通常取 2 表示随距离平方衰减。

• Explains why larger cities attract more commuters and migrants over longer distances.
• 解释了为何大城市能吸引更远距离的通勤者和移民。

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7. Bradshaw Model and Downstream Changes | 布拉肖模型与下游变化

The Bradshaw model predicts how river characteristics vary from source to mouth. Although not a single formula, it summarises expected trends in discharge, velocity, channel shape, and sediment load.

布拉肖模型预测河流特征从源头到河口的变化。虽非单一公式，但它总结了流量、流速、河道形态与输沙量的预期趋势。

Characteristic	Expected downstream change
Discharge	Increases
Mean velocity	Increases
Channel width/depth	Increases
Particle size	Decreases
Wetted perimeter	Increases
Channel roughness	Decreases

The model provides a baseline that can be tested through fieldwork, helping to identify anomalies caused by human intervention or tributary inputs.

该模型提供了可通过野外调查验证的基线，有助于识别由人类干预或支流汇入引起的异常。

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8. Coastal Sediment Budget Equation | 海岸沉积物收支方程

Coastal systems are often analysed through the balance of sediment gains and losses within a cell. This equation underpins the concept of the coastal sediment budget.

海岸系统常通过某单元内沉积物收支平衡进行分析。该方程是海岸沉积物预算概念的基础。

ΔS = Inputs – Outputs

ΔS is the net change in sediment stored. Inputs include longshore drift into the cell, cliff erosion, and river delivery; outputs include longshore drift out, offshore transport, and dredging.

ΔS 为沉积物储量的净变化。输入包括沿岸流输入、悬崖侵蚀和河流输沙；输出包括沿岸流输出、向海搬运和疏浚。

• A positive budget builds beaches; a negative budget leads to erosion.
• 预算为正则海滩增生，预算为负则发生侵蚀。

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9. Spearman's Rank Correlation Coefficient | 斯皮尔曼等级相关系数

This statistical test is frequently used in geography fieldwork to measure the strength and direction of a relationship between two sets of rankable data, such as distance downstream and pebble size.

该统计检验常用于地理野外调查，衡量两组可排序数据之间关系的强弱与方向，如下游距离与砾石粒径。

r_s = 1 – (6 Σ d²) / (n(n² – 1))

where d is the difference in ranks for each pair, and n is the number of pairs. The value of r_s ranges from -1 (perfect negative) to +1 (perfect positive), with 0 indicating no correlation.

式中 d 为每对数据的等级差，n 为数据对数量。r_s 的值域为 -1 (完全负相关) 至 +1 (完全正相关)，0 表示无相关。

• After obtaining r_s, an appropriate significance table is used to test if the correlation could have arisen by chance.
• 得出 r_s 后，需查合适的显著性表以检验该相关是否可能为偶然。

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10. Push-Pull Model of Migration | 推拉迁移模型

Lee's push-pull theory suggests that migration decisions are influenced by negative factors at the origin (push) and positive factors at the destination (pull), mediated by intervening obstacles and personal factors.

李的推拉理论认为迁移决策受源地负面因素 (推力) 和目的地正面因素 (拉力) 影响，并通过中间障碍与个人因素调节。

Common push factors include unemployment, natural hazards, conflict, and poor services. Pull factors include job opportunities, safety, better climate, and education. Fieldwork often uses perception scores to quantify these forces.

常见推力包括失业、自然灾害、冲突和公共服务差；拉力包括就业机会、安全、气候宜人和教育。野外调查常通过感知评分量化这些作用力。

When combined with the gravity model, the push-pull framework helps explain both the volume and direction of migration flows studied in Changing Places.

结合重力模型，推拉框架有助于解释“变化的地点”中所研究的迁移流的量与方向。

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