📚 AS CCEA Geography: Formula & Theorem Quick Reference Handbook | AS CCEA 地理：公式定理速查手册
This handbook provides a concise reference of all essential formulas, equations and key theorems required for the AS CCEA Geography course. It covers both physical and human topics, from population dynamics and river discharge to lapse rates and location quotient. Use it alongside your class notes and past papers to master the quantitative skills and conceptual models that are frequently examined.
本手册为 AS CCEA 地理课程提供所有必要公式、方程及关键定理的速查参考。内容涵盖自然与人文地理，从人口动态、河流流量到气温递减率和区位商数。请结合课堂笔记与历年真题使用，以掌握常考的计算技能与概念模型。
1. Vital Rates and Natural Increase | 人口动态与自然增长率
Crude Birth Rate (CBR) is the number of live births per 1000 people in a given year. It is calculated using the mid‑year population.
粗出生率 (CBR) 是某年每千人中的活产婴儿数，使用年中人口计算。
CBR = (B / P) × 1000
Crude Death Rate (CDR) is the number of deaths per 1000 people in a given year.
粗死亡率 (CDR) 是某年每千人中的死亡人数。
CDR = (D / P) × 1000
Rate of Natural Increase (RNI) is the difference between CBR and CDR, expressed per 1000. It excludes migration.
自然增长率 (RNI) 是 CBR 与 CDR 之差，以千分率表示，不含迁移。
RNI = CBR – CDR (per 1000)
2. Age Structure and Dependency Ratio | 人口结构与依赖比
The Dependency Ratio measures the pressure on the productive population (aged 15–64) from the young (0–14) and the elderly (65+). A higher ratio indicates a greater burden on the workforce.
依赖比衡量非劳动年龄人口（0–14 岁与 65 岁以上）对劳动年龄人口（15–64 岁）造成的压力。比率越高，劳动力负担越重。
Dependency Ratio = [(Pop₀–₁₄ + Pop₆₅₊) / Pop₁₅–₆₄] × 100
Youth dependency and old‑age dependency can also be calculated separately by using only the relevant age group in the numerator.
少儿抚养比与老年抚养比也可分别计算，只需将分子替换为相应的年龄组人口即可。
3. Doubling Time, Population Growth Rate and Net Migration | 倍增时间、人口增长率与净迁移
The population growth rate (in percent) considers natural increase and net migration. It is the percentage change in total population over one year.
人口增长率（百分比）综合考虑自然增长与净迁移，指一年内总人口的变化百分比。
Growth Rate (%) = [(Pₜ – Pₜ₋₁) / Pₜ₋₁] × 100
Doubling time estimates how long it takes for a population to double, assuming a constant growth rate. The ‘Rule of 70’ gives a quick approximation.
倍增时间估算在恒定增长率下人口翻倍所需的时间。“70 法则”提供快速近似。
Doubling Time (years) ≈ 70 / Growth Rate (%)
Net migration rate expresses the difference between in‑migration (I) and out‑migration (E) per 1000 population.
净迁移率表示每千人中迁入与迁出人数之差。
Net Migration Rate = ((I – E) / P) × 1000
4. Urbanisation and Population Density | 城市化与人口密度
Urbanisation level is the proportion of a country’s population living in areas classified as urban. It shows the scale of urban growth relative to total population.
城市化水平是一个国家中居住在城市地区的人口比例，反映城市发展相对于总人口的规模。
Urbanisation (%) = (Urban Population / Total Population) × 100
Population density describes how crowded an area is, often used to compare settlement patterns.
人口密度描述一个地区的拥挤程度，常用于比较聚落格局。
Population Density = Total Population / Area (km²)
5. Location Quotient | 区位商数
The Location Quotient (LQ) identifies the specialisation of an area in a particular industry or occupation compared to a reference region (usually the nation). An LQ greater than 1 indicates a higher concentration than the national average.
区位商数 (LQ) 用于判别某地区在特定产业或职业上的专业化程度，通常与全国水平比较。LQ 大于 1 表示该产业集中度高于全国平均。
LQ = (% of local employment in industry A) / (% of national employment in industry A)
It is widely used in economic geography to explore spatial patterns of employment and industrial clusters.
这在经济地理学中广泛用于探讨就业与产业集群的空间格局。
6. River Hydraulic Geometry and Gradient | 河流水力几何与梯度
As discharge increases downstream, the channel adjusts its width, depth and velocity. The relationships follow power functions, known as hydraulic geometry.
随着下游流量增加，河道会调整其宽度、深度和流速。这些关系遵循幂函数规律，称为水力几何。
w = aQᵇ, d = cQᶠ, v = kQᵐ
Gradient (slope) of a river is calculated over a reach using the vertical fall and the horizontal distance. It is often expressed as a percentage.
河段梯度（坡度）利用高差与水平距离计算，通常以百分数表示。
Gradient (%) = (Δh / Δd) × 100
7. Discharge and Drainage Density | 流量与排水密度
River discharge (Q) is the volume of water passing a cross‑section per unit time, measured in cumecs (m³/s). It is the product of cross‑sectional area and mean velocity.
河流流量 (Q) 是单位时间内通过断面的水体体积，单位为 cumecs (m³/s)。它是横截面积与平均流速的乘积。
Q = A × V (m³/s)
Drainage density is a measure of the total stream length per unit area of a drainage basin. High drainage density suggests rapid runoff and steep slopes.
排水密度是流域内单位面积的河道总长度，高排水密度意味着快速的径流与陡峭的坡地。
Drainage Density (Dd) = ΣL / A (km/km²)
8. Wave Parameters and Breaker Classification | 波浪参数与碎波分类
Wave steepness is the ratio of wave height (H) to wave length (L). It helps to determine breaker type as waves enter shallow water.
波陡是波高 (H) 与波长 (L) 之比，用于判断波浪进入浅水区后的碎波类型。
Wave Steepness = H / L
Breaker types: spilling breakers occur on gently sloping beaches with moderately steep waves; plunging breakers curl over and are associated with moderately steep beaches; surging breakers slide up steep beaches with very low wave steepness. The Irribarren number (ξ) refines this classification.
碎波类型：崩波发生在坡度平缓的海滩且波浪具有一定陡度；卷波形成卷曲状，与中等坡度的海滩有关；激波沿陡峭海滩上涌，波陡极低。伊里巴伦数 (ξ) 对此分类进行了细化。
9. Lapse Rates and Atmospheric Stability | 气温递减率与大气稳定度
The environmental lapse rate (ELR) is the actual change of temperature with altitude at a given place and time, averaging about 6.5 °C km⁻¹.
环境气温递减率 (ELR) 是在特定地点和时间温度随高度的实际变化，平均约 6.5 °C km⁻¹。
ELR ≈ 6.5 °C km⁻¹
Dry adiabatic lapse rate (DALR) applies to unsaturated air, while saturated adiabatic lapse rate (SALR) applies once condensation begins. They determine stability conditions.
干绝热递减率 (DALR) 适用于未饱和空气，湿绝热递减率 (SALR) 则发生于凝结开始后。两者共同决定大气的稳定状况。
DALR = 10 °C km⁻¹, SALR ≈ 5.5 °C km⁻¹
Absolute instability occurs when ELR > DALR; absolute stability when ELR < SALR; conditional instability when SALR < ELR < DALR.
当 ELR > DALR 时为绝对不稳定；ELR < SALR 为绝对稳定；SALR < ELR < DALR 时为条件性不稳定。
10. Map Skills: Gradient, Area and Vertical Exaggeration | 地图技能：梯度、面积与垂直放大率
The gradient between two points on a map is calculated by dividing the difference in elevation by the horizontal ground distance, using the same units.
地图上两点间的梯度用高差除以水平地面距离计算，需保持单位一致。
Gradient = Vertical Interval (m) / Horizontal Equivalent (m)
Vertical exaggeration (V.E.) highlights relief on cross‑sections. It is the ratio of the vertical scale to the horizontal scale.
垂直放大率 (V.E.) 用于突出剖面地形起伏，是垂直比例尺与水平比例尺的比值。
V.E. = Vertical Scale / Horizontal Scale
Area measurement can be done using grid squares or the dot‑grid method, converting map area into ground area using the square of the linear scale.
面积测量可使用方格法或点格法，根据线性比例尺的平方将图面面积换算为实地面积。
11. Fieldwork Calculations: Velocity and Discharge | 野外计算：流速与流量
In fieldwork, surface velocity is measured with a float over a known distance. Mean velocity is estimated by applying a correction factor (typically 0.85) to account for friction with the bed and banks.
野外工作中，使用浮子通过已知距离测量表面流速。平均流速通过乘以修正系数（通常为 0.85）来估算，以补偿床面与岸壁的摩擦力。
Mean Velocity (V) = Surface Velocity × 0.85
Cross‑sectional area (A) is calculated from width and depth measurements taken at regular intervals across the channel, often using the mid‑ordinate or trapezoidal rule.
横截面积 (A) 由河道等间距测得的宽度与水深计算得出，常用中纵坐标法或梯形法。
A = Σ (widthᵢ × depthᵢ)
Discharge is then found using Q = A × V, exactly as in Section 7.
流量则通过 Q = A × V 求得，与第 7 节一致。
12. Key Geographical Models and Theorems | 关键地理模型与定理概览
The Bradshaw Model describes downstream changes in river channel characteristics: width, depth, mean velocity and discharge increase, while gradient, bedload size and roughness decrease. Hydraulic geometry relationships (Section 6) are its quantitative expression.
布拉德肖模型描述了河道特征从上游向下游的变化：宽度、深度、平均流速与流量增加，而梯度、床沙粒径与糙率减小。水力几何关系（第 6 节）是其定量表达。
The Hjulström Curve illustrates the critical velocities required for erosion, transportation and deposition of particles of different sizes. Clay‑size particles require higher velocities to be eroded than sand because of cohesion.
霍尔丁曲线阐明了不同粒径颗粒发生侵蚀、搬运和沉积所需的临界流速。粘粒因粘聚力，反而比沙粒需要更高的流速才能被侵蚀。
The Demographic Transition Model (DTM) links population change to stages of economic development, moving from high fluctuating rates to low fluctuating rates through declining death and birth rates. Its timing and pace are useful for comparing countries.
人口转变模型 (DTM) 将人口变化与经济发展阶段相联系，随着死亡率与出生率先后下降，从高位振荡阶段过渡到低位振荡阶段。其转变时间和速度可用于国家间的对比。
Horton’s Laws of drainage composition state that bifurcation ratio (Rb) averages 3–5 in natural basins, and stream length ratio tends to 2–3. These ratios indicate flood response and network efficiency.
霍顿的河网组成定律指出，天然流域的分叉比 (Rb) 平均为 3–5，河流长度比趋向 2–3。这些比值揭示了洪水响应与河网效率。
Central Place Theory (Christaller) assumes a flat isotropic plain and explains the size, spacing and hierarchy of settlements using the principles of marketing (k=3), transport (k=4) and administration (k=7). The threshold and range of services underpin the model.
中心地理论（克里斯塔勒）假设均质平面，用市场原则 (k=3)、
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