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

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

This quick reference handbook compiles the essential formulas, statistical tests and key theorems required for Year 13 CCEA Geography. Designed for efficient exam preparation and fieldwork data analysis, it covers population dynamics, fluvial hydraulics, coastal processes, atmospheric calculations, inferential statistics and urban indices. Each entry is paired with a concise bilingual explanation to support accurate application in both human and physical geography contexts.

本手册汇总了 Year 13 CCEA 地理课程必备的公式、统计检验及核心定理。内容涵盖人口动态、河流水力、海岸过程、大气计算、推论统计以及城市化指数，旨在帮助考生高效备考与完成实地数据分析。每个条目均附有简明中英双语解释，便于在人文和自然地理双领域中准确运用。

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1. Demographic Formulas | 人口统计公式

Crude Birth Rate (CBR) counts live births per 1000 population per year, ignoring age and sex structure.

CBR = (Number of live births / Total population) × 1000

粗出生率计算单位人口年活产数，未排除年龄性别结构影响，适用于进行国际或区域间的初步横向比较。

Crude Death Rate (CDR) is the number of deaths per 1000 people in a year.

CDR = (Number of deaths / Total population) × 1000

粗死亡率表示一年内每千人的死亡人数，同样受人口年龄构成影响，需结合年龄别死亡率综合分析。

Rate of Natural Increase (RNI) captures the contribution of births and deaths to population change.

RNI (%) = [(CBR − CDR) / 10]

自然增长率以百分比表示，直接由粗出生率与粗死亡率的差值除以10得出，反映未考虑迁移下的增长趋势。

Population Growth Rate incorporates net migration alongside natural change.

Growth rate (%) = RNI + [Net migration / Total population] × 100

人口增长率综合了自然增长和净迁移效应，是衡量区域人口实际变动最常用的指标。在CCEA考试中常用于推演人口政策和未来发展。

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2. Migration and Urbanisation Formulas | 迁移与城市化公式

Net Migration Rate quantifies the difference between immigration and emigration per 1000 population.

Net migration rate = [(Immigrants − Emigrants) / Total population] × 1000

净迁移率以千分比呈现，正值表示净迁入，负值表示净迁出，是解释人口特快变动或劳动力市场变化的关键变量。

Urban Growth Rate isolates the speed of change in a city’s population.

Urban growth rate (%) = [(Urban popₜ₊₁ − Urban popₜ) / Urban popₜ] × 100

城市人口增长率重点关注城市行政边界内的人口变化速度，可用于预测基础设施压力与城市蔓延趋势。

Population Density expresses the number of people per unit area.

Population density = Total population / Land area (km²)

人口密度是评估人居压力、资源分配和公共服务覆盖的基础指标，数值越高通常意味着对土地和资源的竞争越激烈。

Urbanisation Level measures the proportion of a country’s people living in urban areas.

Urbanisation level (%) = (Urban population / Total population) × 100

城镇化率反映从传统农业社会向现代城市社会转型的程度，是CCEA人文地理中城市模型应用的重要背景参数。

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3. River Discharge & Channel Geometry | 河流流量与河道几何公式

Discharge (Q) is the volume of water passing a cross‑section per unit time.

Q = A × V (m³/s)

流量的基本公式为断面面积乘以平均流速，是洪水预报和流域管理中最核心的水文测度，A与V的数据多通过流速仪及断面测量获得。

Hydraulic Radius (R) describes the efficiency of a channel cross‑section.

R = A / P (m), where P is wetted perimeter.

水力半径等于过水面积除以润周，越大代表水流与边壁的摩擦相对越小，用于曼宁公式计算流速时必不可少。

Channel Gradient indicates the slope of a stream reach.

Gradient = Vertical drop (m) / Horizontal distance (m)

河道坡降常用垂直高差除以水平距离，以比值或无量纲数表达，直接影响动能、侵蚀力与沉积过程。

Manning’s Equation estimates velocity in open channels (used for fieldwork approximation).

V = (1/n) × R²⁄³ × S¹⁄²

曼宁公式考虑了糙率n、水力半径和坡降，在CCEA实地考察中可用来估算流速和流量，理解糙率对洪水波速的影响极具应用价值。

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4. Fluvial Theorems and Models | 河流定理与关键模型

Bradshaw Model summarises predictable downstream changes in channel characteristics. The table below captures key expected trends.

Bradshaw 模型总结了河道特性自上游至下游的可预测变化，下表列出CCEA课程强调的核心理论趋向。

Characteristic	Downstream Change	中文释义
Discharge	Increases	流量增加
Channel width & depth	Increase	河宽与水深增大
Average velocity	Increases	平均流速加快
Gradient	Decreases	坡降减小
Bedload particle size	Decreases (more rounded)	推移质粒径减小且圆度增加

Hjulström Curve illustrates the critical erosion velocity and settling velocity for different particle sizes. The key principle: cohesive clays require higher velocities to erode than sand, while silt and fine sand are eroded most easily. The curve is not a single equation but a fundamental theorem linking flow velocity, grain size and erosional/depositional thresholds.

Hjulström 曲线展示不同粒径颗粒的临界侵蚀流速和沉降流速。关键“定理”在于：黏土因粘结力而需要比沙粒更高的流速才能侵蚀，而粉砂与细沙反而最易被搬运。这一关系是理解河流侵蚀、搬运与沉积机制的基石，常在CCEA问答题中作为理论依据出现。

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5. Coastal Calculations | 海岸计算公式

Wave Steepness (S) determines wave stability and breaking conditions.

S = H / L, where H = wave height, L = wavelength

波陡度等于波高除以波长，当S值超过1:7（约0.14）时波浪趋于破碎，是解释激浪带能量释放的核心参数。

Wave Base Depth defines the depth at which wave energy begins to interact with the seabed.

Wave base = L / 2

波浪基面深度约等于波长的一半，在此深度以下沉积物不再受波浪扰动，用于判定海底侵蚀活动的空间下限。

Longshore Drift Rate (simplified) estimates sediment transport along a coast.

Drift volume ∝ V × (H²) × sin(2θ)

沿岸漂移量与流速、波高的平方以及波浪入射角的正弦相关，野外实地测量中常通过染色示踪物估算输沙方向与相对强度。

Beach Sediment Budget balances inputs and outputs of beach material.

Net change = (Inputs − Outputs) over a given time span.

海滩沉积物平衡公式虽然简单，却是海岸管理决策的理论支柱，CCEA海岸单元常要求考生结合海蚀、堆积和人为方案进行预算推演。

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6. Atmospheric and Climatic Formulas | 大气与气候公式

Environmental Lapse Rate (ELR) is the actual temperature decline with altitude in the troposphere.

ELR ≈ 6.5 °C/km (standard average)

环境直减率表示实际大气温度随高度的变化，常用作判断气团稳定性的参照值。

Dry Adiabatic Lapse Rate (DALR) applies to unsaturated rising air parcels.

DALR = 9.8 °C/km

干绝热直减率描述未饱和气团上升时由于膨胀而降温的速率，是理解对流发展和云底形成的关键。

Saturated Adiabatic Lapse Rate (SALR) applies once condensation begins.

SALR ≈ 6 °C/km (varies with temperature and moisture)

湿绝热直减率低于干绝热值，因潜热释放部分抵消冷却效应，CCEA天气系统题目中常需对比DALR、SALR与ELR以判断大气稳定度。

Relative Humidity (RH) indicates how close the air is to saturation.

RH (%) = (Actual vapour pressure / Saturation vapour pressure) × 100

相对湿度反映了空气中水汽含量相对于饱和状态的百分比，是降水预报和气候评估的基本参数。

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7. Statistical Tools for Geography | 地理统计工具

Arithmetic Mean (x̄) measures central tendency of a dataset.

x̄ = Σx / n

算术平均数将所有观测值之和除以样本数，对地理数据初步分析至关重要，但易受极端值影响。

Median and Mode describe other central tendencies: the median is the middle value when sorted, the mode is the most frequent value. Both are used in skewed distributions such as income or river discharge.

中位数和众数是另两类集中趋势量数：中位数为排序后居中值，众数为频数最高值，常用于描述偏态地理数据如家庭收入或洪水序列。

Range is the simplest measure of dispersion.

Range = Maximum value − Minimum value

极差计算简便，但仅反映数据跨度，无法揭示内部变异结构。

Interquartile Range (IQR) reduces the influence of outliers.

IQR = Q3 − Q1

四分位距即上四分位数与下四分位数之差，适合处理存在异常值的地理数据集，例如微气候观测数据。

Sample Standard Deviation (s) quantifies the spread around the mean.

s = √[ Σ(x − x̄)² / (n − 1) ]

样本标准差是CCEA实地考察报告里最常用的离散度指标，分母为n−1以实现无偏估计，常与均值搭配绘制误差棒或进行显著性检验。

Variance (s²) is the square of standard deviation and forms the basis of many inferential tests.

方差为标准差的平方，在卡方检验和方差分析中成为直接运算对象，理解其含义有利于解读统计输出结果。

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8. Spearman’s Rank Correlation | Spearman等级相关系数

Spearman’s Rank Correlation Coefficient (rₛ) tests the strength and direction of a monotonic relationship between two ranked variables. It is widely used in CCEA fieldwork for non‑parametric data such as perceptions, indices or environmental quality scores.

Spearman等级相关系数检验两个排序变量之间单调关系的强度与方向，广泛应用于CCEA实地考察中处理感知评分、环境质量指数等非参数资料。

rₛ = 1 − [ 6 Σd² / (n(n² − 1)) ]

公式中d为每对数据的秩次差，n为样本量。rₛ值介于−1（完全负相关）和+1（完全正相关）之间，接近0表示无单调关系。

In the formula, d represents the difference in ranks for each pair, and n is the number of pairs. The result ranges from −1 to +1, with zero indicating no monotonic association.

在使用该公式前必须先分别对两个变量排序，记下秩次差d，平方求和后代入方程，最后查阅临界值表判断显著性。

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9. Chi-Squared Test (χ²) | 卡方检验

Chi-Squared Test compares observed frequencies with expected frequencies to determine if a significant association exists between two categorical variables. It is a cornerstone of hypothesis testing in CCEA human geography investigations, such as comparing actual land use with expected random distribution.

卡方检验通过比较观测频数与期望频数来判断类型变量间是否存在显著关联，是CCEA人文地理假说检验的核心工具，常用于分析实际土地利用与随机期望分布的差异。

χ² = Σ [ (O − E)² / E ]

式中O为观测频数，E为理论期望频数；对所有类别求和后，将计算得到的χ²值与给定自由度和显著性水平下的临界值比对，以决定是否拒绝零假设。

Where O is the observed frequency and E is the expected frequency. Sum over all categories, then compare the obtained χ² to the critical value at the appropriate degrees of freedom (df = (rows−1)×(columns−1)). A significant χ² implies that the distribution is unlikely to have occurred by chance.

自由度等于(行数−1)×(列数−1)。若计算值大于临界值（通常取p=0.05），则拒绝独立性的零假设，认为变量间存在关联。学员需在实地作业中完整呈现期望值计算、卡方求值和结论陈述。

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10. Indexes and Ratios | 指数与比率

Dependency Ratio measures the pressure on the productive population from non‑working age groups.

Dependency ratio = [(Population 0−14 + Population 65+) / Population 15−64] × 100

抚养比将儿童与老年人口之和除以劳动年龄人口并乘以100，数值越高表明社会抚养负担越大，常用于评估养老金和医疗服务需求。

Location Quotient (LQ) identifies regional specialisation in an economic

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