📚 Year 12 Edexcel Geography Formula & Theorem Quick Reference | Edexcel A Level 地理 Year 12 公式定理速查手册
This handbook compiles all essential formulae, indices and key relationships required for Year 12 Edexcel Geography, supporting both physical and human geography topics, as well as fieldwork analysis. Mastering these equations will sharpen your data-response skills and deepen your understanding of processes from river discharge to urban patterns.
本手册汇编了 Edexcel A Level 地理 Year 12 全部必备公式、指数和关键关系，涵盖自然地理、人文地理及野外考察数据分析。掌握这些公式有助于提升数据分析能力，并加深对河流流量、聚落分布等过程的理解。
1. River Discharge | 河道流量
River discharge is the volume of water passing a point in a river per unit time, commonly expressed in cubic metres per second (cumecs). The fundamental formula is:
河道流量是指单位时间内通过河流某一点的水量，通常以立方米/秒 (cumecs) 表示。基本公式为：
Q = A × V
where Q = discharge (m³/s), A = cross-sectional area (m²), V = mean velocity (m/s).
其中 Q = 流量 (m³/s)，A = 过水断面面积 (m²)，V = 平均流速 (m/s)。
2. Hydraulic Radius and Wetted Perimeter | 水力半径与湿周
Hydraulic radius (R) helps assess river channel efficiency. It relates cross-sectional area to the length of the wetted perimeter.
水力半径 (R) 用于评估河道效率，它将过水断面面积与湿周长度联系起来。
R = A / P
R = hydraulic radius (m), A = cross-sectional area (m²), P = wetted perimeter (m) – the total length of the bed and banks in contact with water.
R = 水力半径 (m), A = 过水断面面积 (m²)，P = 湿周 (m)——河床与河岸接触水的总长度。
A larger hydraulic radius indicates lower frictional resistance and more efficient flow.
水力半径越大，摩擦阻力越低，水流效率越高。
3. Drainage Density | 河网密度
Drainage density measures the total stream length per unit area of a drainage basin. It reveals how well a basin drains and reflects geology, vegetation cover and climate.
河网密度衡量流域单位面积上的河道总长度，可揭示流域排水效率，并反映地质、植被覆盖和气候条件。
D_d = ΣL / A_basin
D_d = drainage density (km/km²), ΣL = total length of all stream channels (km), A_basin = area of the drainage basin (km²).
D_d = 河网密度 (km/km²)，ΣL = 所有河道的总长度 (km)，A_basin = 流域面积 (km²)。
4. Stream Gradient | 河道比降
Stream gradient indicates the steepness of a river channel along a given reach, influencing velocity and erosive power.
河道比降表示某河段的陡峭程度，影响流速和侵蚀力。
Gradient = Vertical drop / Horizontal distance
Commonly expressed as metres per kilometre (m/km) or as a dimensionless ratio.
通常以米/公里 (m/km) 或无量纲比值表示。
High gradient near the source favours vertical erosion; low gradient near the mouth encourages deposition.
上游高比降有利于垂直侵蚀；下游低比降则促进沉积。
5. Sediment Particle-Size (Phi Scale) | 沉积物粒径（φ 值）
The phi (φ) scale transforms grain diameters into a more manageable logarithmic index, widely used in coastal and fluvial sediment analysis.
φ 值将颗粒直径转化为更易于比较的对数指数，广泛用于海岸与河流沉积物分析。
φ = –log₂(D)
D is the grain diameter in millimetres. A larger φ value indicates finer sediment; for example, sand often ranges from +4φ (very fine) to –1φ (very coarse).
D 为颗粒直径 (mm)。φ 值越大表示颗粒越细；例如，沙粒常在 +4φ（极细）至 –1φ（极粗）之间。
6. Wave Energy and Shoreline Processes | 波浪能量与岸线过程
The energy delivered by waves directly shapes coastal landforms. Deep-water wave energy (E) per unit surface area is proportional to the square of wave height.
波浪传递的能量直接塑造海岸地貌。深水区单位面积波能 (E) 与波高的平方成正比。
E = (1/8) ρ g H²
where ρ = density of seawater (approx. 1025 kg/m³), g = acceleration due to gravity (9.81 m/s²), H = wave height (m).
其中 ρ = 海水密度（约 1025 kg/m³），g = 重力加速度 (9.81 m/s²)，H = 波高 (m)。
Destructive waves, with high wave height and steepness, create high energy and erode beaches; constructive waves deliver lower energy and build beaches.
破坏性浪波高大、波陡大，能量高，侵蚀海滩；建设性浪能量较低，堆积海滩。
7. Water Balance Equation | 水量平衡方程
The water balance relates precipitation, runoff, evapotranspiration and changes in storage within a drainage basin over a given timescale.
水量平衡将流域内一定时段内的降水、径流、蒸发蒸腾与蓄水量变化联系起来。
P = Q + E ± ΔS
P = precipitation (mm), Q = runoff (mm), E = actual evapotranspiration (mm), ΔS = change in soil moisture and groundwater storage (mm).
P = 降水量 (mm)，Q = 径流 (mm)，E = 实际蒸发蒸腾 (mm)，ΔS = 土壤含水量与地下水储量变化 (mm)。
This equation is fundamental in studying river regimes and drought-flood cycles.
该方程是研究河流情势及旱涝周期的基础。
8. Population Change and Density | 人口变化与密度
Demographic calculations are essential for human geography topics including globalisation, regeneration and migration studies.
人口计算是全球化、区域再生与迁移等人文地理课题的基础。
Population Density = Total population / Area
Units: persons per km². Crude birth rate (CBR) and crude death rate (CDR) are expressed per 1000 population.
单位：人/平方公里。粗出生率 (CBR) 与粗死亡率 (CDR) 按每千人计算。
CBR = (Live births / Total population) × 1000
Natural increase = CBR – CDR (per 1000). Net migration = Immigration – Emigration.
自然增长率 = CBR – CDR (每千人)。净迁移 = 迁入 – 迁出。
9. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s Rank (rₛ) assesses the strength and direction of a monotonic relationship between two ranked variables, often used in fieldwork hypothesis testing.
斯皮尔曼等级相关系数 (rₛ) 评估两个排序变量之间单调关系的强度与方向，常用于野外调查假设检验。
rₛ = 1 – (6∑D²) / [n(n² – 1)]
D = difference between ranks for each pair, n = number of pairs. Values range from –1 (perfect negative) to +1 (perfect positive correlation).
D = 每对数据的秩差，n = 样本对数。取值从 –1（完全负相关）到 +1（完全正相关）。
Always state the null hypothesis and check critical value tables at the 0.05 significance level.
务必陈述零假设，并查阅 0.05 显著性水平下的临界值表。
10. Nearest Neighbour Index | 最近邻指数
Nearest neighbour analysis (Rn) measures the spatial distribution of points, such as settlements or retail outlets, revealing whether they are clustered, random or evenly spaced.
最近邻分析 (Rn) 衡量点状地物（如聚落或零售店）的空间分布，揭示其为聚集、随机还是均匀分布。
Rn = 2 d̅ √(n / A)
d̅ = mean observed nearest-neighbour distance (km), n = number of points, A = area of the region (km²).
d̅ = 平均最近邻观测距离 (km)，n = 点数，A = 区域面积 (km²)。
Rn < 1 suggests clustering; Rn ≈ 1 indicates random; Rn > 2.15 suggests regular/uniform distribution.
Rn < 1 表示聚集分布；Rn ≈ 1 为随机；Rn > 2.15 表示均匀分布。
11. Location Quotient (LQ) | 区位商
The location quotient quantifies the concentration of a particular industry or employment sector in a local area relative to the national average, an important concept in regeneration and economic change.
区位商衡量某地区特定产业或就业部门的集中程度相对于全国平均水平，是区域再生与经济变化中的重要概念。
LQ = (Local employment in sector / Total local employment) ÷ (National employment in sector / Total national employment)
An LQ > 1 indicates a higher-than-average concentration (possibly an industrial cluster); LQ < 1 indicates under-representation.
LQ > 1 表示高于平均的集中度（可能是产业集群）；LQ < 1 表示比例偏低。
12. Net Primary Productivity (NPP) | 净初级生产力 (NPP)
NPP represents the rate at which plants store chemical energy through photosynthesis minus the energy used for their own respiration, a key component of the carbon cycle.
NPP 表示植物通过光合作用储存化学能并减去自身呼吸消耗的速率，是碳循环的关键组成部分。
NPP = GPP – R
GPP = gross primary productivity (total carbon fixed by photosynthesis), R = autotrophic respiration (carbon used by plants). Units: grams of carbon per m² per year (gC/m²/yr) or equivalent.
GPP = 总初级生产力（光合作用固定的总碳量），R = 植物自养呼吸消耗的碳。单位：克碳/平方米/年 (gC/m²/yr) 或相当单位。
High NPP values indicate efficient carbon sequestration, vital for understanding terrestrial carbon stores.
高 NPP 表明高效的碳汇，对于理解陆地碳储量至关重要。
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