📚 A-Level Eduqas Geography: Formula and Theorem Quick Reference Handbook | A-Level Eduqas 地理：公式定理速查手册
This handbook brings together the essential quantitative formulas, statistical techniques and conceptual theorems you will encounter throughout the A-Level Eduqas Geography course. From river discharge calculations to the Demographic Transition Model, each entry is presented in clear, paired English‑Chinese paragraphs, with tables and bullet lists where helpful. Use it to consolidate your knowledge and as a last‑minute revision aid before the exam.
本手册汇集了A‑Level Eduqas地理课程中必备的量化公式、统计方法以及概念性定理。从河流流量计算到人口过渡模型，每个条目均以清晰的英中对照段落呈现，并配有表格和项目符号辅助理解。可用以巩固知识，也可作为考前最后冲刺的复习工具。
1. River Discharge | 河流流量
Discharge is the volume of water passing a given cross‑section of a river per unit time. It is expressed as Q = A × v, where Q is discharge (m³ s⁻¹), A is cross‑sectional area (m²) and v is mean velocity (m s⁻¹).
流量是指单位时间内通过河流某一断面的水体体积，公式为 Q = A × v，Q 为流量（m³ s⁻¹），A 为横截面积（m²），v 为平均流速（m s⁻¹）。
To calculate cross‑sectional area, measure water depth at regular intervals across the channel and sum the trapezoidal slices: A = Σ (width of slice × average depth of slice).
计算横截面积时，需在河道等间距测量水深，并以梯形法求和：A = Σ（分段宽度 × 分段平均水深）。
Velocity is commonly measured with a flow meter; if only surface velocity is known, multiply by 0.85 to estimate mean velocity.
流速通常用流速仪测量；若仅知表面流速，乘以 0.85 可估算平均流速。
- Q = A × v
- Units: m³ s⁻¹
- Q = A × v
- 单位：m³ s⁻¹
2. Hydraulic Radius and Wetted Perimeter | 水力半径与湿周
Hydraulic radius (R) relates channel shape to flow efficiency. R = A / P, where A is cross‑sectional area and P is wetted perimeter — the length of the channel boundary in contact with water.
水力半径 (R) 反映了河道形状与水流效率的关系。R = A / P，A 为横截面积，P 为湿周，即河道与水接触的边界长度。
A larger hydraulic radius (short wetted perimeter relative to area) indicates less frictional drag and therefore more efficient flow.
水力半径越大（相对于面积湿周较短），表明摩擦阻力越小，水流效率越高。
| Channel shape | Wetted perimeter (P) | Effect on R |
|---|---|---|
| Wide, shallow | Large | Small R → inefficient |
| Narrow, deep | Relatively small | Large R → efficient |
| 河道形状 | 湿周 (P) | 对 R 的影响 |
|---|---|---|
| 宽浅 | 大 | R 小 → 低效 |
| 窄深 | 相对较小 | R 大 → 高效 |
3. Manning’s Equation (Velocity Estimation) | 曼宁公式（流速估算）
Manning’s equation estimates stream velocity when direct measurement is not possible: v = (1/n) R2/3 S1/2, where v is mean velocity (m s⁻¹), n is Manning roughness coefficient, R is hydraulic radius (m) and S is channel slope.
曼宁公式用于无法直接测量时估算流速：v = (1/n) R2/3 S1/2，v 为平均流速（m s⁻¹），n 为曼宁粗糙系数，R 为水力半径（m），S 为河床坡度。
Roughness coefficient n depends on channel material: smooth concrete ≈ 0.012, natural gravel‑bed rivers ≈ 0.03–0.04, and heavily vegetated channels > 0.07.
粗糙系数 n 取决于河道材质：光滑混凝土约 0.012，天然卵石河床约 0.03–0.04，植被茂密的河道 > 0.07。
This equation helps compare channel efficiency and predict changes in discharge with channel modifications.
该方程有助于比较河道效率，并预测河道改造后的流量变化。
4. Drainage Basin Water Balance | 流域水量平衡
The water balance equation states: P = Q + E + ΔS, where P is precipitation, Q is runoff (streamflow), E is evapotranspiration, and ΔS is change in storage (soil moisture, groundwater, lakes).
水量平衡方程：P = Q + E + ΔS，P 为降水量，Q 为径流量（河川径流），E 为蒸发蒸腾，ΔS 为储水变化量（土壤水分、地下水、湖泊）。
Over a long period (e.g., a hydrological year), ΔS tends to zero, thus P ≈ Q + E. This fundamental relationship underpins flood hydrograph analysis and water resource management.
在较长时段内（如一个水文年），ΔS 趋近于零，因此 P ≈ Q + E。这一基本关系是洪水过程线分析与水资源管理的基础。
The runoff coefficient (C) is the proportion of rainfall that becomes streamflow: C = Q / P. Urbanisation typically increases C due to impermeable surfaces.
径流系数 (C) 是降雨转化为径流的比例：C = Q / P。由于地表不透水，城市化通常会增大径流系数。
5. Storm Hydrograph Indices | 暴雨径流曲线指标
Key indices derived from a storm hydrograph include: lag time (time between peak rainfall and peak discharge), rising limb steepness, and recession constant. Discharge per unit area (specific discharge) = Q / basin area (m³ s⁻¹ km⁻²).
暴雨径流过程线的关键指标包括：滞时（降雨峰值与流量峰值的时间间隔）、涨水段坡度及退水常数。单位面积流量（比流量）= Q / 流域面积（m³ s⁻¹ km⁻²）。
Runoff depth (mm) = (total streamflow volume / basin area) × 1000, allowing comparison between catchments of different size.
径流深度（mm）=（总径流体积 / 流域面积）× 1000，便于不同大小流域间的比较。
6. Demographic Rates and Change | 人口统计率与变动
Crude Birth Rate (CBR) = (number of live births / total population) × 1000 per year. Crude Death Rate (CDR) = (number of deaths / total population) × 1000 per year.
粗出生率 (CBR) =（活产数 / 总人口）× 1000/年。粗死亡率 (CDR) =（死亡人数 / 总人口）× 1000/年。
Natural Increase Rate (%) = [(CBR – CDR) / 1000] × 100. When combined with net migration, total population change = natural increase + net migration.
自然增长率 (%) = [(CBR – CDR) / 1000] × 100。结合净迁移，总人口变动 = 自然增长 + 净迁移。
Population doubling time can be estimated by the ‘Rule of 70’: Doubling time (years) = 70 / annual growth rate (%).
人口倍增时间可用“70法则”估算：倍增时间（年）= 70 / 年增长率（%）。
7. Urbanisation and Density Metrics | 城市化与密度指标
Urban population density = total urban population / urban land area (persons km⁻²). The urbanisation rate is the annual increase in the percentage of people living in urban areas.
城市人口密度 = 城市总人口 / 城市土地面积（人 km⁻²）。城市化率指居住在城市地区的人口百分比年增长量。
Location Quotient (LQ) measures the concentration of a particular industry or service in a region relative to a larger reference area: LQ = (ei / e) / (Ei / E), where ei is local employment in sector i, e is total local employment, Ei and E are national equivalents.
区位商 (LQ) 衡量某产业或服务在区域内的集中度，与更大参考区域相比较：LQ = (ei / e) / (Ei / E)，ei 为当地 i 产业就业人数，e 为当地总就业，Ei 和 E 为国家对应数据。
8. Slope and River Gradient | 坡度与河流比降
Gradient is the vertical drop over a horizontal distance. Stream gradient = (elevation change ÷ horizontal distance) expressed as a ratio (e.g., 1:50) or percentage.
坡度是水平距离上的垂直落差。河道比降 =（高程差 ÷ 水平距离），以比率（如 1:50）或百分比表示。
Sinuosity = channel length / valley length (ratio >1.5 indicates a meandering channel). These simple measurements are fundamental in fluvial geomorphology fieldwork.
弯曲度 = 河道长度 / 谷地长度（比值 >1.5 表示蜿蜒河道）。这些简单测量在河流地貌野外考察中至关重要。
9. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s Rank (rs) tests the strength and direction of a relationship between two sets of ordinal or non‑normal data. The formula is: rs = 1 – (6 Σd²) / [n(n² – 1)], where d is the difference between ranks of each pair, and n is the number of pairs.
斯皮尔曼等级相关系数 (rs) 检验两组定序或非正态数据之间的关系强度与方向。公式为：rs = 1 – (6 Σd²) / [n(n² – 1)]，d 为每对数据等级之差，n 为配对数量。
The result ranges from –1 (perfect negative correlation) to +1 (perfect positive correlation). A value close to 0 indicates no significant rank correlation. Compare with critical values for n to determine significance.
结果范围从 –1（完全负相关）到 +1（完全正相关）。接近 0 表示无显著等级相关。需将其与 n 对应的临界值比较以判断显著性。
10. Global Carbon Cycle Metrics | 全球碳循环指标
Net Primary Productivity (NPP) = Gross Primary Productivity (GPP) – Plant Respiration (Rp). NPP represents the carbon absorbed by plants that is available to the rest of the ecosystem. Units: gC m⁻² yr⁻¹.
净初级生产力 (NPP) = 总初级生产力 (GPP) – 植物呼吸消耗 (Rp)。NPP 代表植物吸收的可供生态系统其他部分利用的碳量，单位：gC m⁻² yr⁻¹。
Carbon footprint (kgCO₂ equivalent) measures total greenhouse gas emissions caused directly and indirectly by an individual, event, organisation or product. It can be estimated using consumption data multiplied by emission factors.
碳足迹（kgCO₂ 当量）衡量由个人、活动、组织或产品直接和间接造成的温室气体排放总量。可利用消费数据乘以排放因子进行估算。
11. Key Theoretical Models (Theorems) | 关键理论模型（定理）
Demographic Transition Model (DTM): links population change to economic development through five stages, from high fluctuating birth and death rates to low fluctuating rates.
人口过渡模型 (DTM)：将人口变化与经济发展联系起来，分为五个阶段，从高出生率和高死亡率波动，到低出生率和低死亡率波动。
Bradshaw Model: describes downstream changes in river channel characteristics; variables such as discharge, velocity and hydraulic radius increase, while bedload particle size and gradient decrease.
Bradshaw 模型：描述了河道特征沿下游的变化；流量、流速和水力半径等变量增大，而河床负载粒径和比降减小。
Park’s Urban Model (or Burgess/Hoyt): explains intra‑urban land use patterns; concentric zones (Burgess) or sectors (Hoyt) with a CBD core.
Park 城市模型（或 Burgess/Hoyt）：解释了城市内部土地利用格局；CBD 核心周围的同心圆（Burgess）或扇形（Hoyt）结构。
Clark–Fisher Model: describes the shift of employment from primary to secondary to tertiary sectors as a country develops.
Clark–Fisher 模型：描述了随着国家发展，就业从第一产业向第二、第三产业转移的趋势。
Kuznets Environmental Curve: hypothesises that environmental degradation increases during early economic development then decreases after a turning point of income.
库兹涅茨环境曲线：假设环境退化在经济发展初期加剧，达到收入拐点后逐渐减轻。
12. Standard Deviation and Data Spread | 标准差与数据离散度
Standard deviation (σ) measures the dispersion of a dataset around the mean. Formula: σ = √[ Σ(x – x̄)² / n ] for a population, or using n–1 for a sample.
标准差 (σ) 衡量数据围绕均值的离散程度。公式：总体 σ = √[ Σ(x – x̄)² / n ]，样本则用 n–1。
A small standard deviation indicates data points are closely clustered around the mean; a large value indicates wide spread. This is essential for analysing fieldwork data such as pebble size distributions or rainfall variability.
标准差小表示数据点紧密聚集在均值周围；大则表示分布广泛。在分析野外数据（如卵石粒径分布或降雨变率）时，这一点必不可少。
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