📚 Pre-U WJEC Geography: Quick Reference Handbook of Formulas and Principles | Pre-U WJEC 地理：公式定理速查手册
This quick-reference handbook collates the essential quantitative formulas, key principles, and conceptual models required for the Pre-U WJEC Geography syllabus. Mastery of these tools will strengthen your ability to analyse data, interpret geographical processes, and construct well-supported arguments in both physical and human geography.
本速查手册整理了 Pre-U WJEC 地理大纲所要求的基本定量公式、关键原理和概念模型。掌握这些工具将增强你分析数据、解读地理过程以及在自然与人文地理中构建有据可依的论点的能力。
1. Drainage Basin Hydrology | 流域水文学
River discharge is the volume of water passing a cross-section per unit time. The fundamental equation links cross-sectional area with flow velocity. This relationship underpins flood prediction, river regime analysis, and storm hydrograph construction.
河流流量是单位时间内通过某一横断面的水量。基本方程将横截面积与流速联系起来。这一关系是洪水预测、河流情势分析和暴雨洪水过程线构建的基础。
Q = A × V
Where Q is discharge (m³/s), A is cross-sectional area (m²), and V is mean velocity (m/s). Velocity can be measured using a flowmeter or approximated from surface float measurements multiplied by a correction factor (typically 0.8–0.9).
其中 Q 为流量（m³/s），A 为横截面积（m²），V 为平均流速（m/s）。流速可用流速计测量，或用浮标法测定水面流速并乘以校正系数（通常为 0.8–0.9）来近似。
Another critical index is drainage density, which quantifies the degree of landscape dissection by streams. High drainage density indicates rapid runoff, steep slopes, and impermeable surfaces.
另一个关键指标是水系密度，它量化了河流对地表的切割程度。高水系密度表明径流迅速、坡度陡峭且地表不透水。
Dd = ΣL / Ab
Dd is drainage density (km/km²), ΣL is total length of all stream channels in the basin (km), and Ab is the drainage basin area (km²).
Dd 为水系密度（km/km²），ΣL 为流域内所有河道总长度（km），Ab 为流域面积（km²）。
2. Channel Morphology and Gradient | 河道形态与坡度
Channel gradient is a primary control on stream energy, sediment transport, and valley shape. It is calculated as the ratio of vertical drop to horizontal distance, often expressed as a percentage or in degrees.
河道坡度是控制河流能量、泥沙输移和河谷形态的主要因素。其计算方式为垂直落差与水平距离之比，通常以百分比或度数表示。
Gradient = (Vertical Interval / Horizontal Equivalent) × 100%
The hydraulic radius describes channel efficiency: a larger value indicates a more efficient cross-section with less frictional resistance. This concept is vital when applying the Manning equation to estimate velocity in uniform channels.
水力半径描述河道效率：数值越大，表明横断面越高效，摩擦阻力越小。在应用曼宁公式估算均匀河道的流速时，这一概念至关重要。
R = A / P
R is hydraulic radius (m), A is cross-sectional area (m²), and P is wetted perimeter (m).
R 为水力半径（m），A 为横截面积（m²），P 为湿周（m）。
3. Coastal Processes and Wave Equations | 海岸过程与波浪方程
In coastal systems, the power of waves and the rate of longshore drift can be approximated. Wave energy is proportional to the square of wave height, making storm waves disproportionately more powerful.
在海岸系统中，波浪的能量和沿岸漂移速率可进行近似计算。波浪能量与波高的平方成正比，因此风暴浪的能量远大于其波高增加的比例。
E ∝ H²
Wave steepness determines breaking characteristics and beach morphology. It is the ratio of wave height to wavelength; waves break when steepness exceeds approximately 1:7.
波浪陡度决定破碎特征和海滩形态。它是波高与波长之比；当陡度超过约 1:7 时波浪破碎。
Steepness = H / L
Longshore drift transport rate (Ql) can be modelled using the CERC formula, but a simplified understanding is that it depends on wave energy and angle of approach.
沿岸漂移输沙率（Ql）可用 CERC 公式模拟，但简化的理解是其取决于波浪能量和入射角度。
4. Demographic Indicators and Population Change | 人口指标与人口变化
Population dynamics are expressed through crude birth rate, crude death rate, and natural increase rate. These are fundamental to the Demographic Transition Model and population projection.
人口动态通过粗出生率、粗死亡率和自然增长率来表达。这些是人口转变模型和人口预测的基础。
CBR = (Number of live births / Total population) × 1000
CDR = (Number of deaths / Total population) × 1000
Natural Increase Rate = CBR – CDR (per 1000)
Percentage natural increase is (CBR – CDR) / 10, giving an annual percentage. The rule of 70 allows quick estimation of doubling time for a population growing at a constant rate.
人口自然增长率百分比为 (CBR – CDR) / 10，得到年百分比。70 法则可以快速估算以恒定速率增长的人口倍增所需的时间。
Doubling Time (years) ≈ 70 / Growth Rate (%)
Net migration rate incorporates both immigration and emigration to give the overall migration balance per 1000 population.
净迁移率综合了迁入和迁出，得出每千人的总体迁移平衡。
Net Migration Rate = (Immigrants – Emigrants) / Total population × 1000
5. Population Structure and Dependency | 人口结构与抚养比
Population pyramids reveal age-sex structure and allow calculation of dependency ratios. The total dependency ratio measures the economic pressure on the working-age population.
人口金字塔揭示年龄性别结构，并可计算抚养比。总抚养比衡量了劳动年龄人口所承受的经济压力。
Total Dependency Ratio = [(Pop₀₋₁₄ + Pop₆₅₊) / Pop₁₅₋₆₄] × 100
Youth and old-age dependency can be separated to highlight specific social policy needs. Ageing populations exhibit a high old-age dependency ratio.
少儿抚养比和老年抚养比可以分开计算，以突出特定的社会政策需求。老龄化人口表现为较高的老年抚养比。
Youth Dependency Ratio = (Pop₀₋₁₄ / Pop₁₅₋₆₄) × 100
Old-age Dependency Ratio = (Pop₆₅₊ / Pop₁₅₋₆₄) × 100
Sex ratio is another simple but revealing indicator, especially for understanding migration patterns and cultural preferences.
性别比是另一个简单但能揭示诸多问题的指标，尤其有助于理解迁移模式和文化偏好。
Sex Ratio = (Number of males / Number of females) × 100
6. Migration and Population Projections | 迁移与人口预测
Total population change is the sum of natural change and net migration. This equation is used in the balancing equation for any population unit.
总人口变化是自然变动与净迁移之和。该方程用于任何人口单元的人口平衡方程。
ΔP = (Births – Deaths) + (Immigrants – Emigrants)
Inter-regional migration can be forecast using the gravity model. The model posits that interaction between two places is proportional to the product of their populations and inversely proportional to some power of distance.
区域间迁移可用引力模型进行预测。该模型假设两地之间的相互作用与它们人口的乘积成正比，与距离的某次幂成反比。
Iₐₙ ∝ (Pₐ × Pₙ) / Dₐₙ²
Effort is made to calibrate the model with a friction of distance exponent (often β = 2, but can vary). Migration efficiency measures the net redistribution relative to gross exchanges.
通常会用一个距离摩擦指数（常为 β = 2，但可变化）对模型进行校准。迁移效率衡量净再分配相对于总交换的比例。
7. Urban Geography and Rank-Size Rule | 城市地理与位序—规模法则
Urban hierarchy and primacy are studied using the rank-size rule. This empirical regularity states that the population of a city is inversely proportional to its rank in the urban hierarchy.
城市等级体系和首位度可用位序—规模法则进行研究。这一经验规律指出，城市人口与其在城市等级体系中的位序成反比。
Pₙ = P₁ / n
Where Pₙ is the population of the nth largest city, and P₁ is the population of the largest city. When the rule does not hold, a primate or binary distribution may be observed, indicating particular historical or economic processes.
其中 Pₙ 为第 n 大城市的人口，P₁ 为最大城市的人口。当该法则不成立时，可能出现首位型或双核型分布，表明特定的历史或经济过程。
Urbanisation level is the proportion of people living in urban areas. It is fundamental to tracking global urban transition.
城市化水平是居住在城市地区的人口比例。它是跟踪全球城市转型的基础。
Urbanisation Level = (Urban Population / Total Population) × 100%
Tempo of urbanisation refers to the rate of change of this proportion, often expressed as percentage point change per year.
城市化速度是指该比例的变化率，通常用每年百分点变化表示。
8. Economic and Development Indicators | 经济与发展指标
Gross Domestic Product per capita is a proxy for average income, but it masks inequality. Purchasing Power Parity adjustments improve cross-country comparability.
人均国内生产总值是平均收入的替代指标，但它掩盖了不平等。购买力平价调整提高了跨国可比性。
Location Quotient (LQ) identifies the regional concentration of an industry relative to the national average. LQ > 1 suggests a regional specialisation.
区位商（LQ）用于识别某一产业相对于全国平均水平的区域集中程度。LQ > 1 表明区域专业化。
LQ = (eᵢ / e) / (Eᵢ / E)
Where eᵢ is regional employment in industry i, e is total regional employment, Eᵢ is national employment in industry i, and E is total national employment.
其中 eᵢ 为 i 产业区域就业人数，e 为区域总就业人数，Eᵢ 为 i 产业全国就业人数，E 为全国总就业人数。
The Gini coefficient measures income inequality. It is derived from the Lorenz Curve, where the area between the line of equality and the Lorenz curve is compared to the total area under the line of equality. The coefficient ranges from 0 (perfect equality) to 1 (perfect inequality).
基尼系数衡量收入不平等。它由洛伦兹曲线导出，其中绝对平等线与洛伦兹曲线之间的面积与绝对平等线下的总面积相比较。系数范围从 0（完全平等）到 1（完全不平等）。
Gini = A / (A + B)
A is the area between the line of perfect equality and the Lorenz curve; B is the area below the Lorenz curve.
A 为绝对平等线与洛伦兹曲线之间的面积；B 为洛伦兹曲线下方的面积。
9. Energy, Climate and the Atmospheric System | 能量、气候与大气系统
The Earth’s energy balance can be expressed through net radiation. The basic equation accounts for incoming solar radiation, reflected shortwave, and longwave exchanges.
地球能量平衡可通过净辐射来表示。基本方程考虑了入射太阳辐射、反射短波辐射以及长波辐射收支。
Q* = (K↓ – K↑) + (L↓ – L↑)
Albedo, the fraction of solar radiation reflected by a surface, is central to understanding microclimates and feedback processes. High albedo surfaces (snow, ice) cool the local environment.
反照率，即地表反射的太阳辐射比例，是理解微气候和反馈过程的核心。高反照率表面（雪、冰）使局部环境变冷。
Albedo = K↑ / K↓
The environmental lapse rate and the dry/moist adiabatic lapse rates govern atmospheric stability. The average environmental lapse rate is about 6.5 °C per 1000 m.
环境直减率和干/湿绝热直减率决定大气稳定度。平均环境直减率约为每 1000 米 6.5 °C。
10. Ecosystem Productivity and Biomass | 生态系统生产力与生物量
Primary productivity underpins food chains and biogeochemical cycles. Gross primary productivity is total carbon fixed by photosynthesis; net primary productivity is GPP minus plant respiration.
初级生产力支撑着食物链和生物地球化学循环。总初级生产力是光合作用固定的总碳量；净初级生产力是 GPP 减去植物呼吸消耗。
NPP = GPP – Rplant
Productivity is often expressed in grams of carbon per square metre per year (gC/m²/yr). The efficiency of energy transfer between trophic levels is typically around 10%, a rule known as the ten percent law.
生产力通常以每年每平方米碳克数（gC/m²/yr）表示。营养级之间的能量传递效率通常约 10%，这一规律称为十分之一定律。
Transfer Efficiency = (Energy at trophic level n+1 / Energy at trophic level n) × 100
Biomass accumulation is the net result of NPP minus losses due to herbivory, decomposition, and disturbance.
生物量积累是 NPP 减去植食、分解和干扰损失后的净结果。
11. Hazard and Risk Assessment | 灾害与风险评估
Risk is a function of hazard probability, vulnerability, and exposure. This conceptual formula is used in disaster management planning.
风险是致灾因子概率、脆弱性和暴露度的函数。这一概念性公式用于灾害管理规划。
Risk = Hazard × Vulnerability × Exposure
In seismic hazard analysis, the moment magnitude scale supersedes the Richter scale for large events. The moment magnitude (Mw) relates to the seismic moment (M₀), which depends on fault area, average slip, and rock rigidity.
在地震危险性分析中，矩震级标度取代里氏震级用于大地震。矩震级（Mw）与地震矩（M₀）相关，后者取决于断层面积、平均滑移量和岩石刚度。
M₀ = μ × A × D
μ is rock rigidity, A is fault rupture area, and D is average displacement. Mw is then derived as (2/3) log₁₀M₀ – 10.7.
μ 为岩石刚度，A 为断层破裂面积，D 为平均位移。然后 Mw 由 (2/3) log₁₀M₀ – 10.7 推导得出。
Recurrence intervals for flood events can be estimated from historical records using the Gumbel distribution, but a simple approach determines the rank-based return period.
洪水事件的重现期可利用耿贝尔分布从历史记录估算，但一种简单方法能确定基于排序的重现期。
Return Period (T) = (n + 1) / m
n is the number of years on record, and m is the rank of each flow magnitude.
n 为记录年数，m 为每次流量大小的排序位次。
12. Spatial Interaction and Globalisation | 空间相互作用与全球化
The coefficient of specialisation compares the industrial structure of a region with a reference area. A value of 0 indicates an identical structure; higher values signal greater specialisation.
专门化系数将一个区域的产业结构与参照区进行比较。数值为 0 表示结构相同；数值越高，表明专门化程度越高。
CS = ½ Σ |(eᵢ / e) – (Eᵢ / E)|
Globalisation indices often composite data on trade, FDI, migration, and cultural flows. The KOF Globalisation Index is a commonly cited measure.
全球化指数通常综合了贸易、FDI、移民和文化流动数据。KOF 全球化指数是一个常被引用的指标。
Trade-to-GDP ratio is a simple indicator of an economy’s openness.
外贸依存度是衡量一个经济体开放程度的简单指标。
Trade Openness = (Exports + Imports) / GDP × 100%
These formulas, when applied correctly, provide quantitative evidence for geographical inquiry and support synoptic evaluation across the core themes of the Pre-U specification.
这些公式在正确运用时，能为地理探究提供定量证据，并支持 Pre-U 大纲核心主题的跨专题综合评价。
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