📚 AQA Year 12 Geography: Formula & Theorem Quick Reference Handbook | AQA 12年级地理：公式定理速查手册
This concise handbook gathers all the essential quantitative formulas, statistical tests, and key geographical theorems required for the AQA Year 12 Geography curriculum. From demographic calculations to hydrological equations and fieldwork measures, each entry is paired with clear definitions and practical applications to support revision and exam success.
这本速查手册汇集了 AQA 12年级地理课程中所有关键的定量公式、统计检验以及重要地理定理。从人口统计计算到水文方程和实地测量公式，每一条目都配有清晰的定义和实际应用，帮助巩固复习并提升考试成绩。
1. Demographic Formulas | 人口统计公式
Natural Increase Rate (NIR) reveals how fast a population grows excluding migration. It is expressed as a percentage obtained from crude birth and death rates per 1000 people.
自然增长率 (NIR) 反映了不包含迁移情况下人口的增长速度。它以百分比表示，通过每千人出生率和死亡率计算得出。
NIR (%) = (CBR - CDR) / 10
deaths per 1000 people per year. For example, a CBR of 28 and a CDR of 8 give an NIR of 2.0%.
其中 CBR 为年每千人的活产数，CDR 为年每千人的死亡数。例如，出生率28，死亡率8，自然增长率即为2.0%。
Total Population Growth Rate (PGR) accounts for both natural change and net migration, expressing annual change as a percentage of the mid-year population.
总人口增长率 (PGR) 同时计算自然变动和净迁移，将年变化表示为年中人口的百分比。
PGR (%) = ((Births - Deaths) + (Immigration - Emigration)) / Mid-year pop × 100
The doubling time approximates how many years it takes for a population to double at a constant growth rate, using the 'rule of 70'.
人口倍增时间用"70法则"估算在恒定增长率下人口翻番所需的年数。
Doubling time (years) ≈ 70 / Growth rate (%)
The General Fertility Rate (GFR) calculates births per 1000 women of reproductive age, typically 15-49 years.
一般生育率 (GFR) 计算每千名育龄妇女（通常15-49岁）对应的活产数。
GFR = (Live births / Women aged 15-49) × 1000
Dependency ratio measures the economic burden on the productive population by comparing non-working (under 15 and over 65) to working-age groups.
抚养比通过对比非劳动年龄人口（15岁以下及65岁以上）与劳动年龄人口，衡量生产性人口的经济负担。
Dependency Ratio = ((Pop₀₋₁₄ + Pop₆₅₊) / Pop₁₅₋₆₄) × 100
2. Migration & Urbanisation Metrics | 迁移与城市化指标
Net migration rate quantifies the difference between people entering and leaving a region per 1000 inhabitants.
净迁移率量化了每千名居民中进入和离开某地区的差值。
Net migration rate = (Immigration - Emigration) / Mid-year pop × 1000
Urbanisation level is the percentage of total population living in urban areas, indicating the degree of spatial concentration.
城市化水平指居住在城镇地区的人口占总人口的百分比，反映空间集中程度。
Urbanisation (%) = (Urban population / Total population) × 100
Urban growth rate specifically measures how fast the urban population itself is expanding over time.
城镇人口增长率专门衡量城镇人口随时间扩张的速度。
Urban growth rate (%) = ((Urban popₜ₂ - Urban popₜ₁) / Urban popₜ₁) × 100
Location Quotient (LQ) identifies local specialisation in a particular economic sector compared to the national average.
区位商 (LQ) 通过对比全国平均水平，识别出地方某个经济部门的专业化程度。
/ Total local employment) / (National employment in sector X / Total national employment)
3. Water Balance & Hydrological Cycle | 水文平衡与水循环方程
The fundamental water balance equation links precipitation, runoff, evaporation, and storage change in a drainage basin over a given period.
基本水量平衡方程将一定时期内流域的降水、径流、蒸发和储水量变化联系在一起。
P = Q + E + ΔS
= change in storage (soil moisture, groundwater, surface water). All terms in millimetres.
其中 P 为降水量，Q 为径流量，E 为蒸散量，ΔS 为储水量变化（包括土壤水、地下水、地表水）。所有项均以毫米计。
Runoff coefficient expresses what fraction of precipitation becomes streamflow, indicating catchment wetness and infiltration capacity.
径流系数表示降水中变为河川径流的比例，反映了集水区的湿润程度和下渗能力。
Runoff coefficient = Runoff / Precipitation
Soil moisture deficit arises when potential evapotranspiration (PET) exceeds actual evapotranspiration (AET); the stored water is being depleted.
当潜在蒸散量超过实际蒸散量时出现土壤水分亏缺，意味着储存的水分正在消耗。
Soil moisture deficit = PET - AET (when PET > AET)
Infiltration rate, measured in mm per hour, can be calculated from field data using the drop in water level over time in a ring infiltrometer.
下渗率以毫米每小时计，可通过环式入渗仪中水位随时间的下降值计算得出。
4. River Discharge & Hydraulic Geometry | 河流流量与水力学几何
River discharge, the volume of water flowing past a cross-section per second, is the product of wetted area and mean velocity.
河流流量是每秒通过横截面的水量，由过水断面面积与平均流速相乘得到。
Q = A × v
mean velocity (m/s). Area is calculated from channel width and average depth measurements.
其中 Q 为流量(立方米/秒)，A 为横截面积(平方米)，v 为平均流速(米/秒)。面积通过河宽和平均水深测量值计算。
Hydraulic radius describes the efficiency of the channel cross-section; a larger R indicates less frictional resistance from the bed and banks.
水力半径刻画了河道横断面的效率；较大的 R 值意味着河床与岸壁的摩擦阻力较小。
Hydraulic radius R = A / Pw
Pw is the wetted perimeter (m). In broad shallow channels, R approximates average depth. Bradshaw's model provides key downstream trends in hydraulic geometry: discharge, channel width, depth and mean velocity all increase downstream, while bedload particle size decreases.
Pw 为湿周(米)。在宽浅河道中，R 约等于平均水深。布拉德肖模型给出了水力学几何的关键下游趋势：流量、河宽、水深和平均流速均向下游增加，而河床负荷粒径减小。
5. Coastal Wave Energy & Budget | 海岸波浪能量与沉积物收支
Wave power per unit length of wave crest is a function of wave height and period, determining the energy available for erosion and transport.
单位波峰长度的波浪功率是波高与波周期的函数，决定了可用于侵蚀和搬运的能量。
P = (ρ g² H² T) / (64π)
ight (m), T = wave period (s). Higher, longer-period waves carry dramatically more energy.
其中 ρ 为水体密度(海水取1025千克/立方米)，g = 9.81米/秒²，H 为有效波高(米)，T 为波周期(秒)。更高、周期更长的波浪所携带的能量会剧增。
Sediment budget quantifies gains and losses of material on a coastal cell, much like a bank account.
沉积物收支量化了一个海岸单元内物质的输入与输出，好比一个银行账户。
Net change = Σ Inputs - Σ Outputs
Sources include river discharge, cliff erosion and onshore transport; sinks include offshore bars, deep water loss and dune building. Longshore drift rate (m³/year) can be estimated using trap data or tracer pebbles.
物源包括河流输沙、悬崖侵蚀和向岸搬运；汇则包括离岸沙坝、深水损失和沙丘堆积。沿岸漂移速率(立方米/年)可利用集沙器或示踪砾石数据估算。
6. Carbon Cycle Flux Formulas | 碳循环通量公式
Net primary productivity (NPP) is the chemical energy left in plant biomass after respiration, a key carbon flux in terrestrial ecosystems.
净初级生产力 (NPP) 是植物呼吸作用后残存在生物量中的化学能，是陆地生态系统的关键碳通量。
NPP = GPP - R
GPP is gross primary productivity (total carbon fixed by photosynthesis), and R is autotrophic respiration. Both are expressed in units of gC/m²/year or PgC/year.
GPP 为总初级生产力(光合作用固定的总碳)，R 为自养呼吸。两者均以克碳/平方米/年或百亿吨碳/年表示。
The photosynthesis summary equation shows how carbon dioxide is reduced to carbohydrate, underpinning the carbon fixation process.
光合作用总方程式展示了二氧化碳如何被还原为碳水化合物，构成碳固定过程的基础。
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂
arbon in a store can be approximated as store size divided by inflow rate, though this is often examined qualitatively.
关键的全球碳储量和通量通常以百亿吨(1 Pg = 10¹² 千克)比较。碳在某个储库中的停留时间可用储量除以流入速率近似估算，但考试中多作定性分析。
7. The Hjulström Curve & Sediment Transport | 尤尔斯特伦曲线与沉积物运输
The Hjulström curve graphically relates particle size to the critical flow velocity needed for erosion, transportation, and deposition in rivers.
尤尔斯特伦曲线用图形显示了颗粒大小与河流侵蚀、搬运和沉积所需的临界流速之间的关系。
The curve reveals that fine cohesive clays require higher velocities to erode than sand, because of electrostatic cohesion, but once suspended they travel longest.
该曲线揭示，细颗粒粘性粘土因其静电内聚力，启动侵蚀所需的流速反而比砂粒更高，但一旦悬浮，它们的搬运距离最远。
River competence is the largest particle diameter a river can transport; capacity is the total mass of sediment it can carry. Both increase sharply during floods.
河流搬运力是指河流能搬运的最大颗粒直径；搬运量则是其能携带的沉积物总质量。两者在洪水期均急剧增加。
Stokes' Law for settling velocity indicates that a particle's fall velocity v in still water is proportional to the square of its grain diameter d (v ∝ d²), explaining why fine silts remain in suspension far longer than sands.
沉降速度的斯托克斯定律指出，颗粒在静水中的沉降速度 v 与其粒径 d 的平方成正比(v ∝ d²)，这解释了为何细粉砂比砂粒保持悬浮的时间长得多。
8. Statistical Tests: Spearman's Rank | 统计检验：斯皮尔曼等级相关
Spearman's rank correlation (rₛ) tests the strength and direction of association between two ranked variables; it is widely used in geography fieldwork.
斯皮尔曼等级相关系数 (rₛ) 检验两个排序变量之间的关联强度和方向；该方法在地理实地考察中应用广泛。
rₛ = 1 - (6 ∑ d²) / (n (n² - 1))
of paired observations. The value ranges from -1 (perfect negative) to +1 (perfect positive), with 0 indicating no correlation.
其中 d 为每对数值的等级之差，n 为成对观测值的数量。数值范围从-1(完全负相关)到+1(完全正相关)，0表示无相关。
To test significance, calculated rₛ is compared to critical values at a chosen significance level (usually 0.05) for the given n. If rₛ exceeds the critical value, the correlation is statistically significant and not due to chance.
为检验显著性，需将计算出的 rₛ 与给定 n 和所选的显著性水平(通常0.05)下的临界值进行比较。若 rₛ 大于临界值，则该相关在统计上显著，并非巧合。
9. Statistical Tests: Chi-squared Test | 统计检验：卡方检验
The chi-squared test (χ²) assesses whether there is a significant difference between observed
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