📚 Year 12 CCEA Geography: Formula and Theorem Quick Reference Handbook | Year 12 CCEA 地理：公式定理速查手册
This quick reference handbook summarises key formulas, theorems, and quantitative relationships required for the Year 12 CCEA Geography specification. It draws together essential numerical concepts from fluvial geomorphology, population studies, urban geography, and climatology. Mastery of these tools will strengthen your data-response skills and help you interpret geographical patterns with precision.
这本速查手册汇总了 Year 12 CCEA 地理课程所要求的核心公式、定理和定量关系，涵盖河流地貌、人口研究、城市地理和气候学中的关键数值概念。熟练掌握这些工具将增强你的数据分析能力，帮助你精准地解释地理格局。
1. Stream Ordering (Strahler) | 斯特拉勒河流分级
Strahler’s stream ordering system classifies river channels hierarchically. A first‑order stream has no tributaries. When two streams of the same order join, the resulting stream takes the next order. When streams of different orders meet, the order remains that of the higher order. This classification underpins Horton’s laws of drainage composition.
斯特拉勒河流分级系统将河道进行层次分类。一级河流没有支流；两条同级河流汇合后，级别升高一级；不同级河流汇合则保持较高的级别。这一分类是霍顿水系组成定律的基础。
2. Bifurcation Ratio (Horton’s Law) | 分叉比（霍顿定律）
Bifurcation ratio (Rb) is defined as the number of streams of a given order (Nu) divided by the number of streams of the next higher order (Nu+1). For most natural basins, Rb typically lies between 3.0 and 5.0. Values much above or below this range may indicate structural control or recent disturbance.
分叉比（Rb）定义为某级河流的数量（Nu）除以高一级河流的数量（Nu+1）。在大多数天然流域中，Rb 通常在 3.0 至 5.0 之间。远高于或低于此范围的值可能表明构造控制或近期干扰。
Rb = Nu / Nu+1
3. Drainage Density | 排水密度
Drainage density (D) expresses the total length of stream channels per unit area of a drainage basin. It is a fundamental measure of landscape dissection, reflecting the balance between infiltration and surface runoff. High drainage density implies rapid runoff and steep slopes, while low density suggests permeable geology and gentler terrain.
排水密度（D）表示流域单位面积上的河流总长度，是衡量地表切割程度的基本指标，反映入渗与地表径流之间的平衡。高排水密度意味着快速的径流和陡峭的坡度，而低排水密度则暗示透水性良好的地质和较平缓的地形。
D = ΣL / A
where ΣL = total stream length (km) and A = basin area (km²).
式中 ΣL 为河流总长度（公里），A 为流域面积（平方公里）。
4. Stream Frequency | 河流频率
Stream frequency (F) is the number of stream segments per unit area. Together with drainage density, it helps distinguish between basins with many short, steep headwater channels and those with fewer, longer trunk streams. It is particularly useful in morphometric comparison of catchments.
河流频率（F）是单位面积内的河流段数量。与排水密度一起，它有助于区分拥有大量短小陡峭源头河道的流域和拥有较少但更长干流的流域。在流域形态计量比较中特别有用。
F = N / A
where N = total number of stream segments and A = basin area.
式中 N 为河流段总数，A 为流域面积。
5. Hydraulic Radius and Velocity | 水力半径与流速
Hydraulic radius (R) is the cross‑sectional area of flow divided by the wetted perimeter. It is a key control on flow efficiency: a larger hydraulic radius means less friction relative to the volume of water, producing faster mean velocity. The relationship links channel shape to stream power.
水力半径（R）是过流断面面积除以湿周。它是控制水流效率的关键因素：水力半径越大，相对于水量而言摩擦力越小，从而产生更快的平均流速。这一关系将河道形状与水流功率联系起来。
R = Ac / P
where Ac = cross‑sectional area (m²) and P = wetted perimeter (m).
式中 Ac 为过流断面面积（平方米），P 为湿周（米）。
6. Manning’s Equation | 曼宁公式
Manning’s equation estimates mean velocity (V) in an open channel. It combines hydraulic radius, channel slope, and a roughness coefficient (n). Used widely in flood modelling, the formula shows that velocity increases with greater hydraulic radius and steeper gradient but decreases with higher roughness.
曼宁公式用于估算明渠的平均流速（V）。它综合了水力半径、河道坡降和糙率系数（n）。该公式广泛应用于洪水模拟，表明流速随着水力半径增大和坡度变陡而增加，但随糙率增大而降低。
V = (1/n) R²⁄₃ S¹⁄₂
where R = hydraulic radius, S = channel slope (gradient), and n = Manning’s roughness coefficient.
式中 R 为水力半径，S 为河道坡降，n 为曼宁糙率系数。
7. Population Change Formulas | 人口变化公式
The fundamental demographic equation expresses population change as a function of births, deaths, and net migration. Crude birth rate (CBR) and crude death rate (CDR) are expressed per 1000 population, while the rate of natural increase (RNI) is often given as a percentage.
基本的人口学方程将人口变化表示为出生、死亡和净迁移的函数。粗出生率（CBR）和粗死亡率（CDR）以每千人表示，而自然增长率（RNI）通常以百分比给出。
RNI (%) = (CBR − CDR) / 10
Total population change incorporates net migration:
总人口变化还需计入净迁移：
ΔP = (Births − Deaths) + (Immigration − Emigration)
8. Population Density and Dependency Ratio | 人口密度与抚养比
Population density measures the number of people per unit area. The dependency ratio compares the non‑working‑age population (under 15 and over 64) to the working‑age population (15–64), giving an indication of the economic burden on the productive sector.
人口密度衡量单位面积的人口数量。抚养比将非劳动年龄人口（15 岁以下及 64 岁以上）与劳动年龄人口（15–64 岁）进行比较，反映生产性部门的经济负担程度。
Dependency Ratio = [(P0–14 + P65+) / P15–64] × 100
where each P represents the population in the respective age group.
式中每个 P 代表相应年龄组的人口。
9. Urban Primacy and Rank-Size Rule | 城市首位度与位序-规模法则
The rank‑size rule states that the population of a city is inversely proportional to its rank in the urban hierarchy. If the largest city has population P₁, the nth‑largest city is expected to have a population of P₁ / n. Urban primacy describes a condition where the largest city is disproportionately larger than the second‑ranked city.
位序-规模法则指出，城市的人口与其在城市体系中的位序成反比。如果最大城市的人口为 P₁，则第 n 大城市的人口预期为 P₁ / n。城市首位度则描述最大城市相对于第二大城市过于庞大的现象。
Primacy Index = P₁ / P₂
where P₁ = population of the largest city and P₂ = population of the second‑largest city. A value above 2 often indicates strong primacy.
式中 P₁ 为最大城市的人口，P₂ 为第二大城市的人口。数值大于 2 通常表示较强的首位度。
10. Rainfall Variability and Effective Rainfall | 降雨变率与有效降雨
Rainfall variability expresses the year‑to‑year dependability of precipitation. Effective rainfall (also called runoff depth) is the portion of total precipitation that becomes streamflow after accounting for evapotranspiration and infiltration losses. It is essential for water‑budget calculations.
降雨变率反映降水的年际稳定性。有效降雨（也称径流深）是总降水量中扣除蒸散发和入渗损失后形成河川径流的部分，对水量平衡计算至关重要。
Coefficient of Variation (CV) = (σ / μ) × 100
where σ = standard deviation of annual rainfall and μ = mean annual rainfall.
式中 σ 为年降雨量的标准差，μ 为多年平均降雨量。
Effective Rainfall = Total Precipitation − (Evapotranspiration + Interception + Infiltration)
11. Rate of Erosion and Sediment Yield | 侵蚀速率与产沙量
The rate of cliff or bank retreat can be estimated by dividing the horizontal loss of land by the monitoring period. Sediment yield measures the total mass of sediment removed from a catchment per unit area per year, linking slope processes to basin‑scale denudation.
悬崖或河岸的后退速率可通过将土地的水平损失除以监测时段来估算。产沙量则衡量流域每年单位面积被移走的总泥沙质量，将坡面过程与流域尺度的剥蚀联系起来。
Erosion Rate = Retreat Distance / Time
Sediment Yield = Total Sediment Load / Basin Area / Year
Units are usually metres per year for erosion rate and tonnes km⁻² yr⁻¹ for sediment yield.
侵蚀速率的单位通常为米/年，产沙量为吨/平方公里/年。
12. Infiltration Capacity (Horton) | 下渗容量（霍顿）
Horton’s infiltration model describes how the infiltration capacity of soil declines over time during a rainstorm, starting from an initial maximum (f₀) and falling exponentially to a steady‑state minimum (fc). The curve explains why surface runoff is delayed until rainfall intensity exceeds infiltration capacity.
霍顿下渗模型描述了暴雨期间土壤下渗容量如何随时间下降，从初始最大值（f₀）呈指数衰减至稳定最小值（fc）。该曲线解释了为何只有当降雨强度超过下渗容量时才会产生地表径流。
f(t) = fc + (f₀ − fc) e−kt
where f(t) = infiltration capacity at time t, fc = final constant rate, f₀ = initial capacity, k = decay constant, and t = time since the start of rainfall.
式中 f(t) 为 t 时刻的下渗容量，fc 为最终稳定速率，f₀ 为初始下渗容量，k 为衰减常数，t 为自降雨开始以来的时间。
Published by TutorHao | Geography Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导