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理性公式:峰值径流 Q = C·i·A
Rational Method: peak runoff Q = C·i·A
Q=C·i·A/3.6=4.86m³/s · 径流系数×强度×面积 · 铺装→峰增
More paving (higher C) → higher peak; Q scales linearly with C, i, A
SCS 曲线数法:径流深 Q
SCS Curve Number: runoff depth Q
Q=(P−0.2S)²/(P+0.8S) · S=25400/CN−254 · CN80,P100→Q50.5mm
Q=(P−0.2S)²/(P+0.8S), S=25400/CN−254; higher CN → more runoff
单位线与暴雨过程线卷积
Unit Hydrograph & Storm Convolution
单位净雨直接径流 · 卷积Q(n)=ΣP(m)UH(n−m+1) · 三角形
Storm direct runoff = excess-rainfall hyetograph ✳ unit hydrograph
降雨强度-历时-频率(IDF)曲线
Rainfall Intensity-Duration-Frequency (IDF) Curves
i=a/(d+b)^n · d30→145.6mm/h · 历时↑强度↓ 重现期↑强度↑
Build a return-period family from i = a/(d+b)ⁿ and read the design intensity
汇流时间 Tc(基尔皮奇公式)
Time of Concentration Tc (Kirpich)
Kirpich Tc=0.0195·L^0.77·S^(−0.385)=18.8min · 坡陡Tc小
Estimate the catchment travel time from flow length L and slope S; it sets the design duration
霍顿下渗模型 f(t) 与累积下渗 F(t)
Horton Infiltration Model f(t) & Cumulative F(t)
f(t)=fc+(f0−fc)e^(−kt) · f(1)=15.4→fc=10mm/h · 累积F(t)
Infiltration capacity decays to a steady value; cumulative infiltration is the area under the curve
Gumbel 洪水频率分析
Gumbel Flood Frequency Analysis
x_T=x̄+K_T·s · x100≈970m³/s · 重现期T↔1/T · 频率直线
x_T = x̄ + K_T·s; longer return period T → higher design flood
水库调洪演算(削峰错峰)
Reservoir Flood Routing (attenuation & lag)
蓄量指示法 · (I1+I2)/2−(O1+O2)/2=ΔS/Δt · 削峰错峰
Continuity (I₁+I₂)/2 − (O₁+O₂)/2 = ΔS/Δt; outflow peak is lower and later than inflow
过程线基流分割
Hydrograph Baseflow Separation
直线分割N=0.83·A^0.2天 · 线上直接径流/线下基流 · 体积守恒
Straight-line method: above = direct runoff, below = baseflow; a later endpoint N → more direct runoff
参考蒸散发 · 彭曼组合式
Reference evapotranspiration · Penman combination
ET0=[Δ(Rn−G)+γEa]/(Δ+γ)=4.82mm/d · 辐射+空气动力项
water returning to the atmosphere from soil and plants: radiation and aerodynamic terms set ET₀
马斯京根河道洪水演算
Muskingum channel flood routing
O2=C0I2+C1I1+C2O1 · K/X · C0.048/0.429/0.524和1 · 削峰滞后
routing an upstream inflow hydrograph to the downstream outflow: the flood peak is attenuated and lagged
流域水量平衡
Catchment water balance
P=ET+Q+I±ΔS · 1000=550+300+120+30 · 径流系数Q/P=0.30
conservation of mass for water: precipitation splits into ET, runoff, recharge, with the residual changing storage