Flood Estimation & Flood Routing | Engineering Hydrology - Civil Engineering (CE) PDF Download

Floods, Flood Routing and Flood Control

A flood an unusually high stage in a river, normally the level at which the river overflow its banks and inundates the adjoining area. The design of bridges, culvert waterways and spillways for dams and estimation of score at a hydraulic structure are some examples wherein flood-peak values are required.
To estimate the magnitude of a flood peak the following alternative methods are available:

• Rational method
• Empirical method
• unit-hydrograph technique
• Flood-frequency studies

1. Rational Method
   If t_p ≥ t_c
   Q_p = 1 / 36.k.P_c.A
   Where, Q_p = Peak discharge in m³/sec
   P_C = Critical design rainfall in cm/hr
   A = Area catchment in hectares
   K = Coefficient of runoff.
   t_D = Duration of rainfall
   t_C = Time of concentration
2. Empirical Formulae
   (i) Dickens Formula (1865)
   Where, Q_p = Flood peak discharge in m³/sec
   A = Catchment area in km².
   C_D = Dickens constant, 6 ≤ C_D ≤ 30.
   (ii) Ryve’s formula (1884)
   Q_P = C_R.A^2/3
   Where,
   C_H = Ryve’s constant
   = 8.8 for constant area within 80 km from the cost.
   = 8.5 if distance of area is 80 km to 160 km from the cost.
   = 10.2 if area is Hilley and away from the cost.
   (iii) Inglis Formula (1930)
   Where, A = Catchment area in Km².
   Q_P = Peak discharge in m³/sec.
3. Flood Frequency Studies
   (i) Recurrence interval or return Period:
   T = 1/P where, P = Probability of occurrence 
   (ii) Probability if non-occurrence: q = 1 - P
   (iii) Probability of an event occurring r times in ‘n’ successive years:
   (iv) Reliability: (probability of non-occurrence /Assurance) = qⁿ
   (v) Risk = 1 - qⁿ → Risk = 1(1 - P)ⁿ
   (vi) Safety Factory = Design values of hydrologic parameter adopted / Estimated value of hydrological parameter
   (vii) Safety Margin = design value of hydrological parameter – Estimated value of hydrological parameter 

Gumbel’s Method

The extreme value distribution was introduction by Gumbel (1941) and is commonly known as Gumbel’s distribution. it is one of the most widely used probability distribution functions for extreme values in hydrologic and meteorologic studies for prediction of flood peaks, maximum rainfall, maximum wind speed.
Gunbel defined a flood as the largest of the 365 daily flows and the annual series of flood flows constitute a series of largest values of flows.
Based on probability distribution.

 Where, X_T = Peak value of hydrologic data
K = Frequency factor

y_T = Reduced variate
y_r = -log_∈log_∈(T / T - 1)
T = Recurrence interval in year
y_n = Reduced mean = 0.577
S_n = Reduced standard deviation.
S_n = 1.2825 for N → ∞

Confidence Limit
Since the value of the variate for a given return period, xT determined by Gumbel’s method can have errors due to the limited sample data used. An estimate of the confidence limits of the estimates is desirable the confidence interval indicates the limits about the calculated value between which the true value can be said to lie with specific probability based on sampling errors only.
For a confidence probability c, the confidence interval of the variate x_T is bounded by value x₁ and x₂ given by
X₂ / X₁ = X_T ± f(c) . S_∈
Where, f(c) is a function of confidence probability ‘C’.

S_e = Probability error
Where, N = Sample size
B = factor
σ = Standard deviation

Flood Routing

Flood routing is the technique of determining the flood hydrograph at a section of a river by utilizing the data of flood flow at one or more upstream sections. The hydrologic analysis of problems such a flood forecasting. Flood protection Reservoir design and spillway design invariable includes flood routing.

• Prism Storage: it is the volume that would exist if the uniform flow occurred at the downstream depth. i.e., the volume formed by an imaginary plane parallel to the channel bottom drawn at the outflow section water surface.
• Wedge Storage: it is the wedge like volume formed between the actual water surface profile and the top surface of the prism storage.
• Flood Routing
  

Muskingum Method

S = S_p + S_w
Where, S = Total storage in the channel.
S_p = Prism storage
= if (Q) = function of outflow discharge.
S_w = Wedge storage
= f(I) = function of inflow discharge.
S = f(Q)+f(I)S=k[XI^m + (1-X)Q^m]
Where, X = Weighting factor
M = Constant = 0.6 for rectangular channels
= 1.0 for nature channels
K = storage time constant

Method of Channel Routing
Muskingum Method: Hydrologic channel Routing
where, ΔS → Change in storage in time Δt
Δt → Time interval at which observations are taken. (Routing interval)
i → Avg. in flow rate over the period Δt
Average outflow rate over time period Δt.

• S1 = k[XI₁ + (1 - X)Q₁]
• S₂ = k[XI₂ + (1 - X)Q₂]
• (S₂ - S₁) = k[X(I₂ - X₁)+(1 - X)(Q₂ - Q₁)]
• Q₁ = Q₁
• Q₂ = C₀I₂ + C₁I₁ + C₂Q₁
• Q_n = C₀I_n + C₁I_n-1 + C₂Q_n-1

Where, C₀, C₁ and C₂, are Muskingum constant

• for best result, 2Kx < Δt < k

Synthetic Hydrograph

Synder’s Method: Synder (1938), based on a study of a large number of catchment in the Appalachian Highlands of eastern United states developed a set of empirical equations for synthetic unit hydrograph in those areas .These equations are in use in the USA. And with some modifications in many other countries, and constitute what is known as Synder’s synthetic unit hydrograph.

(i) t_P = C_t[L.L_Ca]^0.3
Where, t_p = Time interval between mid-point of unit rainfall excess and peak of unity hydrograph in hour
L = Length of main stream
L_Ca = The distance along the main stream from the basin outlet to a point on the stream which is nearest to the centrod of basis (in KM)
C_t = Regional constant 0.3 < C_t 0.6
 S = Basin slope.
N = Constant = 0.38.
(iii) t_r = t_p / 5.5 t_r = Standard duration of U.H in hour
(iv) Q_PS = 2.78C_PA / t_P
Where, C_p = Regional constant = 0.3 to 0.92.
A = Area of catchment in km².
Q_PS = Peak discharge in m³/s.
 where, t_R = standard rainfall duration.
t_P = Basin lag for non-standard U.H.
(vi) Q_p = 2.78C_PA / t_P
(vii) t_B = (72 + 3t_P) hour, for a large catchment.
Where, t_B = Base time of synthetic U.H
 for small catchment.
(viii) W₅₀ = 5.87 / (q)^1.08 W₅₀ = width of U.H in hour at 50% peak discharge.
(ix) W₇₅ = W₅₀ / 7.15 W₇₅ = Width of U.H in hours at 75% peak discharge.
(x) q = Q_P / A where, Q_P = Peak discharge in m³/sec.
A = Area in km².