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:
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, XT = Peak value of hydrologic data
K = Frequency factor
yT = Reduced variate
yr = -log∈log∈(T / T - 1)
T = Recurrence interval in year
yn = Reduced mean = 0.577
Sn = Reduced standard deviation.
Sn = 1.2825 for N → ∞
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 xT is bounded by value x1 and x2 given by
X2 / X1 = XT ± f(c) . S∈
Where, f(c) is a function of confidence probability ‘C’.
Se = Probability error
Where, N = Sample size
B = factor
σ = Standard deviation
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.
S = Sp + Sw
Where, S = Total storage in the channel.
Sp = Prism storage
= if (Q) = function of outflow discharge.
Sw = Wedge storage
= f(I) = function of inflow discharge.
S = f(Q)+f(I)S=k[XIm + (1-X)Qm]
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.
Where, C0, C1 and C2, are Muskingum constant
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) tP = Ct[L.LCa]0.3
Where, tp = Time interval between mid-point of unit rainfall excess and peak of unity hydrograph in hour
L = Length of main stream
LCa = 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)
Ct = Regional constant 0.3 < Ct 0.6
S = Basin slope.
N = Constant = 0.38.
(iii) tr = tp / 5.5 tr = Standard duration of U.H in hour
(iv) QPS = 2.78CPA / tP
Where, Cp = Regional constant = 0.3 to 0.92.
A = Area of catchment in km2.
QPS = Peak discharge in m3/s.
where, tR = standard rainfall duration.
tP = Basin lag for non-standard U.H.
(vi) Qp = 2.78CPA / tP
(vii) tB = (72 + 3tP) hour, for a large catchment.
Where, tB = 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 = QP / A where, QP = Peak discharge in m3/sec.
A = Area in km2.