- Annual, seasonal or monthly runoff
- Extreme low flow or dry weather flow
- Peak flow or flood flow

There are different approaches available for estimation of runoff. Generally, Runoff estimation is done based on following methods:

- Statistical or Probability Methods
- Empirical & Regional Methods
- Unit Hydrograph Method

Statistical or Probability methods, used when stream flow data of study area are available, includes graphical methods or flood frequency analysis methods ( Gumbel’s Distribution, Log Pearson Type III, Log Normal Distribution etc ). When rainfall data & catchment characteristics of study area are available, then we can use empirical & regional methods. For Unit Hydrograph method to be used, Unit hydrograph of known duration for a catchment, should be available. Here, in this article I have described different regional ( WESCS/DHM, DHM,MHSP, PCJ 1996 ) & empirical relations ( Rational, Modified Dicken’s, BD Ricard’s, Synder’s method ) for ungauged stations of Nepal.

## WECS/DHM 1990

In Nepalese context, Water and Energy Commission Secretariat (WECS)/Department of Hydrology and Meteorology (DHM) developed empirical relationships for analyzing flood of different frequencies. It is the modification of WESCS approach of 1982.

The formula for 2 year return period is given by

$$Q_{100}=14.63(A_{3000}+1)^{0.7342}$$

where,

Q is design flood in $m^{3}/s$

$A_{3000}$ is basin area($Km^{2}$) below 3000 m elevation.

For other return period,

S=Standard Normal Variate

$\sigma=\frac{ln(Q_{100}/Q_{2})}{2.32}$

Table 1 : Values of T & S

The formula for 2 year retrun period is given by

$$Q_{2}=2.29(A_{3000})^{0.86}$$

The formula for 100 year return period is given by

$$Q_{100}=20.7(A_{3000})^{0.72}$$

where,

Q is design flood in ($m^{3}/s$)

$A_{3000}$ is basin area($Km^{2}$) below 3000m elevation.

where,

S=Standard Normal Variate

$\sigma=\frac{ln(Q_{100}/Q_{2})}{2.32}$

Values of T & S are same as in table 1.

$$Q=kA^{b}$$

where,

Q is peak flood in $m^{3}/s$

The formula for 2 year return period is given by

$$Q_{2}=1.8767(A_{3000}+1)^{0.8737}$$

The formula for 100 year return period is given by$$Q_{100}=14.63(A_{3000}+1)^{0.7342}$$

where,

Q is design flood in $m^{3}/s$

$A_{3000}$ is basin area($Km^{2}$) below 3000 m elevation.

For other return period,

$$Q_{T}=e^{lnQ_{2}+s\sigma}$$

where,S=Standard Normal Variate

$\sigma=\frac{ln(Q_{100}/Q_{2})}{2.32}$

Table 1 : Values of T & S

## DHM 2004

The DHM(2004) method is an update to the WESCS/DHM 1990 method.The formula for 2 year retrun period is given by

$$Q_{2}=2.29(A_{3000})^{0.86}$$

The formula for 100 year return period is given by

$$Q_{100}=20.7(A_{3000})^{0.72}$$

where,

Q is design flood in ($m^{3}/s$)

$A_{3000}$ is basin area($Km^{2}$) below 3000m elevation.

For other return period,

$$Q_{T}=e^{lnQ_{2}+s\sigma}$$where,

S=Standard Normal Variate

$\sigma=\frac{ln(Q_{100}/Q_{2})}{2.32}$

Values of T & S are same as in table 1.

## MHSP 1997

Based on the MHSP method, the flood peak is computed using the relation as below:$$Q=kA^{b}$$

where,

Q is peak flood in $m^{3}/s$

A is basin area in $Km^2$

k and b are constants which depend on the return period T.

Table 2 : Values of k & b

k and b are constants which depend on the return period T.

Table 2 : Values of k & b

## PCJ 1996

The PCJ method calculates design peak flood discharge based on hourly rainfall intensity. This method employs following formula:
Q

_{p}= 16.67a_{p}o_{p}ΦFk_{F}+ Q_{s}
where,

Q

_{p}= Maximum rainfall design discharge for required exceedence probability (p) in m3/sec
a

_{p}= Maximum rainfall design intensity for required exceedence probability (p) in mm/min
a

_{p }= a_{hr}.k_{t,}
where, a

_{hr}= Hourly rainfall intensity for required exceedence probability (p) in mm/min at selected rainfall stations
k

_{t}= Reduction coefficient of hourly rainfall intensity (depends on the size of catchment area)
o

_{p}= Infiltration coefficient of the basin, derived as the function of exceedence probability (p)
Φ = Areal reduction coefficient of maximum rainfall discharge (depends on the size of catchment)

F = Catchment area of drainage basin in sq. km.

k

_{F}= Coefficient for unequal distribution of rainfall in different size of basin, captured by one rain.
Q

_{S}= Discharge by melting of snow, can be taken as 0 to 10% of Q_{P}in the absence of data.## Rational Method

A rational formula, for flood discharge takes into account the intensity, distribution and duration of rainfall as well as the area, slope, and permeability of the basin. This method is applicable to small rural catchments with area not exceeding 12$Km^{2}$ (DHM 2004). A typical rational formula is:

$$Q_{T}=\frac{Ci_{(t_{c},p)}A}{3.6}$$

where,

$Q_{T}$ is the maximum flood discharge in $m^{3}/s$ for required return period T

C is the runoff coefficient and can be selected based on type of basin. The values of C for different types of basins is given in table 3.

Table 3 : Runoff coefficients

A is the catchment area in $Km^{2}$

$i_{(t_{c},p)}$ is the mean rainfall intensity in mm/hour for probability p and time of concentration $t_{c}$

A is the catchment area in $Km^{2}$

$i_{(t_{c},p)}$ is the mean rainfall intensity in mm/hour for probability p and time of concentration $t_{c}$

In the absence of data on rainfall intensity, the mean intensity of rainfall (

**in cm/hr**) can be estimated by using Sherman equation & coefficients given by Rambabu et.al.*$i_{(t_{c},p)}=\frac{KT^{a}}{(t_{c}+b)^{n}}$*

where,

T is return period

**in years**. K, a, b and n are constants for a particular location. For Nepal, these value can be assumed as for Northern India (K = 5.92; a = 0.162; b = 0.5 & n = 1.013). $t_{c}$ is time of concentration (**in hour**) & can be best estimated by Kripich equation as below:*$t_{c}=0.01947L^{0.77}S^{-0.385}$*

where,

$t_{c}$ = time of concentration (

**minutes**)
L = maximum length of travel of water ( m )

S = Slope of catchment

In the context of Nepal, if 24hr maximum rainfall data are available, then intensity corresponding to time of concentration can be estimated from Ricard’s method, Mononobe equation etc.

## Modified Dicken's Method

The modified Dicken’s method is an updated version of the Dicken’s method. The irrigation research institute, Roorkee India has done frequency studies on Himalayan Rivers & suggested the following updated relationship to compute Dicken’s constant.

$$Q_{T}=C_{T}A^{3/4}$$

where,

$Q_{T}$=maximum flood discharge($m^{3}/s$) in T years

A=Catchment area($Km^{2}$)

$C_{T}$=modified dickens constant proposed by the Irrigation Research Institute, Roorkee , based on frequency studies on Himalayan rivers

$C_{T}=2.342\log(0.6T)\log(\frac{1185}{p})+4$

$p=100\frac{a+6}{a+A}$

where,

a = perpetual snow area in $Km^{2}$ & T is return period in years.

## BD Ricard's Method

This method uses rainfall & basin characteristics during estimation of flood. The flood discharge is given by:

$$Q=0.222\times(AIF)$$

Where,

The value of I is calculated by iterative process in which initial value of $T_{c}$ in hours is assumed and following calculations are performed.

$$Q=0.222\times(AIF)$$

Where,

A is Basin area in Sq.Km.

$F=1.09352-0.066628\ln(A)$*I*is the intensity of rainfall corresponding to the time of concentration & F is the aerial reduction factor.The value of I is calculated by iterative process in which initial value of $T_{c}$ in hours is assumed and following calculations are performed.

$I=\frac{R_{TC}}{T_{c}}$

$R_{TC}=0.22127R_{T}T_{c}^{0.476577}$

$K_{R}=0.65I(T_{c}+1)$

$C_{KR}=\frac{0.95632}{K_{R}^{1.4806}}$

$D=1.102\frac{L^{2}}{S}F$

$T_{C3}=DC_{KR}$

$T_{C2}=(\frac{T_{C3}}{0.585378})^{1/2.17308}$

Where, L is the basin length in Km, S is basin slope, $R_{T}$ is 24 hours rainfall for return period T in mm, $T_{C2}$ is the second estimate of time of concentration

Iteration is done with $T_{C}=T_{C2}$ until the difference between them is within 5%

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