CressHelp - A1 - Wind setup

Cress Help -Open Channel Flow, river discharges - Z3.1 -

Maximum discharge in tropical rivers

A method to compute the maximum discharge of a river, given the relation between the largest average rainfall, the drainage area and the duration of the rain. The method has been developed in Indonesia and has been calibrated on data from Java.

Constants and parameters

Input values:

A - Catchment area
L - Length of the river upstream of the control point (e.g. a weir)
h_m - the elevation of the river at a point 0.9 L from the control point (in m above datum, e.g. MSL)
h_w - elevation of the weir in m above datum (e.g. MSL)
R_N - Max. dayly rainfall with a return period of N years
N - the return period of the rainfall data R_N
N₂ - the return period of the requested flood

Output values

Q - flood discharge with a return period N₂
i - Melchior gradient of the river

Equations used

The Melchior gradient is calculated using

The discharge is calculated using the equation:

q is the maximum local rainfall in m³/km²/s, A is the catchment area. a and b are correction factors.

The empirical factor b is is the relation between the average rainfall during 24 hours in an area and the maximum rainfall during the same day, measured in a specific station within that area.

For Jakarta this relation is:

in which t is the duration of the rain and A is the catchment area.

The factor a is the discharge coefficient, giving that part of the rainfall which is not stored in the area, but is directly available for feeding the river:

The coefficient q is an empirical function of the duration of the rainfall:

The duration of the rainfall can be calculated with the following relationship:

The above set of equations can be solved by iteration.

The calculated discharge Q is then transformed to the extreme discharge Q_n using a log-relation with the rainfall intensity once in 70 years as basis:

This equation is an approximation of the tables in the original publication.

The discharge with a probability of 1/70 per year an once per N₂ years is now given by:

Special comments:

The equation for q has been determined using rainfall data in Jakarta over the period 1866-1935, using a regression analysis. The equation for b is based on data from several rivers in the world, and adapted for the typical situation on Java. The equation for a is a German equation, adapted for the situation on Java. T follows from observation on several station in Indonesia.

In the original paper of Der Weduwen the method is presented in the form of Nomograms.

References

Weduwen, J.P. der [1937] Het berekenen van den maximum afvoer van stroomgebieden met een oppervalk van 0 - 100 km², De Ingenieur in Nederlandsch Indië (4) 10, pp135-155