Question

The Modified Puls method is used for reservoir routing while the Muskingum method is used for river routing. Discuss the problems that would occur if one tried to use the Modified Puls method for river routing (i.e. why isn’t the Modified Puls method well suited for river routing?).

Answer 1

1. Muskingum-Cunge has comparable accuracy to other hydrological routing models such as PULS or Kinematic Wave. The disadvantage of hydrological routing appears when the free surface becomes too steep and solution is characterized by a moving hydraulic bore. In such conditions, a St. Venant equation solver is recommended, with a non-linear scheme to capture well bore celerity values even when Courant numbers are low.

2. other advantage of M-C method is that its coefficients are physically based and the numerical solution is independent of time and space intervals when the latter are selected within the spatial and temporal resolution criteria.

3. In many existing flood forecasting systems M-C provides reasonable estimates of the routing time and maximum discharges within limited computational time if the flow remains in the main river channel.

4. Reservoir routing (Storage is a unique function of Outflow Discharge, S = f(Q) )

5. River routing (Storage is a function of both Inflow & Outflow, here we use Muskingam Method) 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.

6. Reservoir Routing

Storage is a unique function of outflow discharge (Q or O).

∴ S = f (O) The relationship is given by a discharge rating curve.

In reservoir routing, we re-arrange the balance equation;

(S2/∆t + O2/2) = (S1/∆t - O1/2) + (I1 + I2)/2

Given, I1, I2, and (S1/∆t - O1/2), we want to estimate the left-hand side.

The first step is to determine the relationships between the water stage (H), S and O. Topographic or bathymetric survey can be used to obtain H-S relationship. Stream discharge measurement is conducted to determine H-O relationship.

7. Muskingum Method

We want to simulate the propagation of a flood wave along a channel. Storage is the function of both I and O.

Profiles of water flowing in a channel reach during the rising limb (a) and recession limb (b) of a flood wave

Assume that storage can be approximated as;

S = K[xI + (1 - x)O]

Where K [s] is a constant, and x is a weighting factor. K is approximately equal to the “residence time” of the flood wave within the stream reach. K has a unit of time, and is a rough measure of the residence time of flood peak in the channel reach. Change in channel morphology may change the value of K.