Flood Routing in Ungauged Catchments Using Muskingum Methods MH Tewolde (MScEng) and Prof. JC Smithers School of Bioresources Engineering and Environmental Hydrology, University of KwaZulu-Natal, Private Bag X01 Scottsville, 3209, Pietermaritzburg, South Africa E- Mail: [email protected], [email protected]

Flood routing can be defined as the mathematical method for predicting the changing magnitude and celerity of flood waves in rivers or reservoirs. Using flood routing techniques, stages, or rates of flow, can be estimated at d sites i during d i flood fl d event. ungauged Flood routing technique may broadly divided in to hydrologic and hydraulic type. The Muskingum flood routing method is one of the most frequently used hydrologic methods used for flood routing and was selected for use in this study. The Muskingum g flood routing g technique q relates temporary storage, inflow and outflow hydrographs as shown below.

St = K[I t X + (1 − X)Q t ]

A B ∆L n

• The Muskingum–Cunge method was selected to estimate the K and X parameters in unguaged catchments catchments.

• Three sub-catchments in the Thukela Catchment selected for analyses, with river lengths of 54, 4 and 21 km.

= = = =

P Q0 R S y Vav Vw

• The performance of Muskingum methods at selected sub-catchments analyzed using calibrated parameters.

• Slope of the river reach (S) and reach length (L) extracted from digital elevation model.

• Manning’s roughness coefficients (n) determined

= = = = = = =

cross-sectional flow area (m2), top flow width (m), routing length (m), Manning’s roughness coefficient (dimensionless), wetted perimeter (m), reference flow (m3.s-1), hydraulic radius (m), slope (m.m-1), depth of flow (m), average velocity (m.s-1), and celerity (m.s-1).

Objectives

30 Inflow 25

Outflow Comp. Outflow, M-Ce

20 15 10 5 0 3/19/69 3/20/69 3/21/69 3/22/69 3/23/69 3/24/69 3/25/69 3/26/69 3/27/69 3/28/69 3/29/69 0:00 0:00 0:00 0:00 0:00 0:00 0:00 0:00 0:00 0:00 0:00 Time (h)

Fig-3 Observed and computed hydrographs at the Mooi River down stream (21 km reach length ).

computed hydrographs compared statistically and graphically against the observed hydrographs. Section Factor & Lacy regime equations were used to estimate flow depth (y) and hydraulic radius of a parabolic river i x-section. ti In I a channel h l where h top t width idth (B) exceeds d mean flow depth by a factor of 20, B≅ P. 2/3

Muskingum flood routing technique using calibrated parameters.

Q 0n = S

P = 4.71 Q0 2/3

of the Muskingum equation at ungauged sites.

• Evaluate the performance of the Muskingum

Q0n ⎛ ⎞ y=⎜ ⎟ ⎝ 0.508 P S ⎠

1 Vav = R2/3 S n Vw = K =

11 V av 9 ΔL VW

50

40 Obs. Inflow 30

Obs. Outflow Comp.Outflow, M-Ce

20

• Hence, the method can be applied in ungauged catchments where inflow and catchment physical characteristics can be estimated.

10

0 9/14/64 12:00 AM

9/17/64 12:00 AM

9/20/64 12:00 AM

9/23/64 12:00 AM

9/26/64 12:00 AM

9/29/64 12:00 AM

10/2/64 12:00 AM

10/5/64 12:00 AM

Time (h)

Qn ⎛ 2yP⎞ ⎛ 2y⎞ AR2/3 = ⎜ ⎟*⎜ ⎟ = 0 3 3 S ⎝ ⎠ ⎝ ⎠

• Develop relationships to estimate the parameters

Muskingum-Cunge method together with empirically determined variables performed well in the three selected catchments.

60

• Flood routing conducted on selected events and the

AR

Conclusions • From the results obtained, it is evident that

Results

equation.

• Calibrate and evaluate the performance of the

equation with parameters estimated using the relationships developed.

35

from field observations.

Discharge (m3.s-1)

temporary storage (m3), inflow (m3. s-1), outflow (m3. s-1), storage constant (s), and weighting factor between inflow and outflow out ow (dimensionless). (d e s o ess).

45 40

reviewed.

Acknowledgements Fig-1 Observed and computed hydrographs at the Mooi River up stream (54 km reach length ). The authors acknowledge the University of Asmara, Eritrea and the Water Resource Commission, South Africa, for funding this study. study 120

100

3/5

80 Discharge (m3.s-1)

= = = = =

List of variables

• Different hydrological flood routing methods were

• Flow variables estimated from empirical equations. • Lateral inflow estimated from the Saint-Venant

where St It Qt K X

Methodology

Discharge (m3.s-1)

Introduction

Obs. Inflow Obs. Outflow Comp. Outflow, M-Ce

60

40

2y R = 3

B ≅ P

&

20

0 11/17/87 12:00 11/18/87 12:00 11/19/87 12:00 11/20/87 12:00 11/21/87 12:00 11/22/87 12:00 11/23/87 12:00 11/24/87 12:00 AM AM AM AM AM AM AM AM

X=

1 Q0 − 2 2BSV w ΔL

Time (h)

Fig-2 Observed and computed hydrographs at the Klip River (4 km reach length ).