Simple flood forecasting methods

Flood routing in river reaches intends to answer the question: to which extend do flood waves from drainage basins get attenuated by the storage effect of the reach. Therefore, methods must be determined, that allow flood forecasting in a longitudinal cross-section of the river, based on observed or computed discharge values at inflow gage sites. For flood forecasting, the time and the magnitude of the peak flood flow are of special interest. Observations at one or several gage sites upstream provide information and allow conclusions about the critical cross-section. All the methods described subsequently are easy to handle, but suffer the disadvantage of relatively inexact results.

7.2.1 Gage relation curve

This method determines the relation between the peak flow water stages at different river cross-sections.

To apply the method, the following assumptions must be made:

Only cross-sections at the same river may be compared, and they may not be located too far apart (causal connection).

Only comparable water stages may be considered. Since there is no definite water stage-discharge connection for instationary flow, the method is limited to the peak stage-discharge water stages (dW/dt = 0).

The analysis of numerous flood discharges eventually provides the gage relation curve (see Figure 7.5). For a given flood event, based on the observations made at gage site A predictions may be made for gage site B downstream. Since the method is very simple, it is especially suitable for approximate real time forecasting.

time t

time t water depth at gage A WA [cm]

water depth at gage A W_A [cm] water depth at gage B W [cm]B

water depth at gage B WB [cm]

Figure 7.5: Analysis of flood waves to determine a gage relation curve

W_Amin W_Amax

water depth at gage A W_A [cm]

water depth at gage B WB [cm]

HW at C MW at C NW at C

Figure 7.6: Gage relation curve including the water stage at a tributary (gage site C)

The application of this method is limited to smaller distances. If no definite connection between the water stages at gage A and B can be determined, lateral inflow may be the cause.

The water stages of a single tributary can be considered by a number of curves (see Figure 7.6). When plotting the chart, one must consider if several rivers contribute to the discharge of the observed river (see Figure 7.7).

cross arrows on this line

Figure 7.7: Gage relation nomogram, prediction of peak flow water stage at gage B based on observations on several gage sites A, C, D

7.2.2 Travel time curve

The travel time curve provides the time of the peak discharge of an expected flood event. To determine the curve, representative flood discharges must be analyzed. To identify the travel time between two river cross-sections, the peak flow must be clearly visible. From the analysis of several flood events the average wave travel times are determined and plotted against the water stage of the observed gage site. (see Figures 7.8 and 7.9).

The cross-sectional shape of the river strongly influences the shape of the travel time curve (see Figure 7.8). In principle, the travel time will decrease with increasing water stages due to greater flow velocities. If the cross-section is enlarged the storage effect increases, this again leads to smaller wave travel velocities. (see Figure 7.8, area €).

The travel velocity of flood peaks is higher than the flow velocity since they proceed with wave velocity.

1

travel time T_l [h]

cross-section between A and B

water depth WA[cm]

A B

Figure 7.8: Travel time curve, influence of the river cross-section on the travel time of the flood peak

travel time T_l [h]

water depth WA [cm]

gage reference curve W_B (W_A)

travel time curve T_l (W_A)

water depth W_B [cm]

Figure 7.9: Gage relation curve and travel time curve to predict magnitude and time of the peak water stage at a critical gage

7.2.3 Prediction of discharge changes

The conversion of water stages to discharge using the stationary discharge curve is not correct in the case of instationary flow. However, the error decreases if the discharge change ∆Q is considered rather than the absolute discharge Q. For short-time forecasting and only small discharge changes the error remains within an acceptable range.

The initial conditions for this method are similar to those of linear translation:

• The travel time Tt of the discharge change ∆Q is considered constant between two cross-sections.

• A discharge change ∆Q at an upstream gage occurs in the same magnitude at a downstream gage.

The discharge changes at the critical gage result from the time lag of the discharge change at an observed gage, not from inflow along the reach (see Figure 7.10).

(

) (

) (

)

vor i t i i t i

Q t t Q t t T Q t T

∆ + ∆ = + ∆ − − − (7.6)

∆Q_vor [m³/s] discharge change at the critical gage Q_i [m³/s] discharge at the observed gage i t₁ [h] time of observation

∆t [h] forecasting time period t_1+∆t [h] forecasting time

T_t,i [h] travel time from observed gage i to the critical gage

here travel time T_t,A

travel time T_t,C

critical gage

outflow at gage B QB [m3/s]outflow at gage A QA [m3/s]outflow at gage C QC [m3/s]

observation time prediction time

Figure 7.10: Forecasting based on discharge change (see ground plan Figure 7.5), critical gage B, observed gages A and C, lag of the discharge change ∆QA and ∆QC by the travel time T_t,A and T_t,C (here T_t,A = ∆t and Tt,C > ∆t)

The more observed gages are taken into consideration, the more accurate the results get. The overall discharge change of the critical gage is the sum of the single discharge changes.

(

) ( )

(

)

1 k

vor vor i

i

Q t t Q t Q t t

=

+ ∆ = +

∑

Q_vor [m³/s] discharge at the critical gage

∆Qi [m³/s] discharge change at the critical gage as a result of the discharge change at the observed gage i

k [1] number of observed gages