T4 Translation and Retention Models

Translation:

• is a pure time shift of a discharge hydrograph, that means the input signal is shifted by n-time steps

• Translation simulates the flow time that a particle needs to travel from point A to point B (For example how long does a drop of precipitation take to reach the lowest point of a catchment area)

Retention:

• describes the process of flow balancing

• input signal is reduced of its peak value by storage effects during runoff formation

• this stretches and compresses the hydrograph —> stretching causes a time delay —> increased in terms of the duration of the signal

• Area below the hydrographs remains identical!

For the canalised course a linear reservoir would be suitable, as only little to none retention (no storage effetcs) is to be expected. Only translation. No enlargemens or reduction of the cross-section, small friction

For a natural watercourse with an adjacent floodplain, the slowed down water in the floodplain lead to a retention of the discharge. For that we model the watercourse with a parallel storage cascade due to the different flow conditions between the foreland and the channel, this allows us to assign individual retention constants.

(Retention in natural watercourses (without floodplains) is caused by roughness as well as width and depth variance.)

Blue = canalized water body (faster and higher discharge velocity)

Green = natural watercourse (slower with lower discharge velocity

With a linear reservoir, it is assumed that the output of a reservoir is linearly dependent on the storage capacity.

This is represented by the retention parameter k, which depends on the time-differences and amounts of the in- & outflow at a certain point.

Continuity equation: Inflow = outflow + storage change (Δ storage)

Qz(t) → S(t) → Qa(t) ➔ Qa(t) = 1/k * S(t)

→ makes the calculation of a storage easier but in reality it is not that simple!

In a time-space diagram, the subareas of the catchment area that are located beween two isochrones are set using the mean flow time. It is used to simulated Translation.

Single linear reservoir (Sewers):

• Used for pure translation models without or low storage effects (retention), e.g. canalized course,

• Limited use in reality, range of delay (retardation) is limited

• Only one retention parameter & reservoir

Cascade of linear reservoirs:

• Used for translation models while taking retention into account, e.g. canalized waters, natural waters

• represents a series of identical single linear reservoirs connected with the same retention constants k (storage time of water)

• It assumes that a given inflow (e.g. precipitation excess) routes through a series of linear reservoirs, while the outflow from the first reservoir being taken as the inflow to the second, and so on

• As the number of reservoirs increases, the curves become flatter and wider, what means that the water needs more time to pass trough a water section→ reflects translation and retention

• Range of delay (retardation) is increased

• 2 parameters: Only one retention parameter but a number of reservoirs n

(( Cascade of parallel reservoirs:

• Used for retention model with storage effects (retention), e.g. natural watercourse with floodplains

• retentions effects lead to different flow systems / conditions → flows need to be separated with individual /different retention constants → parallel storage cascade

• 5 parameters: retention parameter of main channel & of flood plain, number of reservoirs n of main channel & of flood plain and the bankfull discharge QBF

• ))

Channels with floodplain areas should be modeled with a cascade of parallel reservoirs, since retentions effects in the active floodplains lead to different flow systems / conditions. Therefore, the flows need to be separated with individual /different retention constants which is only possible in a cascade of parallel reservoirs. The retention parameter & number of reservoirs is different for the main channel and for the flood plain.