F Bed-level update in SOBEKSIM
F.7 Routines voor aanpassing dwarsprofielen
Zoals in voorgaande is beschreven wordt vanuit DelWAQ de volumeveranderingen per segment doorgegeven aan Sobeksim via de Wqinr.
De volgende tekst beschrijft op welke wijze deze volumeveranderingen vervolgens worden doorgegeven aan de dwarsprofielen in Sobeksim.
After transfer of these volumes, it is necessary to adjust the cross-sections, and recompute conveyance and BOBs. The subroutines for these calculations are originally part of the PARSER, as the calculation of cross-sections in hydrodynamic simulations is only required once at the initialisation. The subroutines from the Parser have been introduced in Sobek.
In SOBEK the schematised cross sections will change so that the number of levels by which it has been schematised remains unchanged for each cross section and that the width at each sub-sequential level will remain unchanged. Only the levels itself do change. Naturally, erosion leads to lower levels of the cross section and sedimentation leads to higher levels.
Three different ways of cross section erosion/sedimentation are available (user selection):
1. erosion and sedimentation is spread equally over the sediment transporting width of the cross section
2. erosion and sedimentation is distributed proportional to a local reference depth across the cross section
If the user selects to spread out the erosion and sedimentation equally over the transport width of the cross section, the procedure is as follows.
Figuur F.1 Cross section with n levels
In Figuur F.1 a cross section with n levels is given. For adaptation of the cross section the following procedure is followed.
1. Find the highest defined level of the cross section below or corresponding with the actual sediment transporting width (level number k)
2. The level k and all levels below this level are lowered or increased by z
3. The value of z is determined using the following formula to compute the change of the
1 1
1
1 1
2,3,..., only if 2
2
i i i
k k
k k+1
t i
i=1
A = W z
A = W W z i k ( k )
W W
A = z
A = A
(F.1)
Note:
Positive value of A corresponds with negative value of z (in other words: an increase of the cross sectional area corresponds with a lowering of the bed level). This leads to the following formula for z:
1
2 t
k k
z = A
W W
(F.2)
Note:
If the transport width is equal to the flow width and the water level is equal or larger than the highest level in the table schematising the cross section, the level k+1 does not exist, so Wk+1 is not defined. In that case Wk+1 = Wk will be used.
SOBEK verifies that all values of zi remain in ascending order: it may occur that z > (zk+1- zk). In that specific case the program terminates the computation giving a message that the aggradation exceeds the maximum allowable aggradation of the cross section.
If the user chooses to distribute the erosion and sedimentation proportional to a local reference depth in the cross section, the following procedure will be applied.
Figuur F.2 Cross section with four levels
juli 2007 Q4239.00 Morfologisch SOBEK model Rijn-Maasmonding
In Figuur F.2 a cross section is given with four levels (as example: the procedure can be used for each cross section with k 2).
The procedure to compute the adapted cross section is now:
1. Find the highest defined level of the cross section below or corresponding with the actual sediment transporting width (in this example: level number k=3)
2. Level k=3 and all levels below this level are lowered or increased by i z 3. The value of ai is computed as follows:
4. in which zb is the lowest level defined in the current cross section and zs is the level corresponding with the prescribed sediment transporting width.
5. The value of z is determined using the following formula to compute the change of the cross sectional area.
6. this leads to the following formula for z:
1
7. sobek verifies that all values of zi remain in ascending order: it may occur that
k z > (zk+1- zk). In that specific case the program terminates the computation while giving a message that the aggradation exceeds the maximum allowable aggradation of the cross section.
In de hiernavolgende tekst is beschreven welke routines zijn gebruikt voor het aanpassen van de dwarsprofielen (overgenomen uit de Sobek-RE-source).
Subroutine moadcs
Module description: Adapt cross section dimensions for a cross section.
The following cross section types are possible:
o sedredge cross sections;
o tabulated cross sections.
Cross sections of type circle can not be processed.
For tabulated cross sections this routine will call a cross section adaption routine depending on the users choice. Two choices are possible for tabulated cross sections:
o erosion/sedimentation spread equally over transport width;
o option = erosion/sedimentation proportional to local depth.
If a grid point is a boundary and the boundary condition is a bed level and sediment is moving in, no delta z is calculated. In that case the ry condition is used to adapt the cross section.
In all other cases the calculated delta A is used to calculate a delta z. For sedredge cross ons this routine will calculate a delta z and update the bottom of the section involved. In case the grid point is a boundary and the boundary conditions is a bed level and sediment is moving on, no delta z is calculated. The new bottom is interpolated from the boundary conditions table and will be assigned to the section involved.
subroutine momlev
Module description: Find highest bed level in cross section which is morphodynamic active.
First the actual transport width is calculated by comparing the actual flow width with the user defined transport width. If the flow width is smaller then the transport width the actual port width will be adapted.
If the actual transport width has been determined the highest bed level of the cross section is searched below or corresponding with the actual transport width. If a rectangular profile is used the lowest level will be chosen.
subroutine moeqdz
Module description: Calculate delta z if morphodynamic option is equally over transport width.
With the level found (momlev) a delta bed level is calculated. The delta bed level is used to adapt
juli 2007 Q4239.00 Morfologisch SOBEK model Rijn-Maasmonding
the levels in the cross section below the found highest bed level.
subroutine moeqtw
Module description: This routine calculates new cross section ons.
The algoritm used will spread out the erosion
and sedimentation equally over the transport width of the cross section. The delta bed level is used to adapt the levels in the cross section below the found highest bed level.
subroutine moseci
Module description: Calculate waterlevel for sed. transporting width Calculate waterlevel where sediment transporting width is defined. This level is used for the adaption cross section algoritm proportional subroutine moprdz
Module description: Calculate delta z if morphodynamic option is portional to local depth.
With the level found (momlev) a delta bed level is calculated. The delta bed level is used to adapt the levels in the cross section below the found highest bed level.
subroutine moprld
Module description: Calculate new cross section proportional to the local water depth
This routine calculates new cross section ons. The algoritm used will distribute the erosion and sedimentation proportional to the local water depth in the cross section. The delta bed level is used to adapt the levels in the cross section below the found highest bed level