Sediment flux
Both the inland and river sediment model take into account sediment flux or transport of sediment in water, either in overland flow or in the stream flow. These two transport are distinguished in two different structures.
Inland Sediment Model
Sediment Flux in overland flow
Once the amount of soil detached by both rainfall and overland flow has been estimated, it has then to be routed and delivered to the river network. Inland routing in sediment models is usually done by comparing the amount of detached sediment with the transport capacity of the flow, which is the maximum amount of sediment that the flow can carry downslope. There are several existing formulas available in the literature. For a wide range of slopes and for overland flow, the Govers equation (1990) seems the most appropriate choice (Hessel et al, 2007). However, as the wflow_sediment model was developed to be linked to water quality issues, the Yalin transport equation was chosen as it can handle particle differentiation (Govers equation can still be used if wflow_sediment is used to only model inland processes with no particle differentiation). For land cells, wflow_sediment assumes that erosion can mobilize 5 classes of sediment:
- Clay (mean diameter of
) - Silt (mean diameter of
) - Sand (mean diameter of
) - Small aggregates (mean diameter of
) - Large aggregates (mean diameter of
).
where
where accucapacityflux
, accupacitystate
functions depending on the transport capacity from Yalin.
The choice of transport capacity method for the overland flow is set up in the model section of the TOML:
[model]
land_transport = "yalinpart" # Overland flow transport capacity method: ["yalinpart", "govers", "yalin"]
Note that the “govers” and “yalin” equations can only assess total transport capacity of the flow and can therefore not be used in combination with the river part of the sediment model.
River Sediment Model
Sediment dynamics in rivers can be described by the same three processes on land: erosion, deposition and transport. The difference is that channel flow is much higher, deeper and permanent compared to overland flow. In channels, erosion is the direct removal of sediments from the river bed or bank (lateral erosion). Sediments are transported in the river either by rolling, sliding and silting (bed load transport) or via turbulent flow in the higher water column (suspended load transport). The type of transport is determined by the river bed shear stress. As sediment particles have a higher density than water, they can also be deposited on the river bed according to their settling velocity compared to the flow velocity. In addition to regular deposition in the river, lakes, reservoirs and floodplains represents additional major sediment settling pools.
Complete models of sediment dynamics based on hydrology and not on hydraulics or hydrodynamics are much rarer than for soil loss and inland dynamics. The simpler models such as the SWAT default sediment river model uses again the transport capacity of the flow to determine if there is erosion or deposition (Neitsch et al., 2011). A more physics-based approach (Partheniades, 1965) to determine river erosion is used by Liu et al. (2018) and in the new SWAT’s approach developed by Narasimhan et al. (2017). For wflow_sediment, the new physics-based model of SWAT was chosen for transport and erosion as it enables the use of parameter estimation for erosion of bed and bank of the channel and separates the suspended from the bed loads.
Running the river model is an option of the wflow_sediment model and is enabled using the TOML file. By default it is false
:
[model]
run_river_model__flag = true
Sediment inputs in a river cell
The first part of the river model assesses how much detached sediment are in the river cell at the beginning of the timestep
River transport and erosion
Once the amount of sediment inputs at the beginning of the timestep is known, the model then estimates transport, and river erosion if there is a deficit of sediments. Transport in the river system is estimated via a transport capacity formula. There are several transport capacity formulas available in wflow_sediment, some requiring calibration and some not. Choosing a transport capacity equation depends on the river characteristics (some equation are more suited for narrow or wider rivers), and on the reliability of the required river parameters (such as slope, width or mean particle diameter of the river channel). Several river transport capacity are available and the choice is set up in the model section of the TOML:
[model]
river_transport = "bagnold" # River flow transport capacity method: ["bagnold", "engelund", "yang", "kodatie", "molinas"]
Simplified Bagnold
Originally more valid for intermediate to large rivers, this simplified version of the Bagnold equation relates sediment transport to flow velocity with two simple calibration parameters (Neitsch et al, 2011):
where wflow_sediment
, the equation was simplified to only get two parameters to calibrate:
Study | River | |||
---|---|---|---|---|
Vigiak 2015 | Danube | 0.5-2 (/) | 0.0001-0.01 (0.003-0.006) | 1-2 (1.4) |
Vigiak 2017 | Danube | / | 0.0001-0.01 (0.0015) | 1-2 (1.4) |
Abbaspour 2007 | Thur (CH) | 0.2-0.25 (/) | 0.001-0.002 (/) | 0.35-1.47 (/) |
Oeurng 2011 | Save (FR) | 0-2 (0.58) | 0.0001-0.01 (0.01) | 1-2 (2) |
Engelund and Hansen This transport capacity is not present in SWAT but used in many models such as Delft3D-WAQ, Engelund and Hansen calculates the total sediment load as (Engelund and Hansen, 1967):
where
Kodatie Kodatie (1999) developed the power relationships from Posada (1995) using field data and linear optimization so that they would be applicable for a wider range of riverbed sediment size. The resulting equation, for a rectangular channel, is (Neitsch et al, 2011):
River sediment diameter | a | b | c | d |
---|---|---|---|---|
281.4 | 2.622 | 0.182 | 0 | |
2 829.6 | 3.646 | 0.406 | 0.412 | |
2 123.4 | 3.300 | 0.468 | 0.613 | |
431 884.8 | 1.000 | 1.000 | 2.000 |
Yang Yang (1996) developed a set of two equations giving transport of sediments for sand-bed or gravel-bed rivers. The sand equation (
And the gravel equation (
where
Molinas and Wu The Molinas and Wu (2001) transport equation was developed for large sand-bed rivers based on the universal stream power
where
Once the maximum concentration
First, the sediments stored in the cell from deposition in previous timesteps
Instead of just setting river erosion amount to just cover the remaining difference
The bed and bank of the river are supposed to only be able to erode a maximum amount of their material
where
In wflow_sediment, the erodibility of the bed/bank are approximated using the formula from Hanson and Simon (2001):
Normally erodibilities are evaluated using jet test in the field and there are several reviews and some adjustments possible to this equation (Simon et al, 2011). However, to avoid too heavy calibration and for the scale considered, this equation is supposed to be efficient enough. The critical shear stress
where
Bank vegetation | |
---|---|
None | 1.00 |
Grassy | 1.97 |
Sparse trees | 5.40 |
Dense trees | 19.20 |
Sediment Fraction | 5 to 50 | 50 to 2000 | ||
---|---|---|---|---|
Sand | 0.15 | 0.15 | 0.65 | 0.15 |
Silt | 0.15 | 0.65 | 0.15 | 0.15 |
Clay | 0.65 | 0.15 | 0.15 | 0.05 |
Gravel | 0.05 | 0.05 | 0.05 | 0.65 |
Then, the repartition of the flow shear stress is refined into the effective shear stress and the bed and bank of the river using the equations developed by Knight (1984) for a rectangular channel:
where
Finally the relative erosion potential of the bank and bed of the river is calculated by:
And the final actual eroded amount for the bed and bank is the maximum between
River deposition
As sediments have a higher density than water, moving sediments in water can be deposited in the river bed. The deposition process depends on the mass of the sediment, but also on flow characteristics such as velocity. In wflow_sediment, as in SWAT, deposition is modelled with Einstein’s equation (Neitsch et al, 2011):
where
where
Mass balance and sediment concentration
Finally after estimating inputs, deposition and erosion with the transport capacity of the flow, the amount of sediment actually leaving the river cell to go downstream is estimated using:
where
A mass balance is then used to calculate the amount of sediment remaining in the cell at the end of the timestep
Reservoir modelling
Apart from land and river, the hydrological wflow_sbm
model also handles reservoir modelling. In wflow_sbm
, reservoir
nodes representing reservoirs, (natural) lakes or other water storage features are modelled using a 1D bucket model at the cell corresponding to the outlet. For the other cells belonging to the reservoir which are not the outlet, processes such as precipitation and evaporation are filtered out and shifted to the outlet cell. wflow_sediment
handles the reservoirs in the same way. If a cell belongs to a reservoir and is not the outlet then the model assumes that no erosion/deposition of sediments is happening and the sediments are transported to the reservoir outlet. Once the sediments reach the outlet, then sediments are deposited in the reservoir according to Camp’s model (1945) (Verstraeten et al, 2000):
where
For reservoirs, coarse sediment particles from the bed load are also assumed to be trapped by the dam structure. This adding trapping is taken into account with a reservoir trapping efficiency coefficient for large particles (between reservoir_water_sediment~bedload__trapping_efficiency = 1.0
, for example for a gravity dam) or only partly (for example for run-of-the-river dams).
Reservoir modelling is enabled in the model section of the TOML and require the extra following input arguments:
[model]
reservoir__flag = true
[input]
reservoir_area__count = "wflow_reservoirareas"
reservoir_location__count = "wflow_reservoirlocs"
[input.static]
reservoir_surface__area = "ResSimpleArea"
"reservoir_water_sediment~bedload__trapping_efficiency" = "ResTrapEff"
Note that in the inland part, reservoir coverage is used to filter erosion and transport in overland flow.
References
- K.C. Abbaspour, J. Yang, I. Maximov, R. Siber, K. Bogner, J. Mieleitner, J. Zobrist, and R.Srinivasan. Modelling hydrology and water quality in the pre-alpine/alpine Thur watershed using SWAT. Journal of Hydrology, 333(2-4):413-430, 2007. 10.1016/j.jhydrol.2006.09.014
- P. Borrelli, M. Märker, P. Panagos, and B. Schütt. Modeling soil erosion and river sediment yield for an intermountain drainage basin of the Central Apennines, Italy. Catena, 114:45-58,
- 10.1016/j.catena.2013.10.007
- F. Engelund and E. Hansen. A monograph on sediment transport in alluvial streams. Technical University of Denmark 0stervoldgade 10, Copenhagen K., 1967.
- G. Govers. Empirical relationships for the transport capacity of overland flow. IAHS Publication, (January 1990):45-63 ST, 1990.
- G.J Hanson and A Simon. Erodibility of cohesive streambeds in the loess area of the midwestern USA. Hydrological Processes, 15(May 1999):23-38, 2001.
- R Hessel and V Jetten. Suitability of transport equations in modelling soil erosion for a small Loess Plateau catchment. Engineering Geology, 91(1):56-71, 2007. 10.1016/j.enggeo.2006.12.013
- J.P Julian, and R. Torres. Hydraulic erosion of cohesive riverbanks. Geomorphology, 76:193-206, 2006. 10.1016/j.geomorph.2005.11.003
- D.W. Knight, J.D. Demetriou, and M.E. Hamed. Boundary Shear in Smooth Rectangular Channels. J. Hydraul. Eng., 110(4):405-422, 1984. 10.1061/(ASCE)0733-9429(1987)113:1(120)
- S.L Neitsch, J.G Arnold, J.R Kiniry, and J.R Williams. SWAT Theoretical Documentation Version
- Texas Water Resources Institute, pages 1-647, 2011. 10.1016/j.scitotenv.2015.11.063
- C. Oeurng, S. Sauvage, and J.M. Sanchez-Perez. Assessment of hydrology, sediment and particulate organic carbon yield in a large agricultural catchment using the SWAT model. Journal of Hydrology, 401:145-153, 2011. 10.1016/j.hydrol.2011.02.017
- A. Simon, N. Pollen-Bankhead, and R.E Thomas. Development and application of a deterministic bank stability and toe erosion model for stream restoration. Geophysical Monograph Series, 194:453-474, 2011. 10.1029/2010GM001006
- G. Verstraeten and J. Poesen. Estimating trap efficiency of small reservoirs and ponds: methods and implications for the assessment of sediment yield. Progress in Physical Geography, 24(2):219-251, 2000. 10.1177/030913330002400204
- O. Vigiak, A. Malago, F. Bouraoui, M. Vanmaercke, and J. Poesen. Adapting SWAT hillslope erosion model to predict sediment concentrations and yields in large Basins. Science of the Total Environment, 538:855-875, 2015. 10.1016/j.scitotenv.2015.08.095
- O. Vigiak, A. Malago, F. Bouraoui, M. Vanmaercke, F. Obreja, J. Poesen, H. Habersack, J. Feher, and S. Groselj. Modelling sediment fluxes in the Danube River Basin with SWAT. Science of the Total Environment, 2017. 10.1016/j.scitotenv.2017.04.236