This document summarizes a presentation on modeling vegetation controls on gravel bed river morphodynamics. It describes two modeling frameworks - one where vegetation is represented as a single biomass and another that considers the role of plant roots. The models reproduce major effects of vegetation on river morphology and show that plant root feedbacks are mediated by a balance between erosion and root resistance that determines vegetation disturbance. While the models provide insights, further development is needed to better represent uprooting mechanisms and apply the models to more complex environments.

1. Laboratory of Hydraulics,
Hydrology and Glaciology
DICAM
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Siviglia Annunziato* 1
*Laboratory of Hydraulics, Hydrology and Glaciology, ETH Zürich, Switzerland
1 Now at the Department of Civil, Environmental and Mechanical Engineering (DICAM),
University of Trento, Italy
Modeling vegetation controls on gravel
bed river morphodynamics
Symposium on Advances in Mathematical Modelling of Hydraulic and Morphodynamic Problems
Delft 13.11.2019

2. 2
▪ River bars and vegetation: the case of the Alpine Rhine river
▪ Modeling framework I: vegetation as a single biomass and
biogeomporphic feedbacks
▪ Modeling framework II: the role of plant roots
▪ Conclusion & Outlook
Outline
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3. • Alternate bar morphology (42 km)
• Reach A: steady bars, Reach B: migrating bars (Adami et al. WRR 2016)
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River bars and vegetation: the case of the
Alpine Rhine river
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4. 4
4. Vegetation patternRiver bars and vegetation: the case of the
Alpine Rhine river
Vegetation establishment on steady bars (Reach A)
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5. 5
4. Vegetation patternRiver bars and vegetation: the case of the
Alpine Rhine river
Vegetation removal on migrating bars
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6. 6
River bars and vegetation: the case of the
Alpine Rhine river
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7. 7
Magra River (Italy)
2007
2011
(before the
big flood )
Can we predict how the shift from a vegetated system to a bare soil
configuration, occur?
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8. Our goal was to advance in the mechanistic understanding and quantification of
some important ecomorphodynamic processes, that so far have been described
only qualitatively.
Our approaches grounded on the deploy, and the development, of models able
to shed light on basic processes functioning, highlighting the importance of
including a sufficient level of details to study ecomorphodynamic processes,
which at the same time allow for a clear identification of cause-effect
relationships. These results may form a more solid basis for further studies and
focus efforts in experiments and models that seek quantification.
8
4. Vegetation patternModeling goal:
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9. 9
3. Basics
BASEMENT has a 1D and 2D sub module
Hydrodynamics
• depth-averaged equations for fluid flow
• finite volume discretization using Riemann solvers
• unstructured grid (2D)
Morphodynamics
• Exner equation
• Uniform sediments
• Bedload
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10. 10
Model framework I: Vegetation description
Vegetation description
Plant
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ζ 𝑢𝑝𝑟
ζ 𝑢𝑝𝑟 = roots length
The vegetation is described by a biomass, B.
Vegetation description Main biogeomorphic feedbacks
Biomass B
Flow resistance
Shear stresses
Sediment cohesion
Vegetation removal

11. • Vegetation dynamics is described by a logistic function:
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𝑑𝐵
𝑑𝑡
= 𝜎 𝐵 𝐵(𝑡) 1 −
𝐵(𝑡)
𝐾(𝑧 𝐵)
𝜎 𝐵 represents the timescale of vegetation growth;
𝐾(𝑧 𝐵) is the carrying capacity, i.e. the maximum vegetation biomass that
can grow at a given bed level.
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Implementation of vegetation dynamics
vegetation growth

12. 12
Implementation of vegetation dynamics
Vegetation: distribution on elevation gradient and
carrying capacity
(Riparia, 2005)
We assume that the carrying capacity distribution is a bell-shaped function of the bed
elevation 𝑧B. Parameters 𝜆1 and 𝜆2 control the rate at which fitness diminishes away
from its maximum, while 𝑧0 is related to the optimal elevation. 𝜙 is a parameter
normalizing the maximum value of 𝐾 𝑧 𝐵 to 1 (𝜙 = 2 𝑖𝑓 λ1 = λ2).
𝑧0 is the elevation with respect to the mean water level 𝑧 𝑤.
𝑧 𝑤 is computed assuming a high value of the soil permeability, i.e. it always matches the
water stage in the main channel. This is numerically computed using an Inverse
Distance Weighted (IDW) algorithm.
𝐾 𝑧 𝐵 =
𝜙
exp 𝜆1 𝑧B − 𝑧W − 𝑧0 + exp −𝜆2 𝑧B − 𝑧W − 𝑧0
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13. λ1 ≠ λ2 𝑧0=5 m
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Implementation of vegetation dynamics
Vegetation: distribution on elevation gradient and
carrying capacity
λ1 = λ2
𝑧0
𝐾 𝑧 𝐵 𝐾 𝑧 𝐵 𝐾 𝑧 𝐵
Parameters 𝜆1 and 𝜆2 control the rate at which fitness diminishes away from its
maximum, while 𝑧0 is related to the optimal
𝜙 = 2 𝑖𝑓 λ1 = λ2
𝑧0=5 m
λ1 = λ2
𝑧𝐵
𝜆 ↑
𝑧w=0 𝑧w=0 𝑧w=0
(Riparia, 2005)
𝐾 𝑧 𝐵 =
𝜙
exp 𝜆1 𝑧B − 𝑧W − 𝑧0 + exp −𝜆2 𝑧B − 𝑧W − 𝑧0
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14. 14
Implementation of vegetation dynamics
Vegetation mortality mechanism (uprooting modeling)
The plant removal by uprooting, within a cell domain (given location (x,y)) , is
modeled assuming that the biomass disappears as soon as the total erosion
during a flood event reaches a given value ζ 𝑢𝑝𝑟. In this way we take into
account the presence of roots assuming that type II uprooting occurs.
(Edmaier et al., 2011)
In gravel bed rivers, uprooting occurs as a
consequence of riverbed erosion that
gradually exposes part of the roots to the
flow thus reducing the anchoring
resistance of the plant (Type II uprooting as
defined by Edmaier et al., 2011).
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Uprooting → 𝐵 → 0 if erosion > ζ 𝑢𝑝𝑟 = roots length

15. It is evaluated as:
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Modelling framework
Eco-morphodynamics
(Corenblit, 2007)
𝑺 𝒇 = 𝑓 𝑡𝑜𝑡𝑎𝑙 𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠 = 𝑓(𝜏)
Flow resistance is a function of the total shear stress :
𝜏 =
𝒖 𝒖
𝑲 𝒔
𝟐
ℎ Τ1 3
𝑲 𝒔 = 𝐾𝑠,𝑔 − 𝐾𝑠,𝑔 − 𝐾𝑠,𝑣
𝐵
𝐾
Where 𝐾𝑠,𝑔 is the roughness
associated to the bare soil
(no vegetation, only sediments!!!)
𝐾𝑠,𝑣 is the Strickler coefficient associated to the vegetation
(can be quantified through image analysis e.g. the Jarvela’s
approach)
𝐾 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦
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16. 16
(1 − 𝑝)
𝜕𝑧 𝐵
𝜕𝑡
+
𝜕𝑞 𝐵𝑥
𝜕𝑥
+
𝜕𝑞 𝐵𝑦
𝜕𝑦
= 0 Exner eqn.
𝛥𝑥
𝛥𝑦
ℎ
𝑧 𝐵
Evaluation of the sediment discharge ByBx qq ,
𝒒 𝐵 = 8(θ − θ 𝑐𝑟) Τ3
2
The modification of the flow field have profound effects on
sediment transport.
where
θ =
τ (𝑡𝑜𝑡𝑎𝑙 𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠)
(ρ 𝑠 − ρ)𝑔𝑑 𝑠
and  =
𝐾𝑠,𝑔
𝐾𝑠,𝑣
2
< 1
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𝜽 𝒄𝒓 = 𝜃𝑐𝑟,𝑔 − 𝜃𝑐𝑟,𝑔 − 𝜃𝑐𝑟,𝑣
𝐵
𝐾
Vegetation roots increase soil cohesion
(increase of 𝜽 𝒄𝒓):

17. 17 17
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Simulations
Lenght Width Slope Unique grain
size
20 km 125 m 0,38 % 34 mm
River bed elevation: Initial configuration for all simulations
Magra, 2014
[m]
Computational mesh + River bed elevation[m]
1500 m3/s for
30 days
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Vegetation parameters
Changing 𝑧0
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[Camporeale, 2006]

19. Eco-morphological interactions
River bed elevation [m]
Biomass distribution
0
500
1000
1500
2000
0 20 40 60 80 100
Q
m3/s
Time (h)
Hydrograph
Initial river bed elevation [m]
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[m]
[m]

20. 20
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2020 20
20
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Results
interactions between vegetation and morphology
Surviving vegetated
patches actively modify
the bed topography
Stream power→ ω=
𝑄 𝑝 𝑠
𝑊
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2121 21
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Results
interactions between vegetation and morphology
Vegetation
abundance
and roots
Ground-water
level
Specialized
vs
Non-specialized
vegetation
Growth rate:
different plant
species
or different
hydrological
regimes
(e.g. time span
between floods)
For the quantitative identification of the threshold between vegetated and un-vegetated configurations
we use the asymmetry of the frequency distribution of bed elevation
(skweness<0→bare soil, skweness>0→vegetated soil)
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22. 22 22
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2222 22
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Results
effect of vegetation spatial distribution
Reduced water availability (lower 𝑧0 )
Reduced water availability (lower 𝑧0 ) results in vegetation growing at lower bed
elevation (panel A) and consequently in increased erosion and vegetation removal
during the flood (Panel B).
𝑧0
𝑧0
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23. • …what we found:
• The inclusion of a simple model for
vegetation can reproduce the major effects
of vegetation on river morphology
• Flood intensity, groundwater level and the
time lag between floods are crucial
parameters for the stabilization of species
in a river environment;
• …still a lot is needed:
• The uprooting mechanism was
oversimplified
• Taking into account the time lag between
floods
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24. 24
Vegetation description Main biogeomorphic feedbacks
Above-ground
Flow resistance
Shear stresses
Sediment cohesion
Vegetation removal
Plant
Below-ground
SEDIMENT
Biomass
allocation
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Biogeomorphic feedbacks: what is the role of
plant roots?
This work is part of the Francesco Caponi’s, PhD thesis
Laboratory of Hydraulics, Hydrology and Glaciology, ETH Zurich

25. 25
Plant root description: a stochastic (mean)
representation
Optimalroot-growzone
Rootingdepth
Groundwater
Rangeofwatertableoscillations
Vertical root
density
distribution
Ratio between
root grow and
decay
Function
accounting for the
stochasticity
Tron et al., 2014, 2015
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26. CAPONIFRANCESCO-ISE2018
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▪ Below-ground biomass changes the
critical Shields parameter:
𝜃𝑐𝑟(ζ) = 𝜃𝑐𝑟,𝑔 − 𝜃𝑐𝑟,𝑔 − 𝜽 𝒄𝒓,𝒗 𝑏 𝑟(ζ)
▪ Uprooting (Type II):
𝛽 =
𝑩 𝒄𝒓
𝐵𝑟
=
‫׬‬0
ζ 𝑢𝑝𝑟
𝑏 𝑟 𝑧 𝑑𝑧
‫׬‬0
ζ 𝑟
𝑏 𝑟 𝑧 𝑑𝑧
Plant-root feedback: uprooting and root-
enhanced soil cohesion
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Experimental evidence suggests that exposure of only part of the entire
root biomass might be sufficient to uproot plants (Edmaier et al., 2015).

27. 27
flow
Vegetated patch
Erosion Potential: maximum scour at equilibrium in the
downstream part ot the patch presence of only above-ground
vegetation, 𝐸𝑒𝑞
NO roots
Top view of the channel
Erosion
Riverbed
equilibrium
Disturbance
Numerical runs: quantifying morphological
disturbance
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28. 28
flow
Vegetated patch
Uprooting depth: erosion that vegetation withstands before
uprooting occurs, ζ 𝑢𝑝𝑟
NO roots
Top view of the channel
Resistance
Eroded vegetation
Deep
or
Numerical runs: including plant roots
Shallow
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29. 29
Results: vegetated patch at equilibrium
Bare
riverbed
Vegetated
riverbed
Erosion potential
Uprootingdepth
Low disturbanceHigh
disturbance
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30. 30
Bare
riverbed
Vegetated
riverbed
Plant root effects are mediated by competition between
erosion and resistance
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31. • …what we found:
• Prediction of the co-evolution of riverbed
and vegetation must account for
vegetation removal by uprooting
• The balance between riverbed erosion
and root resistance mediates the potential
effects of plant-root biogeomorphic
feedbacks
• …still a lot is needed:
• This modeling study may help to focus
experimental and field studies
• Application on more complex morphologies
and environmental conditions can help to
understand the co-evolution of
vegetation and morphology of riparian
areas
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Conclusion and outlook
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Plant mortality mechanisms: uprooting and burial
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Biogeomorphic feedbacks: what is the role of
plant roots?

33. 33
More on this model….
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34. • Find out more:
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Thank you!
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