Presentation by Lisa Jagau (University of Bayreuth, Germany) at the Delft3D User Days, during the Delft Software Days - Edition 2023 (DSD-INT 2023). Thursday, 16 November 2023, Delft.

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3D Hydrodynamic Modeling of Microplastic
Transport in Lakes
Lisa Jagau, Vadym Aizinger
Chair of Scientific Computing
CRC1357 Microplastics | University of Bayreuth
lisa.jagau@uni-bayreuth.de

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Objective
1
Image source: Plastics Europe, 2022
Motivation
▪ Increased usage of plastic products has led to
(micro)plastics pollution in all environmental
compartments
▪ Microplastics (MP) potentially harmful,
many organisms exposed directly in
hydrosphere
▪ Many studies have focused on marine
MP, limnic systems less researched
Approach
▪ Use case study: Großer Brombachsee,
Germany
− Part 1: Set up hydrodynamic model
− Part 2: Add MP transport
Global plastic use by application:

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Study Area
Großer Brombachsee
▪ Surface area 9.1 km2
▪ Average depth 15.9 m
▪ Deepest point 35 m
▪ Main inflow in west, main outflow in
east
▪ Water led from River Danube to River
Main watershed
▪ Main function: supply (dry) Franconia
with water from south of Germany +
buffer flooding of River Altmühl
▪ Strongly varying water level due to
different forms of usage + climatic
conditions
2
Image source: Fischereiverband Mittelfranken, 2022

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Part 1: Hydrodynamic Model

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Density Function for Mesh Generation
4
Scatter set 2
~ 𝑏𝑒𝑑 𝑙𝑒𝑣𝑒𝑙 𝑠𝑙𝑜𝑝𝑒−1
𝑟𝑒𝑓𝑖𝑛𝑒 𝑎𝑙𝑙 𝑎𝑟𝑒𝑎𝑠 𝑤𝑖𝑡ℎ 𝑤𝑎𝑡𝑒𝑟 𝑑𝑒𝑝𝑡ℎ < 15𝑚,
𝑏𝑦 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑦𝑖𝑛𝑔 𝑤𝑖𝑡ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 0.8
Scatter set 1
~ 𝑤𝑎𝑡𝑒𝑟 𝑑𝑒𝑝𝑡ℎ
𝑡𝑎𝑘𝑒 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒 𝑎𝑡 𝑒𝑎𝑐ℎ 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛
Resulting Scatter Set for Mesh Density

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Computational Mesh with Bed Level
5
Computational Mesh
▪ 8718 mesh elements
ranging from 30-120m

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Outflow Boundary
▪ Measured water
discharge
Schematic Model
6
Inflow Boundary
▪ Measured water discharge
▪ Measured water temperature
Wall/ Lake Bed Behavior
▪ No normal flow
▪ Wall: Free-slip
▪ Lake Bed: Constant Manning friction 0.0023 s/m1/3
Free Surface Boundary
▪ 10m wind speed and direction
▪ 2m air temperature
▪ Relative humidity
▪ Cloud cover
▪ Precipitation

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Temperature Measurements 2012
7
-30
-25
-20
-15
-10
-5
0
6 8 10 12 14 16 18 20 22
Depth
[m]
Temperature [°C]
May, 21st
July, 16th
September, 10th
December, 03rd

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May, 21st
July, 16th
September, 10th
December, 03rd
Vertical Mesh Sensitivity Analysis
8
Temperature Profiles, 30 sigma-layers Temperature Profiles, 30 z-layers
Temperature [°C]
Depth
[m]
May, 21st
July, 16th
September, 10th
December, 03rd
Temperature [°C]
Depth
[m]
• z-layer model shows more realistic stratification

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Vertical Mesh Sensitivity Analysis
9
• Vertical grid converges at 60 equidistant z-layers
Temperature [°C]
Depth
[m]
Temperature [°C]
Depth
[m]
May, 21st
July, 16th
September, 10th
December, 03rd
Temperature Profiles, 30 z- / 60 z-layers Temperature Profiles, 60 z- /80 z-layers
30 layers
60 layers
60 layers
80 layers

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Model Calibration
10
Temperature Profiles, September,
Varying horizontal diffusivity
• Realistic profiles, but 1-2°C too cold
• Ice formation not included in model → Repeat simulations with start date in spring
Temperature Profiles, September,
Varying vertical diffusivity
Temperature [°C]
Depth
[m]
1 m2/s
measurements
3 m2/s
5 m2/s
hor. diffusivity:
vert. diff.: 5e-7 m2/s
hor. vis.: 10 m2/s
vert. vis.: 5e-5 m2/s
Temperature [°C]
Depth
[m]
measurements
5e-7 m2/s
1e-6 m2/s
3e-6 m2/s
vert. diffusivity:
hor. diff.: 5 m2/s
hor. vis.: 10 m2/s
vert. vis.: 5e-5 m2/s

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11
May, 21st
July, 16th
September, 10th
December, 03rd
Temperature [°C]
Depth
[m]
Temperature Profiles, Simulation Start in March
Best Calibration Parameters
Horizontal diffusivity: 1 m2/s
Vertical diffusivity: 5e-7 m2/s
horizontal viscosity: 0 m2/s
Vertical viscosity: 5e-6 m2/s
Model Calibration

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Fine Tuning of Computational Mesh
12
Temperature [°C]
Depth
[m]
measurements
refined metalimnion
equidistant layers
Temperature Profiles, September,
Adjusted Vertical Layers
• Refinement of metalimnion results in better temperature profiles
20 z-layers, 1m
30 z-layers, 0.33m
5 z-layers, 0.7m
5 sigma-layers
-15 / -35m 20 x 2.7%
(54%)
-5 / -15m 30 x 0.9%
(27%)
2 / -5m 10 x 1.9%
(19%)

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Fine Tuning of Computational Mesh
13
8718 elements
34872 elements
Temperature Profiles, September,
Increased Horizontal Resolution
Depth
[m]
Temperature [°C]
measurements
34872 elements
8718 elements
• Difference not large enough to justify additional computing ressources

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Summary of Part 1
14
Hydrodynamic Model
▪ Unstructured mesh with 8718 elements
▪ 60 vertical z- layers: refined metalimnion
+ sigma layers near free surface
▪ Ignore lake freezing effects
Best Calibration Parameters
Horizontal diffusivity: 1 m2/s
Vertical diffusivity: 5e-7 m2/s
horizontal viscosity: 0 m2/s
Vertical viscosity: 5e-6 m2/s Image source: Fischereiverband Mittelfranken, 2022

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Part 2: MP Transport

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Motivation
16
Eulerian vs Lagrangian Particle Tracking Approach
▪ Eulerian approach more efficient for large concentrations
▪ More flexible for future applications (aging, interactions,
heteroaggregation, …)
➢ For first impression of how MP distributes in the model use
existing sediments routine of Delft3D FM (non-cohesive
particles)
Image source: Hüffer et al. 2017

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Outflow Boundary
▪ Measured water
discharge
Schematic Model
17
Inflow Boundary
▪ Measured water discharge
▪ Measured water temperature
Wall/ Lake Bed Behavior
▪ No normal flow
▪ Wall: Free-slip
▪ Lake Bed: Constant Manning friction 0.0023 s/m1/3
Free Surface Boundary
▪ 10m wind speed and direction
▪ 2m air temperature
▪ Relative humidity
▪ Cloud cover
▪ Precipitation
0.1 kg/m3

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Example Results – PS Concentration
18
0.1 mm Polystyrene particles (1030 kg/m3)

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Example Results – MP on Lake Bed
19
0.1 mm Polystyrene particles
(1030 kg/m3)
0.5 mm Polystyrene particles
(1030 kg/m3)
0.1 mm Polycaprolactone particles
(1140 kg/m3)

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Challenges and Limitations
20
• Simulating bouyant particles
• Simulating fast-sinking particles
• Computationally expensive to simulate all different types
and sizes of MP particles separately
• Limited options in existing sediments routine of Delft3D FM

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Outlook
21
▪ More MP simulations with existing sediments routine
− Different types of particles
− Different input scenarios
▪ Develop MP module within Delft3D FM based on existing
sediments routine
− Account for MP properties, apart from size and density
− Include aging, interaction and heteroaggregation of MP
particles
− Calibrate and validate with experimental MP data
▪ Validate for different types of lakes
21

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Thank You!
Funded by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) – Project Number 391977956 – SFB 1357

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