Urban lake management can be improved considering their ecological functioning and mathematical models are very useful for this purpose. Modeling accurately ecological processes requires modeling accurately physical processes. For example, basin-scale internal waves have ecological consequences because they modify light availability for phytoplankton. They are often related to strong wind episodes in large and deep lakes but our measurements in Lake Créteil showed that storms, usually associated with a decrease of the air temperature, break thermal stratification. They have been successfully reproduced using 3D hydrodynamic models in large and deep lakes but as far as we are aware they have not yet been successfully modeled in small and shallow lakes. First, we confirmed the presence of wind-forced basin-scale internal waves in Lake Créteil using meteorological variables, water temperature and current velocity collected at high frequency (30 s) in several points of Lake Créteil. A particular episode when the wind amplified the internal wave activity at a frequency of about 17 h was characterized. Then, based on a set-up of the 3D hydrodynamic model Delft3D-FLOW calibrated for Lake Créteil, we evaluated the capability of the model to reproduce the internal wave activity during this episode. Time series plots and PSD analyses of observed and simulated water temperature and current velocity showed that the model reproduced very well the internal wave activity in term of amplitude and frequency.

1. 1
Modeling internal waves with Delft3D-FLOW in a shallow urban lake: Lake Créteil, France
Frédéric Soulignac1*, B. J. Lemaire1,2, R. S. Martins1,3,
I. Tchiguirinskaia1, B. Tassin1 and B. Vinçon-Leite1
1: Laboratoire Eau Environnement Systèmes Urbains (LEESU), Ecole des Ponts ParisTech (ENPC), Champs-sur-Marne, France
2: AgroParisTech, Paris, France
3: Université de Sao Paulo, Brésil
*Corresponding author, e-mail: frederic.soulignac@leesu.enpc.fr

2. 2
Context
• 980 lakes in the Ile-de-France
region (small dots) and 248 larger
than 5 ha (circles)
• Ecosystem services
– Drinking water
– Leisure
– Irrigation
– Storm water retention
– Biodiversity conservation
– Local climate regulation
• Urban lakes management
– A necessity!
– Improvement by considering their
ecological functioning (Birch, 1999)
– Usefulness of numerical models
Water bodies in the Ile-de-France region
from Catherine et al., 2013
Hypothesis: Modeling accurately ecological processes
requires modeling accurately physical processes

3. 3
Objectives
•Wind-forced basin-scale internal waves
–Ecological consequences
•Horizontal and vertical fluxes during stratification (Hodges et al., 2000)
•Light availability (Cuypers et al., 2011)
–Observed and simulated in large and deep lakes (Rueda et al, 2003)
–Observed in small and shallow lakes (Pannard et al., 2011)
–Not yet been simulated in small and shallow lakes…
•Objectives
–To observe basin-scale internal wave in a shallow lake
–To calibrate and verify the 3D hydrodynamic model Delft3D-FLOW
–To evaluate its capability to reproduce observations
•Foreseen application
–To couple Delft3D-FLOW with the biological model DELWAQ-BLOOM in order to reproduce phytoplankton dynamics
–To use the model configuration coupled with weather forecast in a warning system

4. 4
Lake Créteil, France

5. 5
Lake Créteil- Instrumentation
• Services
– Storage of storm water
– Leisure (fishing, bathing, sailing)
– Biodiversity
– Heat wave regulation
• Geometry
– Surface area: 40 ha
– Length: 1.5 km
– Width: 300-400 m
– Mean depth: 4.5 m (max: 5.5 m)
• High frequency monitoring since 2012
– Transmitting buoy at point C (30 s)
• Metrological station
• Chain of sensors
– Current profiler at point C (3 min)
– Chains of sensors at point P and R (30 s)
-0.5 m
-1.5 m
-2.5 m
P Stormwater inlet
Outlet
-0.5 m
-1.5 m
-2.5 m
R
2 m
-0.5 m
-1.5 m
-2.5 m
-3.5 m
-4.5 m
C
Current profiler
Meteorological station
Water temperature

6. 6
Characterization of basin-scale
internal waves period
• Merian formula (mode V1H1)
• Power spectral density analysis
2
2 1
1 2
2 2 1 2 4

  
 

 
H H g
H H
T L H1 ρ1
H2 ρ2
L
g
 
NFFT t
FFT X
PSD


2
t f
PSD
X

7. 7
Water temperature and wind speed at point C
T = 17 h
H1 = 2.5 m ρ1 = 1002.995 kg/m3
H2 = 2.5 m ρ2 = 1003.182 kg/m3
L = 1500 m
g = 9.81 m/s2
T = 17.4 h
Wind amplified internal wave activity
P
C
R

8. 8
Current velocity and water temperature at point C
+
-
- +
17 h
17 h
P
C
R

9. 9
Difference of water temperature between points P and R
•Observations results
–Amplification of wave by wind
–Isotherms: wave amplitude = ±0.5 m
–Horizontal differences of water temperature: ±1 °C
17 h
P C R

10. 10
Delft3D-FLOW
•Domain
–1148 Cartesian grids: 20m x 20m
–Vertical coordinate system Z-model: 50 cm
–Measured bathymetry
•Heat flux model
–Varying cloud cover
–Light extinction
•Turbulence closure model: k-ε
•Bottom shear stress: Manning
•Initial condition and forcing: measurements
•Computational time step: 30 s
•Calibrated in 2012: water temperature and current velocity
•Verified in 2013 and 2014

11. 11
Simulation results: water temperature
P C R
17 h
17 h

12. 12
P C R
Simulation results: north-south current velocity at point C
17 h
17 h

13. 13
Conclusion
•Conclusions
–Confirmation of the presence of wind-forced basin-scale internal waves in Lake Creteil
–Delft3D-FLOW reproduced accurately wind-forced basin-scale internal wave amplitude and frequency
•Foreseen application
–To couple Delft3D-FLOW with the biological model DELWAQ-BLOOM in order to reproduce phytoplankton dynamics
–To use the model configuration coupled with weather forecast in a warning system

14. 14
Thank you for your attention
And thanks to:
TUDelft and Deltares (F. van de Ven and R. Uittenbogaard)
Projet Blue Green Dream (I. Tchiguirinskaia, funding)
Région Ile-de-France (funding)