Development of a 3D hydro- and thermodynamical model of Lake Balaton

Keywords: Lake Balaton, numerical modelling, shallow lake hydrodynamics, wind forcing, 3D hydro- and thermodynamical model

Abstract

We aim to set up a well-validated hydro- and thermodynamic model for the large and shallow Lake Balaton, which can be used for analyzing transport processes, and later also for forecasting. In shallow lakes, wave-affected surface and bottom boundary layers can overlap during windy periods, resulting in complex flow and mixing conditions. In contrast, a weak thermal stratification can develop during calm periods, which typically breaks up during nighttime, resulting in a diurnal cycle. We applied the FVCOM model for numerical simulations and carried out current and temperature measurements at an offshore location and temperatures were recorded at onshore as well in the Keszthely basin. We force the model with a spatially varying wind field to incorporate the effect of internal boundary layer development over the water surface and the mesoscale variability. The former leads to an increasing wind stress along the fetch. We show that inhomogeneous wind forcing is essential to model water level fluctuations accurately around the lake and improve current directions in the middle of the Keszthely-basin. To reliably simulate the thermal structure besides currents, a sensitivity analysis is performed for model parameters, including air-water heat exchange parameters, light extinction coefficient, and the background mixing coefficient of the turbulence model. We compare modeled and observed currents, temperatures, and thermal structures using the potential energy anomaly for the latter one in the middle of the Keszthely-basin. The multi-objective calibration requires a large number of simulations covering a wide parameter space to find an optimal parameter set.

Author Biographies

Gabriella Lükő , Budapest University of Technology and Economics, Faculty of Civil Engineering, Department of Hydraulic and Water Resources Engineering

GABRIELLA LÜKŐ She got her MSc degree in 2020, she is currently a fourth year PhD student at the Budapest University of Technology and Economics, Department of Hydraulic and Water Resources Engineering. During the academic year 2023/24 she is a Fulbright visiting student researcher at the Colorado School of Mines (USA). Her doctoral research focuses on the turbulent processes at the air-water interface of lakes. She is a member of the MHT since 2021.

Péter Torma, Budapest University of Technology and Economics, Faculty of Civil Engineering, Department of Hydraulic and Water Resources Engineering

PÉTER TORMA obtained an MSc degree in civil engineering in 2011 and a Ph.D. degree in 2016. He has been working at the Department of Hydraulic and Water Resources Engineering at the BME since 2011. Starting 2019, he works as an associate professor. Obtaining a Fulbright Scholarship, he was a visiting researcher at UW-Madison (USA) in the 2017/18 academic year. His field of research is physical limnology, hydrometeorology, in particular the measurement of turbulent exchange processes at the water-air interface based on the eddy-covariance principle, the heat balance of lakes, and numerical hydrodynamic modeling.  

References

Anderson, E., Schwab, D.J., Gregory, A.L. (2010). Real-Time Hydraulic and Hydrodynamic Model of the St. Clair River, Lake St. Clair, Detroit River System. Journal of Hydraulic Engineering 136(8). pp. 507-517. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000203

Chen, C., Liu, H., Beardsley, R.C. (2003). An Unstructured Grid, Finite-Volume, Three-Dimensional, Primitive Equations Ocean Model: Application to Coastal Ocean and Estuaries. Journal of Atmospheric and Oceanic Technology 20(1). pp. 159-186. https://doi.org/10.1175/1520-0426(2003)020<0159:AUGFVT>2.0.CO;2

Dong, F., Mi, C., Hupfer, M., Lindenschmidt, K-E., Peng, W., Liu, X., Rinke, K. (2020). Assessing vertical diffusion in a stratified lake using a three-dimensional hydrodynamic model. Hydrological Processes 34. pp. 1131-1143. https://doi.org/10.1002/hyp.13653

Durski, S.M., Glenn, S.M., Haidvogel, D.B. (2004). Vertical mixing schemes in the coastal ocean: Comparison of the level 2.5 Mellor-Yamada scheme with an enhanced version of the K profile parameterization. Journal of Geophysical Research 109. C01015. https://doi.org/10.1029/2002JC001702

Fairall, C.W., Bradley, E.F., Hare, J.E., Grachev, A.A., Edson, J.B. (2003). Bulk parameterization of air-sea fluxes: Updates and verification for the COARE algorithm. Journal of Climate 16(4). pp. 571-591. https://doi.org/10.1175/1520-0442(2003)016<0571:BPOASF>2.0.CO;2

Holthujsen, L.H. (2007). Waves in Oceanic and Coastal Waters. Cambridge University Press. https://doi.org/10.1017/CBO9780511618536

Homoródi K., Józsa J., Krámer T., Ciraolo, G., Nasello, C. (2012). Identifying wave and turbulence components in wind-driven shallow basins. Periodica Polytechnica Civil Engineering 56(1). pp. 87-95. https://doi.org/10.3311/pp.ci.2012-1.10

Ji, Z.G., Jin, K.R. (2006). Gyres and seiches in a large and shallow lake. Journal of Great Lakes Research 32(4). pp. 764-775. https://doi.org/10.3394/0380-1330(2006)32[764:GASIAL]2.0.CO;2

Józsa J. (2001). Sekély tavak cirkulációs áramlásai. MTA Doktori Értekezés, Budapesti Műszaki és Gazdaságtudományi Egyetem.

Józsa J. (2014). On the internal boundary layer related wind stress curl and its role in generating shallow lake circulations. Journal of Hydrology and Hydromechanics 62(1). pp. 16-23. https://doi.org/10.2478/johh-2014-0004

Józsa J., Milici, B., Napoli, E. (2007). Numerical simulation of internal boundary-layer development and comparison with atmospheric data. Boundary-Layer Meteorology 123. pp. 159-175. https://doi.org/10.1007/s10546-006-9134-9

Kang-Ren., J., Zhen-Gang, J. (2005). Application and Validation of Three-Dimensional Model in a Shallow Lake. Journal of Waterway, Port, Coastal, and Ocean Engineering 131(5). pp. 213-225. https://doi.org/10.1061/(ASCE)0733-950X(2005)131:5(213)

Kocsis M., Szatmári G., Kassai P., Kovács G., Tóth J., Krámer T., Torma P., Homoródi K., Pomogyi P., Szeglet P., Csermák K., Makó A. (2022). Soluble phosphorus content of Lake Balaton sediments. Journal of Maps 18(2). pp. 142-150. https://doi.org/10.1080/17445647.2021.2004943

Krámer T. (2006). Solution-adaptive 2D modelling of wind-induced lake circulation. Ph.D. Értekezés. Budapesti Műszaki és Gazdaságtudományi Egyetem.

Laval, B., Imberger, J., Hodges, B.R., Stocker, R. (2003). Modeling circulation in lakes: Spatial and temporal variations. Limnology and Oceanography 48(3). pp. 983-994. https://doi.org/10.4319/lo.2003.48.3.0983

Lükő G., Torma P., Weidinger T. (2022b). Intra-seasonal and intra-annual variation of the latent heat flux transfer coefficient for a freshwater lake, Atmosphere 13. 352. https://doi.org/10.3390/atmos13020352

Lükő G., Torma P., Krámer T., Weidinger T. (2022a). Air-lake momentum and heat exchange in very young waves using energy and water budget closure. Journal of Geophysical Research: Atmospheres 127. e2021JD036099. https://doi.org/10.1029/2021JD036099

Lükő G., Torma P., Weidinger T., Krámer T., Vecenaj, Z., Grisogono, B., Lázár I. (2021). Internal boundary layer development over lake surface in case of very young waves. EMS Annual Meeting Abstracts. https://doi.org/10.5194/ems2021-155

Mellor, G.L. (2008). The Depth-Dependent Current and Wave Interaction Equations: A Revision. Journal of Physical Oceanography, 38(11). pp. 2587-2596. https://doi.org/10.1175/2008JPO3971.1

Niu, Q., Xia, M. (2017). The role of wave-current interaction in Lake Erie’s seasonal and episodic dynamics. Journal of Geophysical Research: Oceans 122. pp. 7291–7311. https://doi.org/10.1002/2017JC012934

Qi, J., Chen, C., Beardsley, R.C., Perrie, W., Cowles, G.W., Lai, Z. (2009). An unstructured-grid finite-volume surface wave model (FVCOM-SWAVE): Implementation, validations and applications. Ocean Modelling 28(1–3). pp. 153–166. https://doi.org/10.1016/j.ocemod.2009.01.007

Torma P., Krámer T. (2017). Wind Shear Stress Interpolation over Lake Surface from Routine Weather Data Considering the IBL Development. Periodica Polytechnica Civil Engineering 61(1). pp. 14–26. https://doi.org/10.3311/PPci.9542

Torma P. (2016). Modelling wind-driven shallow lake hydrodynamics and thermal structure. Doktori értekezés Budapesti Műszaki és Gazdaságtudományi Egyetem, Budapest.

Warner, J.C., Sherwood, C.R., Signell, R.P., Harris, C.K., Arango, H G. (2008). Development of a three-dimensional, regional, coupled wave, current, and sediment-transport model. Computers & Geosciences 34(10). pp. 1284-1306. https://doi.org/10.1016/j.cageo.2008.02.012

Wiles, P.J., van Duren, L.A., Häse, C., Larsen, J., Simpson, J.H. (2006). Stratification and mixing in the Limfjorden in relation to mussel culture. Journal of Marine Systems 60(1-2). pp. 129-143. https://doi.org/10.1016/j.jmarsys.2005.09.009

Zhao, Q., Ren. J., Wang, J.X.L. (2018). Temporal and spatial characteristics of potential energy anomaly in Lake Taihu. Environmental Science and Pollution Research 25. pp. 24316-24325. https://doi.org/10.1007/s11356-018-2204-y

Zhao, Q., Sun, J., Zhu, G. (2012). Simulation and Exploration of the Mechanisms Underlying the Spatiotemporal Distribution of Surface Mixed Layer Depth in a Large Shallow Lake. Advances in Atmospheric Sciences 29(6). pp. 1360-1373. https://doi.org/10.1007/s00376-012-1262-1

Published
2024-04-21
How to Cite
LükőG., & TormaP. (2024). Development of a 3D hydro- and thermodynamical model of Lake Balaton . Hungarian Journal of Hydrology, 104(2/HU), 16-27. https://doi.org/10.59258/hk.15658
Section
Tudományos közlemények