Seiche-aware assimilation of measured water levels in shallow lakes using Kalman Filtering

Témavezető:	Dr. Krámer Tamás
	BME Építőmérnöki Kar, Vízépítési és Vízgazdálkodási Tanszék
email:	kramertamas@gmail.com

Projekt leírás

Standing oscillations of the water surface (seiches) are ubiquitous in lakes, and their excitation by wind forcing can dominate short-term lake-level fluctuations in Lake Balaton or Lake Fertő, for example. Usually, we don’t measure the fluctuations of the lake surface; we only have information from a few gauges around the lakeshore. According to our hypothesis, the motion can be described in terms of a few dominant basin modes, which allows us to estimate water level fluctuations at any point in the lake.

The project aims to develop and test a reduced-order state estimator that combines a pre-computed modal basis (from analytical or numerical eigenmodes) with Kalman filtering techniques. _The goal is to reconstruct in real time the shape of the lake water surface from sparse measurements. _

Students will:

• Derive a modal state-space model for seiche amplitudes (damped linear oscillators forced by wind or pressure setup).
• Formulate the observation operator that maps modal amplitudes to gauge readings.
• Implement a Kalman Filter (KF) and/or Ensemble Kalman Filter (EnKF) for state estimation.
• Test the method with 2D modelled data (known modes + noisy “virtual gauges”).
• Evaluate estimator performance (root-mean-square error, sensitivity to sensor placement, robustness to missing data). *(Optional extension) Apply to real shallow lake data (Balaton or Fertő), using public wind reanalysis and available lake-level records.
• The topic combines analytical derivation, numerical implementation, and statistical inference. It has direct applications in flood monitoring and lake hydrodynamics research.

Expected results

• A working code that assimilates noisy lake-level data into modal amplitudes in real time
• Quantitative assessment of the minimum number and optimal placement of gauges to reconstruct the first few modes
• Visualizations: time series of estimated modal amplitudes, reconstructed lake surface snapshots, error statistics

Előfeltételek

• Linear algebra, ODEs, stochastic processes (basic level)
• MATLAB or Python (NumPy/SciPy; optional: filterpy or similar libraries)
• No prior limnology background required; hydrodynamic context will be introduced

Hivatkozások

• Schwab, D. J. (1978). Simulation and Forecasting of Lake Erie Storm Surges. Monthly Weather Review, 106(10), 1476–1487.
• Austin, J. (2025). Simple linear models of coastal setup and seiching behavior across the Laurentian Great Lakes. Journal of Great Lakes Research, 51(1), 102491.
• Åström & Murray, Feedback Systems (open e-book). Ch. 2.2 “State-Space Models” (building 𝑥̇=𝐴𝑥+𝐵𝑢), Ch. 4 “Dynamic Behavior” (eigenvalues, damping), and Ch. 6–7 (reachability/observability, estimators). These give all the elements for a reduced modal model 𝑎̈+2𝜁𝜔𝑎̇+𝜔2𝑎=𝐹 . Link
• Welch & Bishop – “An Introduction to the Kalman Filter”. Use Sec. 1 “The Discrete Kalman Filter” and the prediction/update equations. Link · Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: principles and practice. OTexts. Link
• Gelb, A. (ed.) (1974). Applied Optimal Estimation. MIT Press. (Use Sec. 1 “The Discrete Kalman Filter” and the prediction/update equations) · Evensen, G. (2009). Data Assimilation: The Ensemble Kalman Filter. Springer. Link
• Evensen, G. (2009). Data Assimilation: The Ensemble Kalman Filter. Springer. Link