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Ensemble Kalman Filter Outperforms Optimal Interpolation in Tsunami Waveform Assimilation
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  • Yuyun Yang,
  • Eric Dunham,
  • Guillaume Barnier,
  • Martin Almquist
Yuyun Yang
Stanford University

Corresponding Author:[email protected]

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Eric Dunham
Stanford University
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Guillaume Barnier
Stanford University
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Martin Almquist
Stanford University
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Abstract

Recent research in real-time tsunami early warning can be broadly classified into two approaches. The first involves the use of seismic and regional geodetic data to calculate the tsunami wavefield indirectly through the estimation of earthquake source parameters. The second directly reconstructs the tsunami wavefield using data assimilation of ocean-bottom pressure sensor data such as those from DONET and S-NET (Maeda et al. 2015, Gusman et al. 2016). Data assimilation interpolates between the numerical solution and the observations to make the forecast more consistent with real data. Currently, the most popular method for forecasting the waveform is optimal interpolation, which uses a Kalman filter (KF) like approach, but holds the Kalman gain matrix fixed to reduce the runtime. This approach, coupled with tsunami Green’s functions, is very efficient and generates useful predictions. Here, we demonstrate that more accurate and stable forecasts can be obtained using the ensemble KF (enKF), a more computationally efficient variant of KF, in which the gain matrix is updated according to the physical model and the evolution of the error covariance matrix. The ensemble representation is a form of dimensionality reduction, in that only a small ensemble is propagated, instead of the joint distribution including the full covariance matrix. This method also provides a means to obtain the probability distribution of the forecast at each grid point location. We use a scenario tsunami in the Cascadia subduction zone, generated from a 2D fully-coupled dynamic rupture simulation (Lotto et al., submitted 2018). Randomly perturbed tsunami wave height data is used in the assimilation process, as we propagate the wave using a 1D linear shallow water code on a staggered grid. Better waveform agreement is achieved even in the early stages of assimilation, with much less fluctuation compared to optimal interpolation. We also explore spatial and temporal aliasing effects, in terms of the relation between observation station spacing and wavelength, as well as between assimilation and forecast time intervals. Although enKF is computationally more expensive, we are working on a fast, parallelized GPU implementation, which will significantly reduce the runtime, taking us a step closer to reliable real-time tsunami early warning.