Ensemble Kalman Filter Outperforms Optimal Interpolation in Tsunami
Waveform Assimilation
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.