統計数理研究所 セミナー室6 (A508)
/ Seminar room 6 (A508) @ The Institute of Statistical Mathematics
Speaker
Dr. Serge Guillas
Reader (US Assoc. Prof.), Dept of Statistical Science, University College London, UK
Title
Dimension reduction for the quantification of uncertainties in tsunami and climate models
Abstract
VOLNA, a nonlinear shallow water equations solver, produces high resolution simulations of earthquake-generated tsunamis. However,
the uncertainties in the bathymetry (from irregularly-spaced observations) have an impact on tsunami waves.
We first employ a stochastic partial differential equation (SPDE) approach to quantify uncertainties in these boundary fields.
These uncertainties are then parametrized to be used as inputs of an emulator of VOLNA.
However, the dimension of these boundary fields is large and must be reduced.
We apply the gradient-based kernel dimension reduction approach (gKDR) by Fukumizu and Leng (2014) and construct an Gaussian Process emulator on this reduced input space.
We propagate uncertainties in the bathymetry to obtain an improved probabilistic assessment of tsunami hazard.
In a separate climate application, we employ the Bayesian calibration of complex computer models using Gaussian Processes, introduced by Kennedy and O'Hagan (2001),
that has proven to be effective in a wide range of applications. However, the size of the outputs, such as climate models'
spherical outputs, leads to computational challenges in implementing this framework.
Covariance models for data distributed on the sphere also present additional challenges compared to covariance models for data distributed over an Euclidean space.
To overcome these various challenges, we make use of the spherical harmonics (SHs) decomposition of the computer model output,
and then apply a Gaussian process assumption to the coefficients in the decomposition. Furthermore, using the SPDE approach, we can capture non-stationarity in the spatial process.
Hence, we generalize further the spherical correlation framework by expanding the SPDE parameters used to quantify the nonstationary behavior in the functional space spanned by the SHs.
We illustrate our findings on several synthetic examples. In particular, our method can outperform the calibration based on principal components.
Finally we show that our technique has the potential to calibrate the Whole Atmosphere Community Climate Model (WACCM).
