A Multi-Fidelity Framework for Ocean Temperature Reconstruction Based on
Model-Inferred Dynamics and Real Time Satellite and Buoy Measurements
Abstract
Despite advancements in computational science, nonlinear geophysical
processes still present important modeling challenges. Physical sensors
(such as satellites, AUVs, or buoys) can collect data at specific points
or regions, but these are often scarce or inaccurate. Here, we present a
method to build improved spatio-temporal models that combine dynamics,
inferred from high-fidelity numerical models (reanalysis data), and data
from sensors. We are motivated by a data set of ocean temperature where
sensor measurements are only available at the surface of the ocean. We
first employ reanalysis data in the form of a 3D temperature field, and
apply standard principal component analysis (PCA) at every ocean surface
coordinate. For each coordinate, the vertical structure of the field can
be represented with just two PCA modes and their corresponding time
coefficients, significantly reducing the dimensionality of the data.
Next, a conditionally Gaussian model, implemented through a temporal
convolutional neural network, is built to predict the time coefficients
of the PCA modes (i.e. vertical structure), as well as their variance,
as a function of the surface temperature. These probabilistic
predictions are made with the satellite data as input, and they are used
with the PCA modes to stochastically reconstruct the full temperature
field. The estimated temperature field is then combined with data from
buoys through a multi-fidelity Gaussian process regression scheme, where
the buoys have the highest fidelity and the satellite-based predictions
have lower fidelity. The techniques described provide a framework for
building less expensive and more accurate models of conditionally
Gaussian estimates for full 3D fields, and they can be applied to
geophysical systems where data from both sensors and numerical
simulations are available. We implement these techniques to estimate the
full 3D temperature field of the Massachusetts and Cape Cod Bay where
temperature can serve as a useful indicator for ocean acidification.
Finally, we discuss how the developed ideas can be leveraged to make
more informed decisions about optimal in-situ sampling and path
planning.