Reconstructing 3D ocean temperature fields from real-time satellite and buoy surface 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 are often scarce or inaccurate. Here, we present a framework to build improved spatiotemporal models that combine dynamics inferred from high-fidelity numerical models with measurements from sensors. Specifically, we are interested in ocean temperature which can serve as a useful indicator for ocean acidification, and we are motivated by a data set of sensor measurements only available at the surface of the ocean. We first apply standard principal component analysis (PCA) at every ocean surface coordinate to a numerical simulation of a 3D temperature field (reanalysis data) over time. For each horizontal location, 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 (TCN) is built to predict the time coefficients of the PCA modes, as well as their variance, as a function of the surface temperature. The full 2D surface temperature field is estimated by a multi-fidelity Gaussian process regression scheme, for which the buoys have the highest fidelity and the satellite measurements have lower fidelity. The surface temperature is then inputted into the neural network to obtain probabilistic predictions for the PCA coefficients, which are used to stochastically reconstruct the full 3D temperature field. 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 Bays, an area with a significant ocean economy. We compare the predictions with in-situ measurements at all depths. Finally, we discuss how the developed ideas can be leveraged to make more informed decisions about optimal in-situ sampling and path planning.