Estimating Ocean Surface Level using the Intrinsic Non-stationary Covariance Function

Abstract:

A spatio-temporal estimation of the ocean surface level poses a challenging problem for reasons including non-stationarity, non-uniformly smooth spatial boundaries and a short range in the temporal dimension of the densely measured satellite altimeter dataset. Gaussian processes using a non-stationary covariance function have shown promise for such a task, as the covariance function adapts to the variable smoothness of the underlying distribution. We present a novel framework which employs the intrinsic non-stationary covariance function for a Gaussian process regression. The intrinsic non-stationary covariance function evaluates intrinsic statistics of the local distribution by assuming that the distribution lies on a Riemannian manifold of positive definite matrices; thereby, the non-stationarity and the non-uniformly spatial variability of the data are captured. Additionally, the framework improves the short range temporal estimates by assimilating data from a correlated process of a temporally longer range dataset. For such a data-assimilation technique, we used the dataset of tide gauge records that measure coastal sea bed levels at a geospatially sparse distribution of global sites. Experiments on satellite altimeter measurements of ocean surface level across the world from 1993 onwards demonstrate improvements in the error metrics for the regression estimates when using our novel framework. Furthermore, assimilating the tide gauge measurements from 1802 onwards gives better estimates for the long-term trends of the ocean surface level. These spatio-temporal estimates of past records of the ocean surface level will enable us to more accurately assess risks arising due to climate change.