Intrinsic Non-stationary Covariance Function for Climate Modeling
This work addresses the challenge of accurate climate modeling for researchers and practitioners by providing an incremental improvement in covariance function design for non-stationary spatial data.
The paper tackles the problem of modeling non-stationary and non-uniformly smooth spatial boundaries in global-scale geospatial datasets, such as climate models, by proposing an intrinsic non-stationary covariance function for Gaussian process regression, resulting in improved error metrics on synthetic and real sea level change data.
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and non-uniformly smooth spatial boundaries. A Gaussian process regression using a non-stationary covariance function has shown promise for this task, as this covariance function adapts to the variable correlation structure of the underlying distribution. In this paper, we generalize the non-stationary covariance function to address the aforementioned global scale geospatial issues. We define this generalized covariance function as an intrinsic non-stationary covariance function, because it uses intrinsic statistics of the symmetric positive definite matrices to represent the characteristic length scale and, thereby, models the local stochastic process. Experiments on a synthetic and real dataset of relative sea level changes across the world demonstrate improvements in the error metrics for the regression estimates using our newly proposed approach.