Robust Software for the Modeling of Spatial Random Fields across Geoscience Disciplines

We have developed theory, algorithmic tools, and two software suites (written in MATLAB and Python) that are openly available for use by the broad geosciences community for the statistical characterization of spatial datasets as finite, discrete random fields. Our software implements robust statistical methods that we have formulated for the simulation and estimation of stationary, isotropic, random fields on a potentially only partially observed grid within the Matérn class of parametric covariance functions. Parametric covariance models characterize the second-order structure of random fields by quantifying their shape through parameters for the amplitude, smoothness, and correlation length. Our tools allow for the analytical calculation of parameter uncertainty for modeled random fields that depend upon the parametric model and the sampling grid, agnostic of the data itself, allowing for the exploration of experimental design. Our software includes a plethora of visualization tools for studying spatial random fields and their sampling grids, including for interrogating the fit of a maximum-likelihood model (and its assumptions) to observed data. Our methodology is readily applicable for use by scientists from broad disciplines who work with (geo)spatial (ir)regularly gridded datasets.

We will present a workflow of our software to demonstrate through visualization the simulation, estimation, and analysis of spatial random fields. A typical modeling procedure for geoscientific applications involves spatial gridded data taken to be stationary, isotropic random fields under the null hypothesis. A single inversion routine estimates the Matérn covariance paramaters by optimizing the spectral-domain debiased Whittle likelihood, which involves the comparison between the modified periodogram and the parametric spectral density blurred by the effects of the observation window. We interpret the quality of our estimate, (1) by simulating additional realizations through a simulation routine that includes a circulant embedding approach, (2) by evaluating the goodness-of-fit of the model and its assumptions through multiple graphical- and test-statistic-based examinations of the model residuals, and (3) by quantifying parameter uncertainty by calculating their covariance from first principles, for which we have designed different implementations depending on the available hardware (prioritizing memory or speed). We provide documentation for multiple well-studied simulation, inversion, and analysis options with default functionality, version control, and extensive demos designed to familiarize users with not only the implementation of our tools, but also the underlying theory and its implications for their data. We share select case studies using real data that we hope will illuminate and inspire future applications, and provide a guide to our software.

Our open-source software is available on GitHub, and includes the MATLAB repositories github.com/csdms-contrib/slepian_juliet and github.com/csdms-contrib/slepian_lima, and the DSWL Python package github.com/arthurBarthe/debiased-spatial-whittle, which is in revision with the Journal of Open Source Software.