Nonparametric spectral methdods for multivariate spatial and spatial-temporal data.

Area of Science:

• Geostatistics
• Environmental Science
• Data Analysis

Background:

• Estimating spatial and spatio-temporal spectra from incomplete gridded data presents significant computational challenges.
• Existing methods often struggle with accuracy and efficiency when dealing with missing data points.

Purpose of the Study:

• To develop computationally efficient, iterative methods for estimating stationary multivariate spatial and spatio-temporal spectra from incomplete gridded data.
• To introduce techniques for decomposing cross-spectral density functions and comparing models across different datasets.

Main Methods:

• Iterative imputation of missing data using a periodic model on an expanded domain.
• Application of circulant embedding techniques to reduce edge effects in periodogram estimation.
• Decomposition of cross-spectral density into a linear model of coregionalization and a residual process.

Main Results:

• Demonstrated computational feasibility on datasets exceeding 200,000 observations.
• Successfully applied methods to storm datasets, including Hurricane Florence (2018).
• Enabled comparison of fitted models from different spatial-temporal datasets.

Conclusions:

• The proposed methods offer a computationally efficient and robust approach for analyzing incomplete spatial and spatio-temporal data.
• These techniques are valuable for environmental studies, particularly in analyzing extreme weather events.
• The methods facilitate accurate spectral estimation and model comparison, enhancing our understanding of spatial processes.