Multi-Resolution Spatial Methods on the Sphere: Efficient Prediction for Global Data

This repository contains the code for the paper:

Multi-resolution approximations of Gaussian processes for large spatial datasets on the sphere Environmetrics, 2025. DOI: 10.1002/env.70092

Spherical multi-resolution regression applied to global sea-surface temperature (SST) data.

Overview

fullmodel-max.R fits the model to the SST annual-maximum dataset and produces:

• predicted SST map (Mollweide projection)
• prediction standard-error map
• raw-data map

The method uses multi-resolution thin-plate splines (MRTS) on the sphere combined with a locally-supported Matérn covariance (Wendland tapering).

Files

File	Description
fullmodel-max.R	Main analysis script for the annual-maximum dataset
fn_pcc_test_pre.R	C++ kernel functions (compiled via Rcpp) and MRTS helpers
fn_0610.R	Variogram objective functions for parameter estimation
effectivefn.R	Matérn effective-range calculator
integral_table2.rds	Pre-computed lookup table for the kernel integrals
data_sst_max_20240419.csv	SST annual-maximum dataset (tracked via Git LFS)

Data

data_sst_max_20240419.csv contains ~6.4 million ocean-grid observations with columns: latitude, longitude, temperature (°C).

The file is stored in this repository via Git LFS. Clone with LFS support:

git lfs install
git clone <repo-url>

Dependencies (R packages)

install.packages(c(
  "icosa", "fields", "sf", "rnaturalearth", "rnaturalearthdata",
  "pracma", "raster", "maps", "SparseM", "ggplot2",
  "RSpectra", "Rcpp", "RcppArmadillo", "RcppEigen",
  "RcppNumerical", "GpGp", "MASS", "Matrix"
))

Usage

Set the working directory to the repo root and run:

source("fullmodel-max.R")

Output PNG files are saved to realdata/.