mrtsSphere
Multi-Resolution Thin-Plate Splines on the Sphere
Constructs multi-resolution thin-plate spline basis
functions on the sphere for use in spatial regression and large-scale
spatial prediction problems. Implements the basis system described in
Huang, Huang, and Ing (2025) "Multi-Resolution Spatial Methods on the
Sphere: Efficient Prediction for Global Data", Environmetrics,
mrtsSphere
Multi-resolution thin-plate spline (MRTS) basis functions on the sphere for large-scale spatial regression and prediction. R implementation of the method in:
Multi-resolution approximations of Gaussian processes for large spatial datasets on the sphere. Environmetrics, 2025. DOI: 10.1002/env.70092
The basis is constructed from the eigen-decomposition of a centered spherical kernel and is evaluated on the prediction grid via a parallel C++ routine (Rcpp + optional OpenMP).
Installation
# install.packages("remotes")
remotes::install_github("STLABTW/multi-resolution-sphere")
The package compiles C++ code on installation; you need a working
toolchain (Xcode CLT on macOS, Rtools on Windows, r-base-dev on
Linux). OpenMP is optional — without it the package still works,
single-threaded.
Quick start
library(mrtsSphere)
# Build a 20 x 10 grid of (lat, lon) locations on the sphere.
n_lon <- 20
n_lat <- 10
lon_seq <- seq(-180, 176, length.out = n_lon)
lat_seq <- seq( -90, 87, length.out = n_lat)
grid <- as.matrix(expand.grid(lat = lat_seq, lon = lon_seq))
# Pick 100 knots at random.
set.seed(1)
knots <- grid[sample(nrow(grid), 100), ]
# 10 multi-resolution basis functions evaluated on the full grid.
res <- mrts_sphere(knots, k = 10, X = grid)
dim(res$mrts) # 200 x 10
A longer worked example that simulates a spherical Gaussian random
field with fields and recovers it through the basis ships with the
package at:
system.file("articles", "mrtsSphere.Rmd", package = "mrtsSphere")
(Render with rmarkdown::render() if you have pandoc installed.)
Reproducing the paper
The original analysis scripts from the paper are bundled under
inst/paper/. After installing the package:
file.path(system.file("paper", package = "mrtsSphere"), "fullmodel-max.R")
The SST input dataset (data_sst_max_20240419.csv) is tracked via
Git LFS in this repository.
Citation
citation("mrtsSphere")
License
GPL (>= 2). See LICENSE for details.