Multi-Resolution Thin-Plate Splines on the Sphere.

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.