Moving-Window Regression Downscaling of Raster Data

Downscales coarse-resolution raster data to a finer grid by fitting local linear regressions of a response, such as a climate variable, on one or more fine-resolution predictors, such as elevation and other terrain indices, within a moving window. Regression coefficients are estimated for every cell using summed-area tables, so the cost is independent of the window size, then resampled to the target resolution and applied to the fine-resolution predictors. Multiplicative and additive anomaly application downscale time series relative to a baseline climatology, following the regression-on-elevation approach used for high-resolution climate surfaces described in Karger et al. (2017) .

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topocast

coarse climate grids at the resolution of your terrain

Downscale a coarse raster onto fine terrain by moving-window regression.

A coarse blocky precipitation grid beside the same field downscaled onto fine terrain, sharing one color scale.

plot of chunk downscale

Give topocast a coarse variable and a fine predictor it tracks. In a window around every cell it learns how the variable depends on the predictor, then evaluates that local relationship on the fine predictor. A 1 km precipitation grid and a 100 m elevation model become a 100 m precipitation grid.

library(topocast)
library(terra)

names(prec_1km) <- "prec"      # coarse variable, what you want at high resolution
names(dem_100m) <- "elev"      # fine predictor it tracks

prec_100m <- topocast(prec ~ elev, data = prec_1km, onto = dem_100m, radius = 15)

prec_100m is precipitation on the elevation model's grid. Coarse to fine is one call: name the response and the predictor in a formula, pass the coarse grid as data and the fine grid as onto.

What goes in, what comes out

data is the coarse variable you want at higher resolution, as a SpatRaster, Raster*, or stars grid. The layer on the left of the formula is the response.
onto is the target: a fine grid holding the predictor(s) the variable tracks, often a digital elevation model. It can also be a set of station or plot points carrying those predictors as attributes.
the result is the response on the geometry of onto, in the class of onto: a raster at the fine resolution for a grid target, a prediction column for a point target.

When the only fine layer you have is the predictor itself, as in the example above, topocast derives the coarse predictor from onto for you, so a single coarse climate layer and a DEM are enough to start.

How it works

The relationship is fit locally, in a square window around every coarse cell, with summed-area tables: each window fit reduces to four lookups per sufficient statistic, so a radius of 30 costs the same as a radius of 3. The fitted intercept and slope grids are resampled to the fine grid and combined with the fine predictors as fitted = intercept + sum(slope * predictor), so the output carries the fine-scale structure of the terrain with locally varying coefficients. This is the regression step behind high-resolution climate surfaces such as CHELSA (Karger et al. 2017); topocast runs it locally and takes any number of named predictors.

What's in the box

One front door. topocast() takes a formula, the coarse data, and the fine onto, and returns the downscaled response.
Any number of predictors. prec ~ elev + slope + twi fits elevation, slope, topographic wetness, or any aligned covariate jointly. The formula names match layers between data and onto, so a missing layer is reported by name.
Several responses in one call. cbind(prec, tmin) ~ elev downscales variables that share the terrain together. The window design is built once and solved against each response, so a second response costs little more than the first.
Constant cost per window. Summed-area tables keep each per-cell fit at four lookups for any radius.
Common spatial classes. SpatRaster, Raster* (raster), and stars grids are all accepted; the result comes back in the class of onto, or the class named by output.
Prediction at points. Pass an sf or SpatVector of stations or plots as onto and receive a prediction column, with the points carrying the fine predictor values.
Time series in one call. Pass a stack of periods as anomaly to fit the baseline once and carry each period onto it, "ratio" for precipitation or "additive" for temperature.
Fit quality on the map. diagnostics = TRUE returns an r.squared grid showing where the terrain relationship is strong, and clamp = TRUE bounds the output to the observed range of the coarse response.
A matrix engine. window_regression() exposes the kernel for callers who hold their data as matrices.

Installation

# install.packages("pak")
pak::pak("gcol33/topocast")

Usage

Several predictors, matched by name between the two grids:

coarse <- c(prec_1km, elev_1km, twi_1km, slope_1km)
names(coarse) <- c("prec", "elev", "twi", "slope")
terrain <- c(elev_100m, twi_100m, slope_100m)
names(terrain) <- c("elev", "twi", "slope")

prec_100m <- topocast(prec ~ elev + twi + slope, data = coarse, onto = terrain,
                      radius = 15)

Several responses that share the terrain, downscaled in one pass and returned as one layer each:

climate_100m <- topocast(cbind(prec, tmin, tmax) ~ elev, data = coarse,
                         onto = terrain, radius = 15)

A monthly series sharing one terrain relationship across periods:

series <- topocast(prec ~ elev, data = coarse, onto = terrain, radius = 15,
                   anomaly = prec_monthly_1km, type = "ratio")

Downscaling straight to plot locations, returned as a column on the points:

at_plots <- topocast(prec ~ elev, data = coarse, onto = plots_sf, radius = 15)

The local coefficient grids, to read the fitted lapse rate:

coefs <- topocast(prec ~ elev, data = coarse, onto = terrain, radius = 15,
                  coefficients = TRUE)

Documentation

Support

"Software is like sex: it's better when it's free." — Linus Torvalds

I'm a PhD student who builds R packages in my free time because I believe good tools should be free and open. I started these projects for my own work and figured others might find them useful too.

If this package saved you some time, buying me a coffee is a nice way to say thanks. It helps with my coffee addiction.

License and citation

MIT. If you use topocast in published work, please cite it:

@software{topocast,
  author = {Colling, Gilles},
  title  = {topocast: Moving-Window Regression Downscaling of Raster Data},
  year   = {2026},
  url    = {https://github.com/gcol33/topocast}
}