Dem Resampling Smoothing Tool

Resampling rebuilds an elevation grid on a new cell spacing, and the arithmetic of the output size follows directly from the resample factor, the target resolution divided by the original. Going from 10 m to 30 m cells gives a factor of 3, so a 1000 by 1200 grid becomes about 333 by 400 and the cell count falls by roughly 89 percent. Storage scales with cell count: at 4 bytes per cell for 32-bit floating point elevations, 1.2 million cells occupy about 4.6 MB and the resampled grid under 0.6 MB. The interpolation kernel matters as much as the geometry. Nearest neighbour copies the closest input value and preserves the original numbers but produces blocky terrain, bilinear averages the four surrounding cells, and cubic convolution weights sixteen cells for the smoothest surface, at the cost of occasionally producing elevations outside the input range. The Nyquist limit sets the honest ceiling on what survives. A grid can only represent features with wavelengths of at least twice the cell spacing, so a 30 m output resolves nothing finer than about 60 m regardless of how detailed the source was. Coarsening without first low-pass filtering aliases that lost detail into spurious large-scale patterns, which is why a smoothing kernel is applied before downsampling. Two limits are worth stating plainly: resampling to finer cells adds no information and only interpolates, and slope statistics are not preserved across resolutions, since coarsening systematically flattens the terrain and lowers computed gradients.

The sampling theory that governs resampling was worked out for communications, not terrain. Harry Nyquist described the relationship between sampling rate and recoverable signal content at Bell Labs in 1928, and Claude Shannon formalised it in his 1949 paper on communication in the presence of noise. When digital image processing emerged in the 1960s and 1970s, largely driven by satellite and planetary imagery at NASA and its contractors, those results transferred directly to two-dimensional grids and established that resampling without prefiltering causes aliasing. The standard kernels arrived in that same period. Nearest neighbour and bilinear interpolation were long-established numerical methods, while cubic convolution was developed for Landsat image rectification in the mid-1970s by Shlomo Rifman and colleagues and given its rigorous analysis by Robert Keys in a 1981 paper in IEEE Transactions on Acoustics, Speech, and Signal Processing. Grid elevation models themselves date to the 1950s and 1960s, with the term digital terrain model coined by Charles Miller and Robert Laflamme at MIT in 1958 for highway design work. As national agencies began distributing elevation data at incompatible resolutions, resampling became a routine preprocessing step rather than a specialist operation. The open-source GDAL library, begun by Frank Warmerdam in 1998, consolidated these algorithms into a common implementation now used underneath QGIS, GRASS, and most commercial GIS packages.