GeoNeural

A digital elevation model is a map of heights: one number for every point on a grid. Built from airborne laser scans and satellite data, these maps show where rivers run, where floods spread and how landscapes change. They are also very large: the 1 m terrain model of North Rhine-Westphalia alone holds about 34 billion heights.

GeoNeural asks whether a small neural network can store such maps in fewer bytes, with every height still within a fixed error, say 25 cm. It competes against standard codecs, the programs that pack scientific data into files and unpack them again. The map above shows one of the thirteen regions, Essen-Ruhr: southern Essen and the Ruhr valley.

The coder works like SZ3, a standard tool for scientific data, in the three steps above. Unlike photo compression, it promises a largest error for every single height. The better the guess, the smaller the file.

The neural predictor is a network of just 3.7 kB. It sharpens each guess and says how sure it is, which lets the coder pack the prediction errors tighter. It travels inside every file, so no byte is left uncounted.

Water flows downhill, so a terrain map decides where streams form, which land drains into which river, and where a flood would spread. Flood maps, erosion and soil models, and hydrological forecasts all start from these flow paths. On flat ground, a few centimeters can send water the other way.

To test this, the same routing runs on the original map and on every decoded one: small pits are filled, water flows to whichever of the eight neighbors is steepest downhill, and a stream starts where water from at least 5 hectares collects. Then the two stream maps are compared, allowing a shift of one cell: missing streams and new, false ones both lower the share of streams found again.

Hard rock tends to form steep ridges, soft rock wide valleys. So the geological map of North Rhine-Westphalia (scale 1:100,000) went into the network as an extra input, one rock unit per 40 m cell. As controls, the network also got a blank map and the real map shifted by 2.56 km. If these help as much, the gain is not geology.

In a first test on two regions, the real map saved up to 1.5% of the coded terrain, more than either control, though in one of eight runs it saved nothing. That hints at real information, but storing the map (1.8 to 3.9 kB) costs more than it saves.

Landscapes form slowly: tectonics lifts the land, rivers cut into it, and soil creeps down the slopes. Simulations step this forward in time. A plain creep law misses how creep speeds up on steep slopes; a network could learn that from data. Here a small network replaces the soil-creep step, learned first from a known simulation, and has to stay accurate over 64 steps of 200 years on surfaces it has never seen.

Many elevation models, especially those from satellites, are coarse. Here a U‑Net, a common image network, learned to turn 40 m averages into 10 m heights. It was trained on four regions and tested on two others, and every result is corrected so that it averages back to the coarse input.

In a first test its mean error was 16 to 19% lower than that of the best method without a network. Given single points instead of averages, it did worse than plain (bicubic) interpolation: much of what it learned was how the coarse map had been made.

By writing the rules down first. Before the final test, a protocol fixed the codecs, the error limits, the measures and the pass marks. Then a fixed rule picked seven new regions across the state, from flat to rough terrain, and the models were frozen. The final test ran once, and its result is reported as it came out.

Each result is an average over regions, with a range that shows how much it varies from region to region. One codec setting, the tuned SZ3, was added after the rules were set; it can only make the neural result harder to reach.