Does the Neretva obey Hack's law?

In August, Quanta Magazine asked why rivers are so mathematical. The centerpiece is Hack’s law: the length of a stream grows with its drainage area to roughly the 0.6 power; if basins simply scaled up like photocopies, it would be 0.5. A second regularity is that tributaries in humid landscapes meet at about 72°.

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I tested both on the Neretva. The short version: with the surface basin from the Copernicus 90 m elevation model (karst fields treated as sinks, 5,358 km²), Hack’s original constant predicts 220 km against the river’s observed 225 km, and the implied exponent is 0.60 on the nose. Add the official basin’s underground contributions from the Trebišnjica and the river is far “too short” for its area, because Hack’s law describes channels carved by surface flow and karst water carves nothing on its way to the Neretva.

Junction angles average 79°, a few degrees wider than the 72° prediction. The Rama, Rakitnica, Neretvica and Drežanka sit on the line; Mostar’s Radobolja and Bijela run long for their size; the Buna, fed underground from the Nevesinje karst field through the Blagaj spring, is the shortest river for its area of all.

Terrain from Copernicus DEM GLO-90, imagery from EOX’s Sentinel-2 cloudless 2020 mosaic (CC BY-NC-SA 4.0), cross-checked against HydroRIVERS. Data tables: tributaries, all sub-basins, fits by threshold.