A Lagrangian framework for detecting and characterizing the descent of foehn from Alpine to local scales

When foehn winds cross the Alps from the south, they often descend abruptly and vigorously into the valleys on the northern side. Although mountain gravity waves and hydraulic theory offer theoretical explanations for this phenomenon, the descent of the Alpine south foehn has never been systematically quantified across real-case events. This study addresses that knowledge gap using kilometer-scale numerical simulations combined with online trajectory calculations.

In the first part, we find that foehn air parcels descend primarily at distinct hotspots immediately downwind of local peaks and ridges, highlighting the anchoring role of local topography. The magnitude of descent correlates clearly with small-scale terrain elevation differences, though other factors also contribute. Since the descent is mostly dry adiabatic, the motion appears to follow downward-sloping isentropes tied to gravity waves. A minority of air parcels undergo diabatic cooling and moisture uptake, mostly south of the Alpine crest.

The second part examines factors governing descent at the local scale, focusing on a prominent hotspot along the Rätikon — a mountain range bordering the Rhine Valley — through two detailed case studies. During periods of intensified descent, gravity waves excited by local Rätikon peaks drive air parcels down into the range's northern tributaries and into the Rhine Valley. The two cases reveal different wave regimes — vertically propagating waves, breaking waves, and horizontally propagating lee waves — none of which is consistently dominant, suggesting no single regime defines foehn descent along the Rätikon. Beyond gravity waves, additional effects matter too: a topographic concavity deflects near-surface flow and promotes strong descent toward the valley floor, while in one case nocturnal cooling creates a smooth virtual topography that suppresses gravity wave development and inhibits foehn descent into the valley.

In summary, applying a Lagrangian framework to a comprehensive multi-case dataset reveals that foehn descent is inherently local, topographically anchored, and shaped by a variety of interacting wave regimes and secondary effects. This perspective not only complements but substantially extends the traditional Eulerian view  of foehn dynamics.