Unified Scaling Law for Lengths of Basaltic Lava Flows: Dependence on Erupted Volume and Effusion Rate

Morphological scaling laws for basaltic lava flows, linking flow dimensions and eruption conditions, are essential for hazard assessment and geological analysis of basaltic eruptions. However, the governing factors influencing flow dimensions remain unclear. We developed a scaling law for lava dimensions based on natural observations, with insights obtained from numerical simulations. We found that lava flow dynamics transition from a volume-limited regime to a cooling-limited regime as the effusion duration increases. In the volume-limited regime, flow length increases with erupted volume raised to the power of 0.67, while in the cooling-limited regime, it increases with effusion rate raised to the power of 0.60. We also found that Mauna Loa's flows follow the volume-limited regime, while Mt. Etna's flows can follow either the volume-limited or cooling-limited regime, reflecting their differing cooling timescales. Consequently, we established a unified scaling law that quantitatively links flow length to erupted volume and effusion rate.