Quantifying volumetric erosion from symbolic expression of landslide morphology

Kushanav Bhuyan , Xuanmei Fan, Chengyong Fang, Lorenzo Nava, Xin Wang, Jie Liu, Maximillian Van Wyk De Vries, Filippo Catani , Ugur Öztürk, Luigi Lombardo 

Landslide volumetric erosion is fundamental to regional sediment budgets and downstream hazard assessment, yet accurately constraining material mobilization remains a primary bottleneck in Earth-system research. Legacy area–volume relations introduce substantial uncertainty when applied across heterogeneous landslide populations. Here, we examine whether the erosional and accumulation (i.e., runout) domains provide information beyond source area alone for volumetric erosion. Using neural-guided symbolic regression, we identify an expression that preserves source area as the first-order control on erosional volume while introducing a dimensionless descriptor of the accumulation counterpart, as a geometric correction. For the 2016 Kaikōura earthquake inventory, the framework estimates a cumulative eroded volume of 54.9 Mm3, compared with the measured 56.5 Mm3. The formulation was additionally applied without recalibration to the independent 2018 Hokkaidō inventory and subsequently used for blind inference on 32 landslides from the 2013 Lushan earthquake, yielding a cumulative estimate of 1.95 Mm3 of volumetric erosion. Because independent volume observations are unavailable for Lushan, this application is treated as inference rather than external validation. Polygon-generalization experiments further indicate that our new formulation remains stable across different mapping resolutions. These results show that scale-normalized planform geometry can provide complementary information to source area when constraining landslide erosion. The proposed framework is therefore intended as an empirical extension to, rather than a replacement for, established area–volume scaling.