Semi-Analytical Prediction of Pyroclastic Flow Distance Using Adomian Decomposition and Real-Time Dome Growth Data: A Case Study of Mount Merapi

Accurate prediction of pyroclastic flow runout distances is crucial for mitigating volcanic hazards, especially for Mount Merapi, Indonesia, where frequent eruptions threaten nearby communities. This study develops a semi-analytical model to forecast flow distances during the May 5–11, 2021 eruption, utilizing the Porous Medium Equation (PME) to capture nonlinear flow dynamics and the Adomian Decomposition Method (ADM) to provide effective, recursive solutions.A custom application built in Replit, leveraging Python with SymPy and NumPy, automates simulations, enabling rapid computation of flow profiles. Initial conditions were iteratively refined from a narrow Gaussian u(x, 0) = 1.5e-100x2 to a broader profile u(x, 0) = 3e-0.68x2, calibrated with BPPTKG’s dome growth data (1.1 × 106 m³). The model predicts runouts up to 3.0 km, validated against six-hourly observations (2km) and tested for sensitivity to the nonlinearity exponent (m = 3).Unlike resource-intensive numerical models or less accurate empirical approaches, this Replit-based solution offers fast and reliable predictions, enhancing semi-analytic methods and improving real-time volcanic hazard forecasting for Merapi