The Taal Volcano underwent a phreatic eruption on January 12, 2020, causing volcanic ashfall that affected adjacent regions. To ensure public safety and minimize damage, rapid and data-driven decisions are required during volcanic eruptions to anticipate the movement of volcanic ash. In this work, we simulate volcanic ash dispersion during the 2020 Taal Volcano eruption using an atmospheric dispersion model governed by a second-order parabolic partial differential equation derived from the law of conservation of mass.

To obtain numerical solutions, we apply the finite difference method and present several case scenarios. Moreover, we estimate the diffusion rate using three approaches. The first approach is based on multiple observations and simulations, where the diffusion coefficient is varied across simulations. The second approach fits the numerical solution of the governing equation to observational data collected during the eruption using the least squares method. The third approach estimates the diffusion rate using the brightness temperature of the eruption.

The estimated diffusion rate provides information on the spatial extent and potential trajectory of volcanic ash dispersion, which is essential for risk assessment and disaster management.