“…Water transport in the mantle can be expressed as where C w is the mantle water content, u is the convective velocity, and S w is the source‐sink term related to regassing; dehydration, such as nonmagmatic excess water migration; and degassing (including dehydration melting). The source‐sink effects of water migration processes are formulated as where ρ m is the mantle density, is the total mass of erupted material, C w is the water content; u z is the radial velocity, C w ,erupt is the water content of the erupted material equivalent to the water content of the molten material (see equation ), C w , ex is the excess water content relative to the water solubility, and u f is the conventional form of fluid migration velocity expressed numerically, which is computed as the ratio of radial grid spacing to the time step size (Nakagawa et al, ; Nakagawa & Spiegelman, ; Nakao et al, ). Note that computing source‐sink fluxes is done by post‐processing; therefore, they do not influence the numerical results directly.…”