  A dynamical four-vertex model of rearranging hydrogen-bonded network in ice,
with a dynamics similar to the Grotthuss mechanism, is proposed. The model
qualitatively explains the unusually high proton-conductivity in ice. It also
serves as an interesting example of self-organized criticality with a
non-conservative dynamics. The model is solved on a linear chain and its steady
state is determined. Using numerical simulations, the model is further studied
on a square lattice, and it is observed that it relaxes by three different
avalanches, each of which follows a simple finite-size scaling.
