  In this paper, we study the well-posedness properties of a stochastic
rotating shallow water system in which the noise is chosen according to the
Stochastic Advection by Lie Transport (SALT) theory. The system is perturbed by
noise modulated by a function that is not Lipschitz in the norm where the
well-posedness is sought. We show that the system admits a unique maximal
strong solution which depends continuously on the initial condition. We also
show that the interval of existence is strictly positive and the solution is
global with positive probability.
