  Motivated by the concept of ``location uncertainty", initially introduced in
\cite{Memin2013FluidFD}, a scheme is sought to perturb the ``location" of a
state variable at every forecast time step. Further considering Brenier's
theorem \cite{Brenier1991}, asserting that the difference of two positive
density fields on the same domain can be represented by a transportation map,
perturbations are demonstrated to consistently define a SPDE from the original
PDE. It ensues that certain quantities, up to the user, are conserved at every
time step. Remarkably, derivations following both the SALT
\cite{Holm2015VariationalPF} and LU \cite{Memin2013FluidFD,
Resseguier2016GeophysicalFU} settings, can be recovered from this perturbation
scheme. Still, it opens broader applicability since it does not explicitly rely
on Lagrangian mechanics or Newton's laws of force. For illustration, a
stochastic version of the thermal shallow water equation is presented.
