  Models under location uncertainty are derived assuming that a component of
the velocity is uncorrelated in time. The material derivative is accordingly
modified to include an advection correction, inhomogeneous and anisotropic
diffusion terms and a multiplicative noise contribution. This change can be
consitently applied to all fluid dynamics evolution laws. This paper continues
to explore benefits of this framework and consequences of specific scaling
assumptions. Starting from a Boussinesq model under location uncertainty, a
model is developed to describe a mesoscale flow subject to a strong underlying
submesoscale activity. As obtained, the geostrophic balance is modified and the
Quasi-Geostrophic (QG) assumptions remarkably lead to a zero Potential
Vorticity (PV). The ensuing Surface Quasi-Geostrophic (SQG) model provides a
simple diagnosis of warm frontolysis and cold frontogenesis.
