  To estimate the displacements of physical state variables, the physics
principles that govern the state variables must be considered. Technically, for
a certain class of state variables, each state variable is associated to a
tensor field. Ways displacement maps act on different state variables will then
differ according to their associated different tensor field definitions.
Displacement procedures can then explicitly ensure the conservation of certain
physical quantities (total mass, total vorticity, total kinetic energy, etc.),
and a differential-geometry-based optimisation formulated. Morphing with the
correct physics, it is reasonable to apply the estimated displacement map to
unobserved state variables, as long as the displacement maps are strongly
correlated. This leads to a new nudging strategy using all-available
observations to infer displacements of both observed and unobserved state
variables. Using the proposed nudging method before applying ensemble data
assimilation, numerical results show improved preservation of the intrinsic
structure of underline physical processes.
