  This article proposes for stochastic partial differential equations (SPDEs)
driven by additive noise, a novel approach for the approximate
parameterizations of the ``small'' scales by the ``large'' ones, along with the
derivaton of the corresponding reduced systems. This is accomplished by seeking
for stochastic parameterizing manifolds (PMs) introduced in a previous work by
the authors(*), which are random manifolds aiming to provide --- in a mean
square sense --- such approximate parameterizations. Backward-forward systems
are designed to give access to such PMs as pullback limits depending through
the nonlinear terms on the time-history of the dynamics of the low modes when
the latter is simply approximated by its stochastic linear component. It is
shown that the corresponding pullback limits can be efficiently determined,
leading in turn to an operational procedure for the derivation of non-Markovian
reduced systems able to achieve good modeling performances in practice. This is
illustrated on a stochastic Burgers-type equation, where it is shown that the
corresponding non-Markovian features of these reduced systems play a key role
to reach such performances.
