  In recent years, stochastic parametrizations have been ubiquitous in
modelling uncertainty in fluid dynamics models. One source of model uncertainty
comes from the coarse graining of the fine-scale data and is in common usage in
computational simulations at coarser scales. In this paper, we look at two such
stochastic parametrizations: the Stochastic Advection by Lie Transport (SALT)
parametrization introduced by Holm and the Location Uncertainty (LU)
parametrization introduced by M\'emin. Whilst both parametrizations are
available for full-scale models, we study their reduced order versions obtained
by projecting them on a complex vector Fourier mode triad of eigenfunctions of
the curl. Remarkably, these two parametrizations lead to the same reduced order
model, which we term the helicity-preserving stochastic triad (HST). This
reduced order model is then compared with an alternative model which preserves
the energy of the system, and which is termed the energy preserving stochastic
triad (EST). These low-dimensional models are ideal benchmark models for
testing new Data Assimilation algorithms: they are easy to implement, exhibit
diverse behaviours depending on the choice of the coefficients and come with
natural physical properties such as the conservation of energy and helicity.
