  We introduce a simple, stochastic, a-posteriori, turbulence closure model
based on a reduced subgrid scale term. This subgrid scale term is tailor-made
to capture the statistics of a small set of spatially-integrate quantities of
interest (QoIs), with only one unresolved scalar time series per QoI. In
contrast to other data-driven surrogates the dimension of the ``learning
problem" is reduced from an evolving field to one scalar time series per QoI.
We use an a-posteriori, nudging approach to find the distribution of the scalar
series over time. This approach has the advantage of taking the interaction
between the solver and the surrogate into account. A stochastic surrogate
parametrization is obtained by random sampling from the found distribution for
the scalar time series. Compared to an a-priori trained convolutional neural
network, evaluating the new method is computationally much cheaper and gives
similar long-term statistics.
