  A new efficient ensemble prediction strategy is developed for a general
turbulent model framework with emphasis on the nonlinear interactions between
large and small scale variables. The high computational cost in running large
ensemble simulations of high dimensional equations is effectively avoided by
adopting a random batch decomposition of the wide spectrum of the fluctuation
states which is a characteristic feature of the multiscale turbulent systems.
The time update of each ensemble sample is then only subject to a small portion
of the small-scale fluctuation modes in one batch, while the true model
dynamics with multiscale coupling is respected by frequent random resampling of
the batches at each time updating step. We investigate both theoretical and
numerical properties of the proposed method. First, the convergence of
statistical errors in the random batch model approximation is shown rigorously
independent of the sample size and full dimension of the system. Then, the
forecast skill of the computational algorithm is tested on two representative
models of turbulent flows exhibiting many key statistical phenomena with direct
link to realistic turbulent systems. The random batch method displays robust
performance in capturing a series of crucial statistical features of general
interests including highly non-Gaussian fat-tailed probability distributions
and intermittent bursts of instability, while requires a much lower
computational cost than the direct ensemble approach. The efficient random
batch method also facilitates the development of new strategies in uncertainty
quantification and data assimilation for a wide variety of complex turbulent
systems in science and engineering.
