  To make weather/climate modeling computationally affordable, small-scale
processes are usually represented in terms of the large-scale,
explicitly-resolved processes using physics-based or semi-empirical
parameterization schemes. Another approach, computationally more demanding but
often more accurate, is super-parameterization (SP), which involves integrating
the equations of small-scale processes on high-resolution grids embedded within
the low-resolution grids of large-scale processes. Recently, studies have used
machine learning (ML) to develop data-driven parameterization (DD-P) schemes.
Here, we propose a new approach, data-driven SP (DD-SP), in which the equations
of the small-scale processes are integrated data-drivenly using ML methods such
as recurrent neural networks. Employing multi-scale Lorenz 96 systems as
testbed, we compare the cost and accuracy (in terms of both short-term
prediction and long-term statistics) of parameterized low-resolution (LR), SP,
DD-P, and DD-SP models. We show that with the same computational cost, DD-SP
substantially outperforms LR, and is better than DD-P, particularly when scale
separation is lacking. DD-SP is much cheaper than SP, yet its accuracy is the
same in reproducing long-term statistics and often comparable in short-term
forecasting. We also investigate generalization, finding that when models
trained on data from one system are applied to a system with different forcing
(e.g., more chaotic), the models often do not generalize, particularly when the
short-term prediction accuracy is examined. But we show that transfer-learning,
which involves re-training the data-driven model with a small amount of data
from the new system, significantly improves generalization. Potential
applications of DD-SP and transfer-learning in climate/weather modeling and the
expected challenges are discussed.
