  Increasing the resolution of a model can improve the performance of a data
assimilation system: first because model field are in better agreement with
high resolution observations, then the corrections are better sustained and,
with ensemble data assimilation, the forecast error covariances are improved.
However, resolution increase is associated with a cubical increase of the
computational costs. Here we are testing an approach inspired from images
super-resolution techniques and called "Super-resolution data assimilation"
(SRDA). Starting from a low-resolution forecast, a neural network (NN) emulates
a high-resolution field that is then used to assimilate high-resolution
observations. We apply the SRDA to a quasi-geostrophic model representing
simplified surface ocean dynamics, with a model resolution up to four times
lower than the reference high-resolution and we use the Ensemble Kalman Filter
data assimilation method. We show that SRDA outperforms the low-resolution data
assimilation approach and a SRDA version with cubic spline interpolation
instead of NN. The NN's ability to anticipate the systematic differences
between low and high resolution model dynamics explains the enhanced
performance, for example by correcting the difference of propagation speed of
eddies. Increasing the computational cost by 55\% above the LR data
assimilation system (using a 25-members ensemble), the SRDA reduces the errors
by 40\% making the performance very close to the HR system (16\% larger,
compared to 92\% larger for the LR EnKF). The reliability of the ensemble
system is not degraded by SRDA.
