  Data assimilation techniques are widely used to predict complex dynamical
systems with uncertainties, based on time-series observation data. Error
covariance matrices modelling is an important element in data assimilation
algorithms which can considerably impact the forecasting accuracy. The
estimation of these covariances, which usually relies on empirical assumptions
and physical constraints, is often imprecise and computationally expensive
especially for systems of large dimension. In this work, we propose a
data-driven approach based on long short term memory (LSTM) recurrent neural
networks (RNN) to improve both the accuracy and the efficiency of observation
covariance specification in data assimilation for dynamical systems. Learning
the covariance matrix from observed/simulated time-series data, the proposed
approach does not require any knowledge or assumption about prior error
distribution, unlike classical posterior tuning methods. We have compared the
novel approach with two state-of-the-art covariance tuning algorithms, namely
DI01 and D05, first in a Lorenz dynamical system and then in a 2D shallow water
twin experiments framework with different covariance parameterization using
ensemble assimilation. This novel method shows significant advantages in
observation covariance specification, assimilation accuracy and computational
efficiency.
