  We test the reliability of two neural network interpretation techniques,
backward optimization and layerwise relevance propagation, within geoscientific
applications by applying them to a commonly studied geophysical phenomenon, the
Madden-Julian Oscillation. The Madden-Julian Oscillation is a multi-scale
pattern within the tropical atmosphere that has been extensively studied over
the past decades, which makes it an ideal test case to ensure the
interpretability methods can recover the current state of knowledge regarding
its spatial structure. The neural networks can, indeed, reproduce the current
state of knowledge and can also provide new insights into the seasonality of
the Madden-Julian Oscillation and its relationships with atmospheric state
variables.
  The neural network identifies the phase of the Madden-Julian Oscillation
twice as accurately as linear regression, which means that nonlinearities used
by the neural network are important to the structure of the Madden-Julian
Oscillation. Interpretations of the neural network show that it accurately
captures the spatial structures of the Madden-Julian Oscillation, suggest that
the nonlinearities of the Madden-Julian Oscillation are manifested through the
uniqueness of each event, and offer physically meaningful insights into its
relationship with atmospheric state variables. We also use the interpretations
to identify the seasonality of the Madden-Julian Oscillation, and find that the
conventionally defined extended seasons should be shifted later by one month.
More generally, this study suggests that neural networks can be reliably
interpreted for geoscientific applications and may there
