  A model based on a convolutional neural network (CNN) is designed to
reconstruct the three-dimensional turbulent flows beneath a free surface using
surface measurements, including the surface elevation and surface velocity.
Trained on datasets obtained from the direct numerical simulation (DNS) of
turbulent open-channel flows with a deformable free surface, the proposed model
can accurately reconstruct the near-surface flow field and capture the
characteristic large-scale flow structures away from the surface. The
reconstruction performance of the model, measured by metrics such as the
normalised mean squared reconstruction errors and scale-specific errors, is
considerably better than that of the traditional linear stochastic estimation
(LSE) method. We further analyse the saliency maps of the CNN model and the
kernels of the LSE model and obtain insights into how the two models utilise
surface features to reconstruct subsurface flows. The importance of different
surface variables is analysed based on the saliency map of the CNN, which
reveals knowledge about the surface-subsurface relations. The CNN is also shown
to have a good generalization capability with respect to the Froude number if a
model trained for a flow with a high Froude number is applied to predict flows
with lower Froude numbers. The results presented in this work indicate that the
CNN is effective regarding the detection of subsurface flow structures and by
interpreting the surface-subsurface relations underlying the reconstruction
model, the CNN can be a promising tool for assisting with the physical
understanding of free-surface turbulence.
