  Wind speed at sea surface is a key quantity for a variety of scientific
applications and human activities. Due to the non-linearity of the phenomenon,
a complete description of such variable is made infeasible on both the small
scale and large spatial extents. Methods relying on Data Assimilation
techniques, despite being the state-of-the-art for Numerical Weather
Prediction, can not provide the reconstructions with a spatial resolution that
can compete with satellite imagery. In this work we propose a framework based
on Variational Data Assimilation and Deep Learning concepts. This framework is
applied to recover rich-in-time, high-resolution information on sea surface
wind speed. We design our experiments using synthetic wind data and different
sampling schemes for high-resolution and low-resolution versions of original
data to emulate the real-world scenario of spatio-temporally heterogeneous
observations. Extensive numerical experiments are performed to assess
systematically the impact of low and high-resolution wind fields and in-situ
observations on the model reconstruction performance. We show that in-situ
observations with richer temporal resolution represent an added value in terms
of the model reconstruction performance. We show how a multi-modal approach,
that explicitly informs the model about the heterogeneity of the available
observations, can improve the reconstruction task by exploiting the
complementary information in spatial and local point-wise data. To conclude, we
propose an analysis to test the robustness of the chosen framework against
phase delay and amplitude biases in low-resolution data and against
interruptions of in-situ observations supply at evaluation time
