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

翻译：海面风速是多种科学应用和人类活动的关键物理量。由于该现象的非线性特性，在小尺度和大空间范围上对该变量的完整描述难以实现。依赖数据同化技术的方法——尽管是数值天气预报领域的当前最优方案——无法提供与卫星图像相媲美的空间分辨率重建结果。本文提出了一种基于变分数据同化与深度学习概念的框架，并将其应用于恢复时间密集、高分辨率的海面风速信息。我们采用合成风数据及原始数据的高分辨率和低分辨率版本的不同采样方案设计实验，以模拟时空异质观测的真实场景。通过大量数值实验系统评估了低分辨率和高分辨率风场及原位观测对模型重建性能的影响。研究表明，具有更丰富时间分辨率的原位观测在模型重建性能方面具有附加价值。我们进一步展示了一种多模态方法——通过显式告知模型观测数据的异质性——能够利用空间和局部点状数据中的互补信息提升重建任务。最后，我们提出一项鲁棒性分析，检验所选框架在低分辨率数据的相位延迟与振幅偏差、以及评估阶段原位观测数据供应中断情况下的表现。