  Historical records of climate fields are often sparse due to missing
measurements, especially before the introduction of large-scale satellite
missions. Several statistical and model-based methods have been introduced to
fill gaps and reconstruct historical records. Here, we employ a recently
introduced deep-learning approach based on Fourier convolutions, trained on
numerical climate model output, to reconstruct historical climate fields. Using
this approach we are able to realistically reconstruct large and irregular
areas of missing data, as well as reconstruct known historical events such as
strong El Ni\~no and La Ni\~na with very little given information. Our method
outperforms the widely used statistical kriging method as well as other recent
machine learning approaches. The model generalizes to higher resolutions than
the ones it was trained on and can be used on a variety of climate fields.
Moreover, it allows inpainting of masks never seen before during the model
training.
