Assimilation of diurnal satellite retrieval of sea surface temperature with convolutional neural network

The sea surface temperature (SST) is the most examined and monitored ocean feature within the satellite era. A variety of SST datasets have been produced in recent years, each one of them with almost unique characteristics that differ from the SST variable of ocean general circulation models. The direct assimilation of such datasets is sub optimal requiring a mapping to the first model level that is non-trivial and depends on the specific characteristics of the dataset as well as local weather condition. In this work we employ a data-driven approach to construct the projection operator with machine learning (ML). The benefit is that it can be used over different SST dataset by only re-training the network. We compare conventional methodologies (climatology, linear regression) and ML networks with increasing complexity (random forest, U-Net, pix2pix). Conventional approaches are able to correct the first momentum (bias) but fail in correcting the second momentum (RMSE) in a distribution sense. The pix2pix is the most effective operator and we test it over several one-year-long reanalysis-like experiments at $1/4^{\circ}$ using different ML-assisted approaches for SST assimilation. The ML-based observation operator is beneficial mainly in the tropics but degrades in the areas of strong mesoscale activities that probably require higher resolution or longer training. The ML-unbiased approach instead improves globally the subsurface vertical temperature RMSE up to 20% against independent in situ data, when SST is the only variable assimilated. In a realistic set-up, assimilating also in situ observation and sea level anomaly retrievals, the global improvement is about 10%. The ML-unbiased operator is easily applicable to any assimilation system.