Abstract
Abstract. DINCAE (Data INterpolating Convolutional Auto-Encoder) is a neural network used to reconstruct missing data (e.g., obscured by clouds or gaps between tracks) in satellite data. Contrary to standard image reconstruction (in-painting) with neural networks, this application requires a method to handle missing data (or data with variable accuracy) already in the training phase. Instead of using a standard L2 (or L1) cost function, the neural network (U-Net type of network) is optimized by minimizing the negative log likelihood assuming a Gaussian distribution (characterized by a mean and a variance). As a consequence, the neural network also provides an expected error variance of the reconstructed field (per pixel and per time instance). In this updated version DINCAE 2.0, the code was rewritten in Julia and a new type of skip connection has been implemented which showed superior performance with respect to the previous version. The method has also been extended to handle multivariate data (an example will be shown with sea surface temperature, chlorophyll concentration and wind fields). The improvement of this network is demonstrated for the Adriatic Sea. Convolutional networks work usually with gridded data as input. This is however a limitation for some data types used in oceanography and in Earth sciences in general, where observations are often irregularly sampled. The first layer of the neural network and the cost function have been modified so that unstructured data can also be used as inputs to obtain gridded fields as output. To demonstrate this, the neural network is applied to along-track altimetry data in the Mediterranean Sea. Results from a 20-year reconstruction are presented and validated. Hyperparameters are determined using Bayesian optimization and minimizing the error relative to a development dataset.
Highlights
The data coverage often contains large gaps in space and time. This is in particular the case with in situ observations
As the altimetry observations do not resolve as many small scales as sea surface temperature, a larger domain was chosen for the altimetry test case
We found that multivariate reconstruction can improve the reconstruction, but the largest improvement was obtained by changing the structure of the neural network by using a newly implemented different type of skip connection and refinement pass
Summary
Ocean data are generally sparse and inhomogeneously distributed. The data coverage often contains large gaps in space and time. The information of the observation is injected via the loss function and propagated backward in a way which is similar to the 4D-var backward in time integration of the adjoint model Another interesting neural network architecture has been proposed in the form of the Inception network (Szegedy et al, 2015), where the output of intermediate layers, here in the form of a preliminary reconstruction, are used in the loss function (in addition to the output of the final layer). While for gridded satellite data, approaches based on empirical orthogonal functions and convolutional neural networks have been shown the be successful, it is difficult to apply similar concepts to non-gridded data as these methods typically require a stationary grid.
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