Remote sensing of oceanographic data often yields incomplete coverage of the measurement domain. This can limit interpretability of the data and identification of coherent features informative of ocean dynamics. Several methods exist to fill gaps of missing oceanographic data and are often based on projecting the measurements onto basis functions or a statistical model. Herein, we use an information transport approach inspired from an image processing algorithm. This approach aims to restore gaps in data by advecting and diffusing information of features as opposed to the field itself. Since this method does not involve fitting or projection, the portions of the domain containing measurements can remain unaltered, and the method offers control over the extent of local information transfer. This method is applied to measurements of ocean surface currents by high frequency radars. This is a relevant application because data coverage can be sporadic, and filling data gaps can be essential to data usability. Application to two regions with differing spatial scale is considered. The accuracy and robustness of the method is tested by systematically blinding measurements and comparing the restored data at these locations to the actual measurements. These results demonstrate that even for locally large percentages of missing data points, the restored velocities have errors within the native error of the original data (e.g., <10% for velocity magnitude and <3% for velocity direction). Results were relatively insensitive to model parameters, facilitating a priori selection of default parameters for de novo applications.
Plain Language SummaryResearchers measure many geophysical phenomena by remote sensing. One example is the measurement of the ocean surface currents by land-based radar stations. The data are useful for understanding coastal dynamics and how material is transported near the ocean surface. Based on various factors, these measurements are prone to incomplete coverage. The measured data field on the map is like an incomplete image with spatial gaps where data are missing. The incompleteness in the data field reduces its utility, especially for analyses that rely on continuous coverage such as tracking the movement of objects or identifying coherent flow patterns. Several methods have been proposed to restore lost data. Inspired by a technique from image processing, we developed a method to restore incomplete field data. This method uses equations that aim to transport features in the data field into missing parts, as opposed to directly transporting the field data itself. We present this method applied to remote measurements of ocean surface currents and evaluate its ability to restore missing information. However, this approach can be applied to restore other types of incomplete field measurements to improve usability and interpretation of such data.