mSTAR: Multicriteria Spatio Temporal Altimetry Retracking

Observing coastal sea-level change from satellite altimetry is challenging due to land influence on the estimated sea surface height (SSH), significant wave height (SWH), and backscatter. In recent years specialized algorithms have been developed which allow retrieving meaningful estimates up to the coast. Among these, the Spatio Temporal Altimetry Retracker (STAR) has introduced a novel approach by partitioning the total return signal into individual sub-signals which are then processed leading to a point-cloud of potential estimates for each of the three parameters which tend to cluster around the true values, e.g., the real sea surface. The original STAR algorithm interprets each point-cloud as a weighted directed acyclic graph (DAG). The spatio-temporal ordering of the potential estimates induces a layering, and each layer is fully connected to the next. The weights of the edges are based on a chosen distance measure between the connected vertices. The STAR algorithm selects the final estimates by searching the shortest path through the DAG using forward traversal in topological order. This approach includes the inherent assumption that neighboring SSHs etc. should be similar. However, a drawback of the original STAR approach is that each of the point clouds for the three parameters can only be treated individually since the applied standard shortest path approach can not handle multiple edge weights. Therefore, the output of the STAR algorithm for each parameter does not necessarily correspond to the same sub-signal. To overcome this limitation, we propose to employ a multicriteria approach to find a final estimate that takes the weighting of two or three point-clouds into account resulting in the multicriteria Spatio Temporal Altimetry Retracking (mSTAR) framework. An essential difference between the single and the multicriteria shortest path problems is that there is no single optimal solution in the latter. We call a path Pareto-optimal if there is no other path that is strictly shorter for all criteria. Unfortunately, the number of Pareto-optimal paths can be exponential in the input size, even if the considered graph is a DAG. A simple and common approach to tackle this complexity issue is to use the weighted sum scalarization method, in which the objective functions are weighted and combined to a single objective function, such that a single criteria shortest path algorithm can find a Pareto-optimal path. Varying the weighting, a set of Pareto-optimal solutions can be obtained. However, it is in general not possible to find all Pareto-optimal paths this way. In order to find all Pareto-optimal paths, label-correcting or label-setting algorithms can be used. The mSTAR framework supports both scalarization and labeling techniques as well as exact and approximate algorithms for computing Pareto-optimal paths. This way mSTAR is able to find multicriteria consistent estimates of SSH, SWH, and backscatter.