Computation-Efficient Parameter Estimation for a High-Resolution Global Tide and Surge Model

In this study, a computation-efficient parameter estimation scheme for high-resolution global tide models is developed. The method is applied to Global Tide and Surge Model with an unstructured grid with a resolution of about 2.5 km in the coastal area and about 4.9 million cells. The estimation algorithm uses an iterative least squares method, known as DUD. We use time-series derived from the FES2014 tidal database in deep water as observations to estimate corrections to the bathymetry. Although the model and estimation algorithm run in parallel, directly applying of DUD would not be affordable computationally. To reduce the computational demand, a coarse-to-fine strategy is proposed by using output from a coarser model to replace the fine model. There are two approaches; One is completely replacing the fine model with a coarser model during calibration (Coarse Calibration) and the second is Coarse Incremental Calibration, that replaces the output increments between the initial model and model with modified parameters by coarser grid model simulations. To further reduce the computation time, the parameter dimension is reduced from O(10(6)) to O(10(2)) based on sensitivity analysis, which greatly reduces the required number of model simulations and storage. In combination, these methods form an efficient optimization strategy. Experiments show that the accuracy of the tidal representation can be improved significantly at affordable cost. Validation for other time-periods and using coastal tide-gauges shows that the accuracy is improved significantly. However, the calibration period of two weeks is short and leads to some over-fitting of the model. Plain Language Summary The accuracy of global tide models is currently significantly affected by the gaps in the available bathymetric data, i.e. depth of the ocean, in many regions around the world. At the same time, tides can be measured accurately by satellite radar altimetry. Here, we correct the bathymetry by reducing the disagreement between the model output and observations using mathematical methods. Computational demand for this optimization is large because a single high-resolution model simulation costs much computational time and to optimize the parameters, the model has to be run hundreds of times. We propose two ways to reduce the computational cost. First, we replace the high-resolution model with a lower resolution model being faster but less accurate. This significantly reduces the total computation time. Second, we decrease the number of parameters to an affordable number, by combining the less sensitive parameters into larger areas. Together these two methods form a complete optimization scheme for the estimation of bathymetry and significantly improve the accuracy of the tides computed by the model.