Accurate parameter estimation for the Global Tide and Surge Model (GTSM) benefits from observations with long time-series. However, increasing the number of measurements leads to a large computation demand and increased memory requirements, especially for the ensemble-based methods that assimilate the measurements at one batch. In this study, a memory-efficient parameter estimation scheme using model order reduction in time patterns is developed for a high-resolution global tide model. We propose using projection onto empirical time-patterns to reduce the model output time-series to a much smaller linear subspace. Then, to further improve the estimation accuracy, we introduce an outer-loop, similar to Incremental 4D-VAR, to evaluate model-increments at a lower resolution and subsequently reduce the computational cost. The inner-loop optimizes parameters using the lower-resolution model and an iterative least-squares estimation algorithm called DUD. The outer-loop updates the initial output from the high-resolution model with updated parameters from the converged inner-loop and then restarts the inner-loop. We performed experiments to adjust the bathymetry with observations from the FES2014 dataset. Results show that the time patterns of the tide series can be successfully projected to a lower dimensional subspace, and memory requirements are reduced by a factor of 22 for our experiments. The estimation is converged after three outer iterations in our experiment, and tide representation is significantly improved, achieving a 34.5% reduction of error. The model's improvement is not only shown for the calibration dataset, but also for several validation datasets consisting of one year of time-series from FES2014 and UHSLC tide gauges.

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(10⁶) to O(10²) 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.

Previous studies are mainly limited to temperature and salinity (T/S) profiling data assimilation, while data assimilation based on Argo float trajectory information has received less research focus. In this study, a new method was proposed to assimilate Argo trajectory data: The middepth (indicates the parking depth of Argo floats in this study, ~1200 m) velocities are estimated from Argo trajectories and subsequently assimilated into the Regional Ocean Model System (ROMS) using four-dimensional variational data assimilation (4DVAR) method. This method can avoid a complicated float trajectory model in direct position assimilation. The 2-month assimilation experiments in South China Sea (SCS) showed that this proposed method can effectively assimilate Argo trajectory information into the model and improve middepth velocity field by adjusting the unbalanced component in the velocity increments. The assimilation of the Argo trajectory-derived middepth velocity with other observations (satellite observations and T/S profiling data) together yielded the best performance, and the velocity fields at the float parking depth are more consistent with the Argo float trajectories. In addition, this method will not decrease the assimilation performance of other observations [i.e., sea level anomaly (SLA), sea surface temperature (SST), and T/S profiles], which is indicative of compatibility with other observations in the 4DVAR assimilation system.