Application of Continuous Data Assimilation in High-Resolution Ocean Modeling

Abstract

We demonstrate a formulation of the Azouani-Olson-Titi (AOT) algorithm in the MPAS-Ocean implementation of the primitive equations of the ocean, presenting global ocean simulations with realistic coastlines and bathymetry. We observe an exponentially fast decay in the error before reaching a certain error level, which depends on the terms involved and whether the AOT feedback control term was handled implicitly or explicitly. A wide range of errors was observed for both schemes, with the implicit scheme typically exhibiting lower error levels, depending on the specific physical terms included in the model. Several factors seem to be contributing to this wide range, but the vertical mixing term is demonstrated to be an especially problematic term. This study provides insight into the promises and challenges of adapting the AOT algorithm to the setting of high-resolution, realistic ocean models.

Figures (14)

• Figure 1: Figures showing average over time of kinetic energy for the reference solution (top left) with surface level temperature (top right), salinity (bottom right), and kinetic energy (bottom left) for an ocean state using AOT. The values for kinetic energy, temperature, and salinity are given with units $m^2s^{-2}$, degrees Celsius, and PSU (Practical Salinity Unit), respectively.
• Figure 2: Kinetic energy along the surface of the ocean for simulated solution with optimal parameters after 30 days of simulation. Optimal parameters can be found in \ref{['table: trials']}. This figure shows a zoomed out version of the bottom left panel of \ref{['fig:4_Piece']} with a rescaled colorbar.
• Figure 3: Diagram of flood fill interpolation algorithm. Observation data is first initialized with data (given by colorings) from observed cells and zero on unobserved cells (left), then the algorithm loops based on distance from observed cells (middle and right), where information from active cells is propagated to neighboring cells via arrows. In case of conflicts cell data is averaged over all cells attempting to propagate to it as indicated via a green coloring in the central cells in the rightmost image.
• Figure 4: Convergence rates for varying $dt$ choices. The "SE" (Split Explicit) in the legend refers to the barotropic baroclinic splitting scheme used in the time integration.
• Figure 5: Convergence to static ocean state for an implicit and explicit implementations of the AOT term. Note: The output times for MPAS-Ocean are much larger than the time-step, and hence the above plot only shows the error after the first hour of simulation.