Quantification of Physical and Numerical Mixing in a Coastal Ocean Model Using Salinity Variance Budgets. (17th April 2023) - Schlichting, Dylan; Qu, Lixin; Kobashi, Daijiro; Hetland, Robert
Abstract: Numerical mixing, the spurious mixing primarily generated by the discretization of advection, is often significant in estuarine and coastal models due to sharp, energetic fronts. We compare on‐ and offline estimates of numerical mixing in a submesoscale‐resolving realistic simulation of the ocean state over the Texas‐Louisiana continental shelf. While offline estimates of numerical mixing differ from online estimates, offline methods may be the only analysis available. We use two methods to estimate numerical mixing offline based on the residuals of the salinity squared s 2 and volume‐mean salinity variance s ′ 2 s^′ ^2 budgets. The s ′ 2 s^′ ^2 budget overestimates the time‐averaged online numerical mixing by 60% at hourly output. The s 2 budget compares poorly due to large truncation errors associated with the tendency and advection terms. The residual of the s 2 budget starts to converge to the s ′ 2 s^′ ^2 budget as output frequency increases to 10 min—an unrealistic frequency for long‐term coastal ocean simulations—but neither method unconditionally converges to the online method and therefore cannot be recommended for generic analysis of numerical mixing. We also investigate the effects of horizontal resolution on numerical mixing using a two‐way nested grid with the online method. The volume‐integrated numerical mixing constitutes 57% of the bulk physical mixing—the mixing prescribed by the turbulence closure scheme—in the coarse model and may exceed the physical mixing by half an order of magnitude. We find numerical mixing is reduced by 35% on average in the nested model, likely due to new dynamical processes that emerge in the nested simulation. Plain Language Summary: Numerical models are powerful tools for studying the general circulation of the ocean, allowing us to examine the ocean's complex relationship with Earth's weather and climate in greater detail than observations allow. However, numerical ocean models are prone to several types of numerical errors because they represent physical processes with discrete approximations. One of these errors is numerical mixing, a process by which the discretized transport of tracers by currents generates spurious mixing. Recent studies suggest numerical mixing can be as large as the physical mixing prescribed by a parameterization, especially in regions with strong tracer gradients, such as in estuaries or the coastal ocean. In this study, we examine numerical salinity mixing using a combination of on‐ and offline methods in a model of the ocean state over the Texas‐Louisiana continental shelf in the Gulf of Mexico. Offline methods rely on existing model output and are often easier to implement than online methods. However, offline methods trade numerical accuracy for convenience because online methods require modifying a model's source code and re‐running it. We find offline estimates of numerical mixing should not be used because they may be inaccurate even at impractically high resolution. Key Points: We use offline salinity variance budgets to quantify numerical mixing due to the discretization of advection in a coastal ocean model Numerical mixing estimated from s 2 and s ′ 2 s^′ ^2 budgets does not converge to the online method at high model output frequencies Online analysis indicates the volume‐integrated numerical mixing exceeds the physical mixing for a significant portion of the simulation