# New paper on The Naval Seafloor Evolution Architecture

Allison Penko and I just published a Naval Research Laboratory Technical Report about our seafloor evolution modeling framework. You can read the whole report at DTIC or arXiv.

The core model isn't new (Traykovski (2007), Nelson and Voulgaris (2015), Penko et al. (2017)), but I've been working over the last few years on extending its capabilities, turning the Naval Seafloor Evolution Model (NSEM) into the Naval Seafloor Evolution Architecture (NSEA). We have replaced the original Fortran implementation with one written in Julia, which lets us easily do some cool things such as running NSEA on the GPU using GPUArrays.jl. I've also developed tools for statistical inference that use seafloor roughness observations to estimate sediment transport parameters like the sediment grain size and the critical shear stress.

I am especially proud of the section that draws out the connection between NSEM and a particular stochastic sediment flux model. NSEM doesn't model the actual transport of sediment and formation of bedforms. Instead, it uses some heuristics, scaling arguments and empirical parameterizations to model the evolution of the power spectrum of the seafloor roughness. This works surprisingly well when the seafloor roughness is predominantly small-scale ripples formed by wind waves, but it runs into trouble when you want to apply it to different settings like current-driven ripples or bedforms created by internal waves because those empirical parameterizations fail in these situations.

The power spectrum is a statistical description of the seafloor roughness: it defines a probability distribution over the seafloor elevation, and we can ask what sediment transport models will generate a similar probability distribution. The simplest one is a kind of stochastic heat equation, where the sediment flux is proportional to the gradient in the seafloor elevation augmented by a random flux with a particular correlation function. That correlation function is determined by the empirical ripple geometry parameterization in the model and is basically related to the size of the waves at the seafloor. If you work out the power spectrum of a seafloor governed by this stochastic heat equation, it evolves in time just like NSEM says it does. In other words, NSEM is what you get if you average over the random sediment flux in this stochastic heat equation.

This realization is not particularly useful on its own because our observations are typically too coarse to resolve the evolution of the seafloor at the fast time scales of the stochastic sediment flux. We are typically better off averaging over the random flux and directly modeling the statistical properties of the seafloor like the power spectrum or characteristic length scales for the ripples. However, when we think about extending NSEM to different kinds of hydrodynamic and sediment transport processes, we don't want to just tack new empirical parameterizations onto the already somewhat unwieldy NSEM. Instead, we might be able to start by devising a high-resolution model for the sediment flux that respects the fundamental physics of these processes, but that represents the complex turbulent interactions between the bottom boundary layer and the seafloor with appropriate stochastic processes. Averaging over that randomness, we derive a new version of NSEM corresponding to the given sediment flux model. We can then compare the predictions of NSEM with high spatial resolution observations from imaging sonars to test different stochastic formulations.

This stochastic approach is one way to bridge the gap between small scales, where we can faithfully model the physics of sediment transport, and larger scales, where the effects of seafloor roughness on hydrodynamics or acoustics are felt, while systematically accounting for the uncertainty generated by unresolved processes.

If you have any thoughts or questions, feel free to let me know!