Global prediction of abyssal hill roughness statistics for use in ocean models from digital maps of paleo-spreading rate, paleo-ridge orientation, and sediment thickness

Abyssal hills are the dominant small-scale roughness fabric over much of the ocean floor. Created at mid-ocean ridges by combined volcanic and tectonic processes, they are rafted away by plate spreading and modified through time by mass wasting and sedimentation. Abyssal hills are morphological indicators of spreading rate and direction: they are lineated parallel to the ridge at the time of formation, and their heights and widths are inversely correlated to spreading rate. Knowledge of abyssal hill roughness statistics is important for high-resolution models, including models of internal wave generation and mixing driven by tidal and low-frequency flows over the rough bottom. In this paper we present a prediction of abyssal hill roughness statistical parameters world-wide via relationships for the average statistical properties of abyssal hills as a function of spreading rate and direction, and for the modification to these roughness parameters as a function of sediment thickness. These relationships are constrained by new publicly-available digital maps of paleo-spreading rate and direction, and sediment thickness. We also develop a new method for generating synthetic topography with variable statistical properties over a grid, and present an example of synthetic abyssal hill roughness generated for the North Atlantic on a 1/2-min grid.