Inferring Large-Scale Bottom Velocities from Sparse Data

Over the next decade there will be a revolution in data coverage of the abyssal oceans, led by networks of deep ARGO floats and deep gliders. Undoubtedly the data coverage will be too sparse to accurately map bottom velocities from direct measurements: e.g. the deep ARGO program proposes 1200 deep ARGO floats to give roughly 5°x5° spacing by 2030. However, bathymetry exerts a powerful influence on the near-bottom flow that can be exploited. We show how high-resolution bathymetric data can be combined with sparse, deep hydrographic data to generate an improved, high-resolution map of the bottom geostrophic velocity. By assuming geostrophic balance and hydrostatic balance hold near the bottom, and assuming the bottom flow conserves the bottom neutral density to leading order, we derive a simple expression for the bottom velocity that depends only on the bottom neutral density and the bathymetry, and can be expected to hold over an extended region. A critical part of the expression is a "reference depth" -- similar to but different from a traditional level of no motion -- which is a function of bottom neutral density and empirically derived from the sparse hydrographic data. The approach is tested by sub-sampling data from eddy-permitting ocean state estimates to mimic the data that will be collected by deep ARGO floats, gliders, and/or moorings. Implications for the design of bottom measurement arrays will be discussed.