Ocean drifter velocity data assimilation, Part 1: Formulation and diagnostic results

Abstract

Numerical ocean circulation forecasts diverge from reality due to non-deterministic processes. Through data assimilation, ocean forecasting systems routinely make corrections to scalar ocean variables of temperature and salinity derived from ocean observations. Velocity observations, however, are vector quantities that require different processing. To assimilate existing ocean velocity observations, which generally are depth limited, vertical error covariances are needed to relate the velocity errors throughout the water column. In this paper we show a velocity assimilation approach that relies on historical observations and geostrophy to relate velocity, temperature, and salinity. Geopotential calculations transform temperature and salinity covariances into corresponding geopotential covariances. This paper describes the methods and examines details of the solution process for ocean velocity data assimilation. The approach employs two separate three-dimensional variational (3DVAR) analyses combined to create one set of initial conditions during each daily forecast cycle. The first 3DVAR analysis utilizes temperature, salinity, and sea surface height anomaly data and reduces the background error variance based on these observations. The second 3DVAR analysis uses the reduced error variance and performs velocity data assimilation using surface drifter data, and these observations further reduce the error variance of temperature and salinity for the next cycle. The second 3DVAR analysis for velocity data assimilation utilizes the new full depth error covariances. We show diagnostic results from a Gulf of Mexico simulation during extensive drifter deployments in the summer of 2020. Results reveal that the two-step data assimilation cycle applies vector velocity innovations to create increments that correct the background field towards a geostrophic balance in temperature and salinity.