Two-Step Ocean Velocity Data Assimilation in the Gulf of Mexico

This paper describes a two-step 3D variational (3DVAR) analysis methodology for achieving velocity data assimilation in an ocean forecasting system. Two separate 3DVAR analyses are performed during each daily forecast cycle. The first 3DVAR analysis utilizes data streams of temperature, salinity, and sea surface height anomaly data in a traditional 3DVAR analysis. The second 3DVAR analysis performs velocity data assimilation using surface drifter data. The covariance model relates the errors between temperature and salinity with geopotential. Geostrophic coupling then relates geopotential to velocity. Steric height calculations convert temperature and salinity vertical error covariances into geopotential covariances. Thus, velocity innovations influence scalar quantities and visa versa. The ocean numerical model is baroclinic, hydrostatic, Boussinesq, has a free-surface, and for this experiment, runs at 4 km resolution with 50 vertical levels that are terrain following near shallow topography and z-levels everywhere else. The data assimilation component performs the two 3DVAR analyses on the same model grid, once per day with a 6-hour incremental insertion hindcast. For each daily cycle, the first 3DVAR analysis creates an analysis that becomes the background for the second 3DVAR analysis. Because the 3DVAR analysis system corrects mesoscales, the increments from the first analysis are added to the 9 three hourly forecast from the previous cycle. These modified forecasts are then averaged together as the background for the 2nd 3DVAR analysis. The surface drifter locations provide velocity trajectories. Positions are decimated to one observation per drifter per day, such that their trajectories represent "nearly" the average velocity for that drifter for each day in order to minimize the effects of inertial oscillations. Since both the observations and the background represent a daily average, the resulting innovations consistently represent daily variability. The approach approximates mesoscale velocity observations compatible with the horizontal length scales typically constrained in the 3DVAR analysis system. Validation compares forecasted speed and direction relative to the in situ drifter trajectory speed and direction. Comparisons of twin experiments with/without velocity data assimilation suggest that the two-step 3DVAR analysis with velocity data assimilation has superior skill.