Efficient sensor placement for ocean measurements using low-dimensional concepts

Using simulation results from three different regional ocean models (HOPS, ROMS and FVCOM) we show that only a few spatio-temporal POD (proper orthogonal decomposition) modes are sufficient to describe the most energetic ocean dynamics. In particular, we demonstrate that the simulated ocean dynamics in New Jersey coast, Massachusetts Bay and Gulf of Maine is energetically equivalent to the wake dynamics behind a cylinder at low Reynolds number. Moreover, the extrema of the POD spatial modes are very good locations for sensor placement and accurate field reconstruction. We employ a modified POD theory to incorporate a limited number of measurements in reconstructing the velocity and temperature fields, and we study systematically the corresponding reconstruction errors as a function of the sensor location, number of sensors, and number of POD modes. This new approach is quite accurate in short-term simulation, and hence it has the potential of accelerating the use of real-time adaptive sampling in data assimilation for ocean forecasting.