Enhanced estimation of sonobuoy trajectories by velocity reconstruction with near-surface drifters

Abstract

An investigation to improve trajectory prediction using Lagrangian data is presented. The velocity field of a data assimilating model, EAS-16, is corrected using drifter observations taken during an experiment off Taiwan. The results are tested using another independent Lagrangian data set provided by sonobuoys launched in the same area. The latter have instrument chains that extend well into the water column. Consequently the corrected model velocities were projected into the water column in order to calculate sonobuoy trajectories. The drifter and sonobuoy trajectories both show two distinct regimes in the considered area of approximately 1/2° square. One regime is dominated by shelf dynamics, the other by meandering of the Kuroshio, with a sharp boundary dividing the two. These two regimes are not reproduced by the trajectories of the EAS-16 model. When the drifter data are blended with the model velocities, synthetic sonobuoy trajectories track the observed ones much better, and the two regimes are clearly depicted. Two different methods for the velocity reconstruction are tested. One is based on a variational approach and the other on a normal mode decomposition. Both methods show qualitatively similar improvements in the prediction of sonobuoys trajectories, with a quantitative improvement in the total rms error of approximately 50% and 25%, respectively.

Introduction

Operational forecasting systems are based on two complementary components, a monitoring system and an ocean modeling system. The model ocean state is routinely corrected using the data from the monitoring system, and forecasts are provided running the model forward starting from a corrected (constrained) initial state. Forecast skills have dramatically increased in the last years, but their main limiting factor may well be related to the density and quality of the observations that are used to constrain the analysis and re-initialize the model.

For many applications, there is now a significant demand for Lagrangian products from operational models. Examples are search and rescue, drifting sensor arrays, and mitigation in case of pollutants, such as oil spills. Lagrangian predictability, i.e. prediction of particle motion, is especially demanding for a number of reasons. Particle trajectories are obtained by integrating the velocity, so that even small errors in the forecasts of Eulerian velocity tend to accumulate and grow (Griffa et al., 2004). Also, particle motion is often inherently chaotic, namely it exhibits a high dependence on initial conditions even in very simple flows (Aref, 1984). Thus, even a slight difference in initial conditions in space and time can result in significantly different behaviors. A natural avenue to improve trajectory prediction appears to be the assimilation of Lagrangian data that provide direct trajectory information.

In the last decade, a number of schemes for using Lagrangian data for forecasting have been proposed. Lagrangian instruments are floating devices (acting as proxies for fluid particles) that provide information on their positions and possibly on other environmental parameters at discrete time intervals. Velocity information can be obtained from consecutive position observations, provided that the time interval is smaller than the typical Lagrangian time scale T_L, namely the time over which particle velocity is self-correlated. For the surface ocean, T_L typically varies in the range of 1–5 days (Bauer et al., 2002, LaCasce, 2008). Various methods have been suggested for both velocity reconstruction (Toner et al., 2001, Taillandier et al., 2006a) and actual assimilation (Molcard et al., 2003, Taillandier et al., 2006b, Kuznetsov et al., 2003). The former consists of improving the velocity field from off-line circulation model output by blending it with the Lagrangian data, while assimilation implies that the circulation model itself is corrected (often by sequential re-initialization) using the corrected velocity fields and adequately balanced mass fields. Reconstruction can be seen as a first step toward assimilation, but it is also valuable per se, especially for operational purposes, since it is extremely flexible and can be applied to the output of any model used in case of an accident or emergency, even when the model does not have a full assimilation capability.

Two main approaches have been followed for the reconstruction and assimilation of Lagrangian data. The first approach is based on estimating velocities along trajectories as the ratio between observed position differences and time increments (e.g., Hernandez et al., 1995) and directly using these velocities to correct the model results. The second approach introduces an observational operator based on the particle advection equation and corrects the Eulerian velocity field by requiring the minimization of the difference between observed and modeled trajectories (e.g., Molcard et al., 2003). These approaches have been implemented using several methodologies, including optimal interpolation (OI; Molcard et al., 2003, Özgökmen et al., 2003, Molcard et al., 2005), mode decomposition techniques (Toner et al., 2001), Kalman filtering (Ide et al., 2002, Kuznetsov et al., 2003, Salman et al., 2006), variational methods (Kamachi and O’Brien, 1995, Taillandier et al., 2006a, Taillandier and Griffa, 2006, Nodet, 2006), and particle filter methods (Salman, 2008b, Salman, 2008a, Krause and Restrepo, 2009). Apte et al. (2008) have developed a Markov-chain Monte Carlo sampling strategy for Lagrangian data assimilation that eliminates problems with the Kalman filter approach near saddle points in the flow field. Such Bayesian methods should play an increasingly important role in assimilating and blending Lagrangian and Eulerian data.

While these methods have been thoroughly tested using synthetic data in the framework of numerical models, application to in situ data and actual operational testing are just beginning. The variational method of Taillandier et al. (2006a) has been applied to Argo float data assimilation in the northwestern Mediterranean Sea (Taillandier et al., 2006b, Taillandier et al., 2010) and to drifter data reconstruction in the Adriatic Sea (Taillandier et al., 2008). An application of the mode-decomposition method to 50 m drogued drifters and a primitive equation model of the Gulf of Mexico has been reported in Toner et al. (2001). These studies show significant and consistent changes in the ocean circulation and in the Lagrangian pathways, but a full and quantitative evaluation of the approaches using independent data is still lacking. This study provides the first such assessment.

Here, we address this issue with a unique data set collected from an exercise off Taiwan in October 2007. The data are composed of 30 SVP (Surface Velocity Program) drifters and 28 sonobuoys with instrumented chains deployed in a small grid (approximately 1/2° square) over three days during a Littoral Warfare Advanced Development experiment (LWAD07). The SVP drifters are carefully designed to follow the flow field at approximately 15 m, while the sonobuoys respond to the flow along the entire length of the instrument chain. In addition to this data, hindcasts for the experiment are provided from a data assimilating model, the Naval Research Laboratory East Asian Seas 1/16° ocean model (EAS-16). In the present investigation, the velocity field is reconstructed using two different methods that blend the output of EAS-16 with the data from the SVP drifters and statistically project the velocity correction over the water column. The corrected velocity fields are then independently tested using the sonobuoy data. Synthetic sonobuoy trajectories are computed using an appropriate drag model applied to the corrected velocities, and they are quantitatively compared with the observed sonobuoy trajectories. The dense array of Lagrangian data from drifting sensors that respond to currents at different depths and the near-operational high resolution data assimilating model provide an opportunity to evaluate Lagrangian predictability.

Our investigation has a number of unique and novel aspects. It provides an example of a truly operational application, targeted to predict the motion of sonobuoys within the framework of an LWAD exercise. The region of application is interesting and challenging, since it is located along the shelf break at the boundary of the Kuroshio, encompassing two distinct flow regimes in a relatively small area, divided by a geostrophic front. Predicting the exact location of the front at such scales is challenging for a numerical model. Also, the use of two different methods of reconstruction provides an interesting opportunity to evaluate the utility of Lagrangian data blending with different approaches. Finally and most importantly, the present application provides a first example of independent testing of the results, since the reconstruction is based on drifter data only, while the testing is performed using the sonobuoy trajectories. Sonobuoys not only respond differently to currents than drifters do, but they also have been launched at slightly different times (order of one day difference) from the drifters, which is significant for Lagrangian applications characterized by time scales of 1–2 days. Positive results in the case of sonobuoy trajectory prediction are expected to be meaningful also for other applications that involve forecasts of floating quantities in the upper ocean. Potential applications include prediction of the pathways of pollutants or invasive species such as jelly fish.

The paper is organized as follows. The LWAD07 experiment and the data sources are described in Section 2. In Section 3, the two methods used to blend the Lagrangian data with EAS-16 are discussed and their results are shown. (More details on the methods are provided in the Appendices.) The assessment of the reconstructed velocities using sonobuoy data is given in Section 4. We conclude with a summary of our findings and a discussion of the role of Lagrangian data in enhancing Lagrangian forecasts.