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A Hierarchy of Stochastic Particle Models for Search and Rescue (SAR):
Application to Predict Surface Drifter Trajectories Using HF Radar Current Forcing
Malcolm L. Spaulding, Atsu Isaji, Paul Hall, and Arthur A. Allen

A hierarchy of stochastic particle models, where the object’s position, velocity, and acceleration are progressively represented as Markovian processes, is summarized. Numerical implementation and testing of the first and second order models (random walk and random flight) against an analytic solution to the diffusion equation show very good agreement provided that 2000 or more independent simulations are ensemble averaged. The random flight model is shown to predict smaller search areas than the random walk model, with a long term reduction in the area proportional to the dispersion coefficient times the velocity autocorrelation time scale. This offset ramps in immediately after the release, and occurs over the velocity autocorrelation time scale. The particle models were applied to predict the trajectories of seven US Coast Guard, Self Locating Datum Marker Buoys (SLDMB) Argos tracked drifters (Davis like) deployed in three clusters: one located in western Block Island Sound and the other two, near the coast and shelf break in the New York Bight. The buoys were deployed for a 35-day period starting on July 27, 2004. High frequency coastal radar (CODAR) measurements were collected during the same time period by a short range system (50 km range and 5 km resolution) operated by the Universities of RI and Connecticut for the Block Island Sound and adjacent shelf area and by the long range system (150 km range, 6 km resolution) operated by Rutgers University for the Mid Atlantic Bight. The motion of the buoys was dominated by a mean southwesterly shelf transport and inertial and semi-diurnal tidal oscillations. A cluster analysis of the very limited number of SLDMBs gives dispersion coefficients in the range of 40 to 80 m2/sec. Analysis of the CODAR velocity errors and variances gives values in the range of 40 to 700 m2/sec, with velocity autocorrelation time scales in the range of 4 to 7 hours, depending on the velocity component, the location, and whether the current record used to determine the autocorrelation time scale is de-tided. Comparison of the velocities derived from the drifters and the radar system show differences comparable to the observed speeds. Scatter plots for the Block Island Sound (Mid Atlantic Bight) show a correlation of less than 0.1 (greater than 0.75) for the east-west component and greater than 0.6 (less than 0.4) for the north-south component. Correlation coefficients were observed to be much lower in areas where the percent data return was below 50%. Statistically independent simulations were performed using SARMAP, a search and rescue model, to predict the daylong trajectories at successive (non-overlapping) locations along the paths of the seven SLDMBs in the Mid Atlantic Bight. Model predicted and observed locations at the end of one day (typical search and rescue model prediction time scale) showed an averaged difference of 9.3 km, with an error in location comparable (about 80%) to the distance the drifter traveled in one day. Errors were significantly higher in areas where the CODAR data return rates were less than 50%. Estimates of the dispersion coefficients necessary as input to the search and rescue model, to ensure that the predicted and observed locations of the drifters were within the model predicted search area, were made and gave values ranging from 20 to 500 m2/sec, with a median value of 90 m2/sec. The largest dispersion coefficients were associated with areas where the radar data returns were lowest. The various estimates of the dispersion performed (cluster analysis, radar velocity variance, and trajectory analysis) gave values consistent with Okubo’s relationship. Random flight models offered no improvement in predictive perform for any of the applications due to the substantial uncertainty in estimates of the dispersion coefficient.

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