Calculating lateral plume spreading with surface Lagrangian drifters

This work provides a rare quantification of lateral spreading from Lagrangian measurements in a buoyant river plume by comparing four methods. Drifter motions, including along-stream shear and rotation, can be incorrectly interpreted as lateral spreading. This work aims to improve estimates of lateral spreading by identifying additional motions in drifter trajectories. The techniques applied are first evaluated and compared using an idealized group of drifters undergoing specific types of motion, and then applied to in situ data from 27 surface Lagrangian drifters released in the Merrimack River plume (Massachusetts) under a variety of different environmental conditions. The techniques tested include two methods using the standard deviation of drifter position with respect to various interpretations of mean drifter direction and two methods using a rotating elliptical coordinate reference frame. The idealized trajectories are modeled analytically with each type of motion (i.e., spreading, rotation, and shear) separately, then in different combinations, to identify the method that best resolves and isolates lateral spreading. The idealized experiments demonstrate that three of the methods are sensitive to shear and rotational motion in various combinations. The most robust method resolving lateral spreading is the time-step method, which applies a reference frame that follows the mean flow at each time step, calculated as the average direction of the drifters between two time steps. This method also successfully identifies lateral spreading in observations, which is maximized in classic bulge-shaped plume deployments. This work is applicable to other river plume systems as well as other propagating oceanographic phenomena.