General characteristics of relative dispersion in the ocean

Abstract

The multi-scale and nonlinear nature of the ocean dynamics dramatically affects the spreading of matter, like pollutants, marine litter, etc., of physical and chemical seawater properties, and the biological connectivity inside and among different basins. Based on the Finite-Scale Lyapunov Exponent analysis of the largest available near-surface Lagrangian data set from the Global Drifter Program, our results show that, despite the large variety of flow features, relative dispersion can ultimately be described by a few parameters common to all ocean sub-basins, at least in terms of order of magnitude. This provides valuable information to undertake Lagrangian dispersion studies by means of models and/or of observational data. Moreover, our results show that the relative dispersion rates measured at submesoscale are significantly higher than for large-scale dynamics. Auxiliary analysis of high resolution GPS-tracked drifter hourly data as well as of the drogued/undrogued status of the buoys is provided in support of our conclusions. A possible application of our study, concerning reverse drifter motion and error growth analysis, is proposed relatively to the case of the missing Malaysia Airlines MH370 aircraft.

Figure 1. Surface ocean dynamics partition utilized in this work, based on the annual mean wind stress (vectors) and wind-stress curl (color shading, multiplied by −1 in the Southern Hemisphere).

Based on, and modified from Figs S9.3a, S10.2a and S11.03a of the book “Descriptive physical oceanography: an introduction” by Talley et al., Academic Press (2011), reproduced with permission. For a list of acronyms used in the figure and in the body of the paper see Table 1.

Figure 2. FSLE computed on the Global Drifter Program data set subdivided in eleven ocean basins (see Fig. 1).

Colors are associated to the drogue status of the SVP drifter pairs: red = drogued (1,1); green = drogued/undrogued (1,0); blue = undrogued (0,0); black = any status. The FSLE scaling exponent, λ(δ) ~ δ^−β, corresponds to: Richardson’s dispersion (β = 2/3), shear/ballistic separation (β = 1), and standard eddy-diffusion (β = 2). Exponential separation rates, i.e. λ(δ) ≃ constant, are indicated as λ_ms, for the mesoscales, and as λ_sms, for the submesoscales (when resolved). Maximum initial separation allowed: Δ = 10 km. Amplification ratio . The FSLE λ(δ) is inversely proportional to the characteristic time scale of dispersion at scale δ. Panel generated with GNUPLOT 5.0 (Williams, T. and Kelley, C., 2011; Gnuplot 5.0: an interactive plotting program; URL: http://gnuplot.info).

Figure 3. Drifter pair statistics of the FSLE analysis.

Colors are associated to the drogue status of the drifter pairs. The numbers plotted on the top right corner of each panel are the total number of pairs analyzed for each drogue status: drogued (1,1); drogued/undrogued (1,0); undrogued (0,0); any status. The statistics is also determined by the filter imposed to the maximum allowed initial separation of the drifters (Δ = 10 km). Panel generated with GNUPLOT 5.0 (Williams, T. and Kelley, C., 2011; Gnuplot 5.0: an interactive plotting program; URL: http://gnuplot.info).

Figure 4. FSLE computed for the GPS-tracked drifter data set.

The relative dispersion rates measured by the FSLE for the sub-mesoscale (below ~1 km) range are significantly higher (about an order of magnitude) than for the mesoscale range (~10–100 km). GPS-tracked drifter positions are affected by ~10⁻⁵ degree errors. Only drifter pairs with drogue status (1,1) were considered. Maximum initial separation allowed: Δ = 10 km. Amplification ratio . The data refer to the global ocean (with no geographic constraint). Color map generated with GNUPLOT 5.0 (Williams, T. and Kelley, C., 2011; Gnuplot 5.0: an interactive plotting program; URL: http://gnuplot.info).

Figure 5. Major dispersion regimes observed in the 11 sub-basins of the ocean partition.

Colors refer to the type of relative dispersion: red = submesoscale exponential, yellow = mesoscale exponential, water green = Richardson, cyan = Shear/Ballistic, blue = Taylor. Gray squares represent the order of magnitude of the average latitude-depending Rossby radius scale. The numerical values of the physical parameters (exponential separation rates, turbulent dissipation, shear velocity, eddy diffusion coefficients) were obtained by fitting the corresponding scaling laws to the FSLE data, see Fig. 2. Panel generated with GNUPLOT 5.0 (Williams, T. and Kelley, C., 2011; Gnuplot 5.0: an interactive plotting program; URL: http://gnuplot.info).

Figure 6. Estimate of MH370 impact area in the Southern Indian Ocean.

The hypothetical impact region is the white shaded circular area centered in −35°S, 86°E. Drifter identification numbers are: 24746 (red), 70854 (orange), 70969 (green) and 83341 (cyan). Localization errors associated to each ending point of the drifters are the circular areas of radius ~10³ km of the same color as the corresponding drifters. The gray circle represents the 7^th BTO arc measured from Inmarsat of radius ≃ 4750 km centered in 0°, 64.5°E. The black circle represents the maximum flight range from the last known position of MH370 of radius ≃ 4800 km centered in 6°N, 96°E. This map was generated with free online utility GPS Visualizer (http://www.gpsvisualizer.com/) and Google Earth (https://www.google.com/earth/).