Lagrangian Ocean Observing

Eric A. D’Asaro

A “Lagrangian” measurement platform moves with the surrounding water and, ideally, measures the changing properties of the same water over time. In contrast, an ideal “Eulerian” measurement platform stays at one location and measures the velocity and varying properties of different water masses as they move past. Neither is perfect; Lagrangian platforms cannot exactly follow water molecules, particularly their vertical motion, while Eulerian platforms always move, particularly in strong currents, due to surface waves. The advantages and problems of the Lagrangian approach are discussed here.

The ocean is complicated. Resolving this complexity is only possible with a large number of measurements. Even in physical oceanography with only a few basic variables, sampling the vast range of spatial and temporal scales, millimeters to megameters and seconds to decades or longer, presents a difficult challenge. For chemistry and biology, with an equal degree of variability, but many more things to measure, the challenge is greater. Many of the great successes of oceanography, for example, real-time, eddy-resolving models (Bell et al., 2015) and accurate decadal monitoring of the ocean heat content (Riser et al., 2016), rely on large and continuous data streams, satellite altimetry, and the Argo float array, respectively. Future progress is likely to require lots of measurements in lots of places.

Lagrangian instruments are well suited to deployment in large numbers. They move with the flow by having a high drag and a density close to that of the water, either being slightly buoyant (a “surface drifter”; Lumpkin et al., 2017) or accurately matching their density to that of the water so as to float at a subsurface depth (a “float”; Rossby, 2007). The minimal instrumentation is a measurement of their position, which usually requires small electronics and little power (Rossby et al., 1986). Small size and lightweight construction are easily possible and an advantage, increasing the drag and making near-neutral buoyancy easier. Lagrangian instruments thus tend to be inexpensive so that deploying large numbers is feasible. Thus, the Global Drifter Program (Lumpkin and Pazos, 2007) maintains a global array of about 1500 drifters. The average of velocities computed from these drifters measure the average and variability of ocean surface currents both globally (Figure 1) and regionally. Similarly, hundreds of subsurface floats measured the circulation of the North Atlantic (Bower et al., 2002) and Brazil Basin (Hogg and Owens, 1999). Hundreds of drifters have been deployed in dense local arrays (Poje et al., 2014) to study smaller-scale eddy properties.

Figure 1. Mean current speeds (colors) from Global Drifter Program trajectories with streamlines (black lines). Adapted from Lumpkin and Johnson (2013)

Accurate Lagrangian measurements, like all oceanographic measurements, require attention to instrumental details. For surface drifters, minimizing the effects of wind and waves requires a sufficiently large underwater drogue area (Lumpkin and Pazos, 2007) relative to the surface expression, or a clever design backed by laboratory and field evidence (Novelli et al., 2017). Subsurface floats require careful ballasting and attention to the compressibility and thermal expansion coefficients of the instrument relative to seawater (Rossby, 2007). Measuring the three-dimensional trajectories, including the vertical as well as horizontal components, is possible with care (Rossby et al., 1985; D’Asaro, 2003). However, most so-called “Lagrangian” measurements, including surface drifters and Argo floats, only measure the horizontal component of the trajectory.

With appropriate instruments, Lagrangian sampling allows measurement of unique flow characteristics. The average of many Eulerian velocity measurements in a region can define the average and variability of the currents. However, only Lagrangian methods directly measure where the water goes and how it spreads. For example, a week of measurements at the mouth of a river may indicate that the water is moving south at 0.5 ± 0.3 m s–1, but give little information as to where that water, and any pollutants that it carries, will be in a week. The positions of an array of Lagrangian sensors deployed at the river mouth directly measure both this and the area over which the river water has spread. A large literature tackles the details of such “dispersion” statistics (LaCasce, 2008) and has developed a number of sophisticated Lagrangian diagnostics (Samelson, 2013), including methods to detect “coherent structures” that trap and transport water masses. The relationship between these Lagrangian properties and Eulerian statistics and dynamical understanding is an important, but difficult problem.

Lagrangian measurements of scalar properties, for example, temperature, salinity, and oxygen, can yield additional insights. The equation for variation in the concentration of ascalar C, advected by currents, mixed by a diffusivity and with a growth/decay rate S is

Often, we want to estimate the left-hand terms in order to measure S or κ. Using Eulerian measurements, three quantities in the left-hand terms must be measured: the rate of change of C, the velocity and the gradient. Using Lagrangian measurements, only the center term, the Lagrangian rate of change of C, is necessary. For a conserved quantity (S = 0), the rate of change of C following a Lagrangian trajectory (DC/Dt) directly measures the effect of mixing.

Figure 2. Variation of temperature and depth along a three-dimensional trajectory of a Lagrangian float during deep convection in the Labrador Sea (Steffen and D’Asaro, 2002) illustrate the cycle of warming and cooling that drives the convection. Water parcels cool and become heavier at the surface and thus sink, carrying cold water downward and warming slightly by mixing with the surrounding water. At about 600 m depth, they encounter warmer, saltier water at the bottom of the convective layer, and warm by mixing with this water. They then move upward, carrying warmer water, until they reach the surface to repeat the cycle.

For example, temperature changes measured along a three-dimensional Lagrangian trajectory during deep convection in the Labrador Sea (Figure 2) shows the cycle of surface cooling, downward transport of cold, heavy water, warming by entrainment at the bottom of the convective layer, and finally transport upward to the surface. This cycle is implicit in the traditional Eulerian formulations of convective heat flux, but is explicitly demonstrated by Lagrangian measurements. Such Lagrangian data have been used to compute the value of κ in a stratified fluid (D’Asaro, 2008) and heat, salt, and oxygen flux profiles within a boundary layer (D’Asaro 2004; D’Asaro and McNeil, 2007). Biogeochemical rates (S) can similarly be computed by measuring quantities following a Lagrangian instrument. For example, Landry et al. (2009) measured changes in phytoplankton and zooplankton biomass along Lagrangian trajectories in the California upwelling system and compared them with incubation-based growth and grazing rates to close budgets for the biomass.

Lagrangian instruments are often said to follow a “parcel” of water. However, the mass of water initially near a Lagrangian instrument usually does not remain localized, but spreads over a wide region, with its molecules eventually becoming distributed over the entire ocean and beyond. A single Lagrangian instrument can at best follow only one of many trajectories originating in its vicinity and provides no information on the surrounding water. Arrays of Lagrangian instruments (Poje et al., 2014) address this issue, but alone often do not provide sufficient measurements of the right type in the right places.

The combination of an Eulerian survey conducted around a Lagrangian instrument effectively combines the advantages of both approaches. The advective effects are minimized by moving with water, so that Equation (1) can be used, while the surrounding surveys provide a context for these measurements and allow corrections due to lateral and vertical shear. For example, during the 2008 North Atlantic Bloom Experiment (Alkire et al., 2012), four gliders surveyed around a mixed layer float for 60 days supplemented by several ship surveys. Variants of Equation (1) were used to diagnose the bloom’s evolution (Bagniewski et al., 2011) along the float trajectory, while the surveys revealed the importance of submesoscale eddies in its dynamics (Mahadevan et al., 2012). Associated chemical and biological measurements made from a ship were critical to these interpretations. Similar approaches have proved successful even in the extreme currents and shears of the Gulf Stream (Thomas et al., 2016). Combinations of Lagrangian instruments, dye, and ship surveys can also be very powerful (Boyd et al., 2007).

The broader lesson is that a variety of sampling approaches—Lagrangian, Eulerian, or other—are necessary to address the variety of sampling problems faced in measuring the complicated ocean. Autonomous technologies have given us many new and powerful measurement tools; many more will become available. Each of these tools has strengths and weaknesses, and the best combination to address any particular problem will depend on the problem. My experience has been that combinations of these tools are often the most effective approach (Figure 3).

Figure 3. Experimental design for the autonomous components of the SPURS-II program shows a combination of Eulerian and Lagrangian components (from Lindstrom et al., 2017). A central mooring (star) provides intensive Eulerian measurements; Seagliders and Wave Gliders survey around it. A Lagrangian float (orange), launched at the mooring, is advected eastward in the strong currents and provides a reference point for a Seaglider (purple) and Wave Glider (green) surveying around it. The inset figure, rotated to align to the direction of the float drift, shows the Seaglider and Wave Glider trajectories relative to the float. A region approximately 20 km around the float is surveyed every few days. This design addresses the central goal of SPURS-II, which is understanding the salinity dynamics in this region by measuring both Eulerian and nearly Lagrangian time series and the spatial context of both.



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Bagniewski, W., K. Fennel, M.J. Perry, and E.A. D’Asaro. 2011. Optimizing models of the North Atlantic spring bloom using physical, chemical and bio-optical observations from a Lagrangian float. Biogeosciences 8:1,291–1,307,​10.5194/bg-8-1291-2011.

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Figure 1. Mean current speeds (colors) from Global Drifter Program trajectories with streamlines (black lines). Adapted from Lumpkin and Johnson (2013)



Eric A. D’Asaro, Applied Physics Laboratory, University of Washington, Seattle, WA, USA,