Chapter 10 - Geostrophic Currents
10.8 Lagrangean Measurements of Currents
Oceanography and fluid mechanics distinguish between two techniques for measuring
currents: Lagrangean and Eulerian. Lagrangean techniques follow a
water particle. Eulerian techniques measure the velocity of water at a fixed
Lagrangean techniques track the position of a drifter that
follows a water parcel either on the surface or deeper within the water column.
The mean velocity over some period is calculated from the distance between
positions at the beginning and end of the period divided by the period. Errors
are due to:
- The failure of the drifter to follow a parcel of water. We assume the drifter
stays in a parcel of water, but external forces acting on the drifter can
cause it to drift relative to the water.
- Errors in determining the position of the drifter.
- Sampling errors. Drifters go only where drifters want to go. And drifters
want to go to convergent zones. Hence drifters tend to avoid areas of
||Figure 10.13 Satellite systems, especially
System Argos, use radio signals transmitted from surface buoys to determine
the position of the buoy. The satellite S receives a radio signal
from the buoy B. The time rate of change of the signal, the Doppler shift, is
of buoy position and distance from the satellite?s track. The recorded Doppler
signal is transmitted to ground stations E, which relays the information to processing
centers A via
control stations K. From Dietrich et al. (1980).
Satellite Tracked Surface Drifters
Surface drifters consist of a drogue plus
a float. It's position determined by the Argos system on meteorological
satellite (Swenson and Shaw, 1990) or calculated from GPS data recorded continuously
by the buoy and relayed to shore.
Argos-tracked buoys carry a radio transmitter
with a very stable frequency F0.
receiver on the satellite receives the signal and determines the
Doppler shift F as
a function of time t (Figure 10.13). The Doppler
where R is the distance to the buoy, c is
the velocity of light. The closer the buoy to the satellite the more rapidly
the frequency changes. When F =
range is a minimum. This is the time of closest approach, and the satellite's
velocity vector is perpendicular to the line from the satellite to the buoy.
The time of closest approach and the time rate of change of Doppler frequency
at that time gives the buoy's position relative to the orbit with a 180° ambiguity
(B and BB in the figure). Because the orbit is accurately known, and because
the buoy can be observed many times, its position can be determined without ambiguity.
The accuracy of the position depends on the stability of the frequency transmitted
by the buoy. The Argos system tracks buoys with an accuracy of ±1–2 km,
collecting 1–8 positions per day depending on latitude. Because 1 cm/s
≈ 1 km/day, and because typical values of currents
in the ocean range from one to two hundred centimeters per second, this is an
very useful accuracy.
The most widely used, satellite tracked drifter is the holey-sock. It consists
of a circular, cylindrical drogue of cloth 1m in diameter by 15m long with 14
large holes cut in the sides. The weight of the drogue is supported
by a submerged float set 3 m below the surface. The submerged float is
tethered to a partially submerged surface float carrying the Argos transmitter.
The buoy was designed for the Surface Velocity Program and it was extensively
tested. Niiler et
(1995) carefully measured the rate at which wind blowing on the surface float
pulls the drogue through the water, and they found that the
buoy moves 12 ± 9° to the right of the wind at a speed
where DAR is the drag
area ratio defined as the drogue?s drag area divided by
the sum of the tether's drag area and the surface float's drag area, and D is
the difference in velocity of the water between the top of the cylindrical drogue
the bottom. Frifters typically have a DAR of
40, and the drift
Us < 1 cm/s for
U10 < 10m/s.
||Figure 10.14 The Autonomous Lagrangean Circulation
Explorer (ALACE) drifters are widely used by the World Ocean Circulation
to measure deeper currents within the
ocean. Left: Schematic of the drifter. To ascend,
the hydraulic pump moves oil from an
internal reservoir to an external bladder, reducing the drifter?s density. To
descend, the latching valve is opened to allow oil to flow back into the internal
reservoir. The antenna is
mounted to the end cap. Right: Expanded schematic
of the hydraulic system. The motor rotates the wobble plate actuating the piston
which pumps hydraulic oil.
From Davis et
The most widely used subsurface floats are the Argo floats. The floats (Figure
10.14) are designed to cycle between the surface and some predetermined depth.
Most floats drift for 10 days at a depth of 1 km, sink to 2 km, then rise
to the surface. While rising, they profile temperature and salinity as a function
of pressure (depth). The float remains on the surface for a few hours, relays
data to shore via the Argos system, then it sinks again to 1 km. Each float
carries enough power to repeat this cycle for several years. The float thus
measures currents at 1 km depth and density distribution in the upper ocean.
Three thousand Argo floats are being deployed in all parts of the
ocean for the Global Ocean Data Assimilation Experiment GODAE.
Lagrangean Measurements Using Tracers
The most common method for measuring flow in the deep ocean is to track parcels
of water containing molecules not normally found in the ocean.Perhaps the best
way for following water parcels is to tag the parcel with molecules not normally
found in the ocean. Thanks to atomic bomb tests in the 1950s and the recent exponential
increase of chlorofluorocarbons in the atmosphere, such tracers have been introduced
into the ocean in large quantities. See §13.4 for a list of tracers used
in oceanography. The distribution of trace molecules is used to infer the movement
of the water. The technique is especially useful for calculating velocity of
deep water masses averaged over decades and for calculating eddy diffusivities.
The distribution of trace molecules is calculated from the concentration of
the molecules in water samples collected on hydrographic sections and surveys.
Because the collection of data is expensive and slow, there are few repeated
sections. Figure 10.15 shows two maps of the distribution of tritium in the
North Atlantic collected in 1972–1973 by the Geosecs Program and in 1981,
a decade later. The sections show that tritium, introduced into the atmosphere
during the atomic bomb tests in the atmosphere in the 1950s to 1972, penetrated
to depths below 4 km only north of 40°N by 1971 and to 35°N by 1981.
shows that deep currents are very slow, about 1.6 mm/s in this example.
Because the deep currents are so small, we can question what process are
responsible for the observed distribution of tracers. Both turbulent diffusion
and advection by currents can't the observations. Hence, does Figure 10.15
give mean currents in the deep Atlantic, or the turbulent diffusion of tritium?
||Figure 10.15 Distribution of tritium along a section through
the western basins in the North
Atlantic, measured in 1972 (Top) and remeasured
in 1981 (Bottom). Units are tritium
units, where one tritium unit is 1018 (tritium atoms)/(hydrogen atoms) corrected
to the activity levels that would have been observed on 1 January 1981. Compare
this figure to the
density in the ocean shown in figure 13.9. From Toggweiler (1994)
Another useful tracer is the temperature and salinity of the water. We
will consider these observations in §13.3 where we describe the core method
for studying deep circulation. Here, we note that AVHRR observations of surface
temperature of the ocean are an additional source of information about currents.
|Figure 10.16 Ocean temperature and current
patterns are combined in this AVHRR analysis. Surface currents were computed
tracking the displacement of small thermal or sediment
features between a pair of images. A directional edge-enhancement filter was
applied here to define better the different water masses. From Ocean
Imaging, Solana Beach, California,
Sequential infrared images of surface temperature are used to calculate the
displacement of features in the images (Figure 10.16). The technique is especially
useful for surveying the variability of currents near shore. Land provides reference
points from which displacement can be calculated accurately, and large
temperature contrasts can be found in many regions in some seasons.
There are two important limitations.
- Many regions have extensive cloud cover, and the ocean cannot be seen.
- Flow is primarily parallel to temperature fronts, and strong currents can
exist along fronts even though the front may not move. It is therefore
essential to track the motion of small eddies embedded in the flow near
the front and not the position of the front.
The Rubber Duckie Spill
On January 10, 1992 a 12.2 m container with
29,000 bathtub toys (including rubber ducks) washed overboard from a container
ship at 44.7°N, 178.1°E. Ten months later the toys began washing ashore
near Sitka, Alaska. A similar accident on May 27, 1990 released 80,000 Nike-brand
shoes at 48°N, 161°W when waves washed containers from the Hansa
Carrier (Figure 10.17). The spill and the eventual recovery of the toys
proved to be a good test of a numerical model for calculating the trajectories
spills developed by Ebbesmeyer and Ingraham (1992, 1994). They calculated
the possible trajectories of the spilled rubber ducks using the Ocean Surface
Current Simulations OSCURS numerical model driven by winds calculated from
the Fleet Numerical Oceanography Center?s daily sea-level pressure data. The
calculated trajectories agreed well with observed locations of drifters found
on the shore. Using a 50% increase in windage coefficient and a 5° decrease
angle of deflection function, the toys arrived near Sitka, Alaska at the time
the first recoveries on November 16, 1992.
||Figure 10.17 Trajectories that spilled rubber
duckies would have followed had they been spilled on January 10 of different
Five trajectories were selected from a set of 48
simulations of the spill each year between 1946 and 1993. The trajectories begin
on January 10 and end two years later (solid symbols). Grey symbols
indicate positions on November
16 of the year of the spill. Hence the grey circle gives the location where rubber
ducks first came ashore near Sitka. The code at lower left gives the
dates of the trajectories. From
Ebbesmeyer and Ingraham (1994).