8.4: Geostrophic Currents

Ekman transport of surface layer water tends to produce sloping sea surfaces by “piling up” the water in some locations and “removing” surface water from others. Geostrophic currents are the result of horizontal pressure gradients in the water column below the surface caused by such variations in sea surface level (CC13).

Ekman Transport, Sea Surface Slope, and Pressure Gradient

If winds blew continuously, Ekman transport would cause the sea surface slope to increase continuously unless other water movements caused the sea surface to return to a flat configuration. Although sloping sea surfaces do develop, the slopes are always very small—so small that we perceive the sea surface to be flat even in regions of the most persistent winds. Water movements associated with Ekman transport that tend to restore the flat sea surface configuration are driven by the horizontal pressure gradients created under sloping sea surfaces (Fig. 8-6). Horizontal pressure gradients develop in response to the Earth’s gravitational force on the water.

The pressure gradient force tends to move water from the high-pressure region under the elevated part of the sea surface toward the lower-pressure region under the depressed part (Fig. 8-6). This direction is opposite to that of the Ekman transport. The flow induced by the pressure gradient tends to reduce the gradient and sea surface slope, restoring a flat sea surface.

Ekman transport occurs only in the wind-driven layer, which usually occupies only the upper few tens of meters of the water column. The mean water flow in the wind-driven layer is toward the highest point of sea surface elevation. However, the pressure gradient created when Ekman transport generates a sloping sea surface extends to depths beyond the wind-driven layer and is not restricted by shallow pycnoclines. As a result, the mean flow below the wind-driven layer is directed away from the area of maximum sea surface elevation (Fig. 8-6). In the area of maximum elevation, water is downwelled from the surface to below the wind-driven layer to join the pressure gradient flow.

Balance between Pressure Gradient and Coriolis Effect

All fluids, including air and water, are subject to the Coriolis effect when they flow horizontally (CC12). In the wind-driven layer, the Coriolis effect causes Ekman transport at approximately 90° cum sole to the wind direction. Ekman transport stores wind energy as potential energy associated with the elevation of the sea surface in one area relative to another. Water flows in response to the horizontal pressure gradient created by the sea surface elevation. As the water flows, it is accelerated and deflected cum sole. If allowed to develop long enough, the resulting currents, called “geostrophic currents” (CC13), are deflected to flow parallel to the contours of constant pressure (or along the side of the “hill” parallel to the sea surface height contours), and the Coriolis deflection is balanced by the pressure gradient force.

Geostrophic currents generated under ideal conditions beneath sloping sea surfaces are shown in Figure 8-6. These ideal conditions would be established only if winds blew at uniform speed over the entire area represented in the figure for several days or more. Such equilibrium conditions are never fully met in the oceans. Consequently, Figure 8-6 shows only the general characteristics of geostrophic currents. In reality, the currents are continuously changing as winds vary.

Geostrophic current speed and direction are determined by the magnitude and distribution of the horizontal pressure gradient (CC13). The pressure gradient can be determined from the sea surface slope and the water density. For example, the pressure at point C in Figure 8-6a is greater than the pressure at the same depth at point D by an amount that is equal to the additional weight per unit area of water column at point C. The additional weight is equal to the water density multiplied by the difference in sea surface height between the locations. Using these simple relationships, oceanographers have been able to estimate some surface current speeds by measuring sea surface height differences very precisely with satellite radar sensors.

Sea surface slopes that are created by wind-driven currents and that sustain geostrophic currents are extremely small. For example, one of the fastest ocean currents is the Florida Current, a part of the Gulf Stream that flows around the tip of Florida from the Gulf of Mexico into the Atlantic Ocean. The Florida Current flows at about 150 cm•s^–1 (5.4 km•h^–1). This current flows on a sea surface with an approximate height difference of only 20 cm across about 200 km—a slope of 1 in 1 million. Most sea surface slopes are even smaller, and the geostrophic currents are correspondingly slower.

Dynamic Topography

Measuring very tiny sea surface height differences to determine current speeds would appear to be a very difficult task. However, oceanographers have learned to measure the differences indirectly. They carefully measure the density of seawater throughout the depth of the water column at different locations and calculate the dynamic height.

The dynamic height is the height of the water column calculated from a measured density profile of the water column between the surface and a depth below which it is assumed there are no currents. We can see how the calculation of dynamic height works if we remember that density is mass per unit volume. Consider several columns of water, each with a 1-cm² surface area, in different locations (Fig. 8-7). If the total mass of water in each column were the same, the height of the column with a lower average density would be greater than that of the column with higher average density (Fig. 8-7). From several calculated dynamic heights, we can estimate the average sea surface slope between locations. By making such calculations for many different locations, we can draw a detailed map of sea surface height called a “dynamic topography map.” Detailed water density distribution data can also be used to identify slopes on pycnoclines, which are then used to estimate geostrophic current speeds and directions in deep-ocean water masses.

Figure 8-7. Calculations of dynamic height can be used to determine sea surface slopes. The height of the water column above a “depth of no motion” is calculated from measurements of the distribution of density with depth. The depth of no motion is a depth below which it can be reasonably assumed that there are no currents flowing. If the average density of the water column above the depth of no motion is known for several locations, the height of the sea surface at each location and the horizontal pressure gradients between the locations can be calculated.

This procedure for calculating dynamic height or sea surface slope is relatively simple, but it involves assumptions that are usually not fully met. First, we must select a depth of no motion below which we assume there are no currents. The pressure at this depth must be the same at all locations; otherwise, the horizontal pressure difference would cause water to flow horizontally. Because pressure does not vary at the depth of no motion, the mass of water above this depth must be the same at any location.

Until just the past few years, dynamic topography maps were generated from measurements made at many different individual locations at various times, sometimes months or years apart. The necessary measurements of salinity and temperature were made from research vessels, which take many weeks to complete a series of measurements at stations spaced across an ocean. As a result, until relatively recently, dynamic topography maps represented average conditions over many weeks or months, and we knew very little about short-term (up to months) variations in geostrophic currents. 

Oceanographers still rely on indirect calculations of dynamic height to investigate geostrophic currents. However, the development of unattended moored arrays, autonomous floats, and satellite sensors now allows simultaneous data to be gathered at many locations. Moored vertical strings (arrays) of instruments at key locations and autonomous floats that profile the water column can collect and send back to shore-based facilities continuous data that can be used to calculate dynamic height. More than 4000 autonomous floats are currently deployed. Satellite radar sensors have now become sensitive enough to measure sea surface heights directly, and with sufficient precision that the data can be used to draw detailed dynamic topography maps of any part of the ocean every few days. Although the satellite data give only the dynamic height at the sea surface, these data, when combined with the data collected by moored and autonomous instruments, have drastically improved our ability to observe geostrophic currents. As a result, we are just beginning to understand their complexities and variability.

Energy Storage

Geostrophic currents flowing near the surface are generated by winds because they depend on Ekman transport to establish the sea surface slopes under which they flow. However, geostrophic currents continue to flow even if winds abate, because Ekman transport stores wind energy as potential energy by piling up the water. The stored potential energy is converted to momentum to maintain geostrophic currents during intervals when winds are light or cease.

The length of time during which geostrophic currents continue to flow after winds abate depends on the magnitude of the sea surface slope and the area over which the slope occurs. The larger the area of sloping sea surface and the greater the slope, the longer it takes for geostrophic currents to restore the sea surface after winds abate. Where local winds create sea surface slopes over small areas, geostrophic currents restore the sea surface and cease to flow within a few hours after the winds abate. This is often the case for geostrophic currents created by the interaction of storms and coastal water masses.