SIO 210 Talley Topic 3: Dynamical quantities, transports and forcing

Lynne Talley, 1997
Back to SIO 210 index.
Reading and study questions for topic 3 - click here

1. Dynamical quantities for the general circulation

1.1 Velocity. Horizontal velocity is measured directly using various current-measuring devices, or calculated from the horizontal pressure gradient. In the latter case, for the large-scale circulation, geostrophy is assumed. Vertical velocity for the large-scale circulation cannot be measured as it is too small, only inferred from the horizontal velocities.

Direct current measurements - require time and space averaging and/or filtering to remove unwanted signals such as those from tides and internal waves. The remaining signal still contains all of the time scales of the large-scale circulation. It is more or less the case that long time scales go with large horizontal spatial scales. There is no hard and fast rule about how long the time average must be that corresponds with a velocity estimate associated with the pressure gradient. (current meter results, float trajectories and averages - see aquarium lecture .)

Pressure gradients can be used to calculate geostrophic flows. Pressure can be measured in several ways. Altimetry provides the sea surface height to within several centimeters, which is not adequate for the "mean" circulation, but is adequate for determining the variability of the surface currents about an unknown mean. Pressure gauges on the ocean bottom can be calibrated with direct current measurements (say from current meters), and then used in pairs to calculate geostrophic flow. As with direct current measurements, time series signals must be averaged or filtered.

Finally, pressure gradients can be determined from dynamic height (density field), again to within an unknown pressure at each position (next subsection). The unknown can be thought of as due to the unknown exact sea surface height relative to the geoid (and which altimetry is mainly not quite adequate to measure).

Velocities associated with the general circulation are then mostly calculated from the pressure gradients, with a number of techniques used to estimate the absolute pressure at each point and hence the absolute velocity.

1.2 Dynamic height. To calculate pressure at a point relative to a deeper or shallower point at the same horizontal location, from the measured density field.

Use hydrostatic balance, which is the force balance between the vertical pressure gradient and gravity*density.

The practical details of the calculation are beyond the scope of these notes and class, but an example is worked through in class. (Figure in class: dynamic height at the sea surface relative to a deeper pressure for the Pacific, from Wyrtki [1971], and adjusted steric height for the Pacific, from Reid [1997].)

1.3 Transports. We often wish to express how much total water or heat or salt or carbon is moving around. Transports are the total flux of whatever property through a given area. The general expression for transports is the integral over the area of the property*velocity.

Volume transport: integral of velocity over the area. Units are m^3/sec. A typical transport for a major current is on the order of 10 to 100 x 10^6 m^3/sec. We use the unit "Sverdrup" where 1 Sv = 1 x 10^6 m^3/sec.

Mass transport: integral of density*velocity over the area. Units are kg/sec. A typical transport for a major current is order 10 to 100 x 10^9 kg/sec (since density is roughly 1000 kg/m^3).

Heat transport: integral of heat*velocity over the area. Units are Watts (e.g. Joules/sec). Heat must be calculated using Kelvin degrees. Heat transport through a closed area, through which there is no net mass transport, is basically proportional to the temperature difference between water entering and water leaving across the closed boundaries, so degrees Celsius are fine for this practical use. Net heat transport across various latitude lines which close at boundaries range from -1.0 to 1.0 x 10^15 Watts. We sometimes use the unit 1 Petawatt = 1 x 10^15 Watts.

Freshwater transport: Salt in the ocean is not gained or lost over the time scales of interest to us. However freshwater is exchanged with the atmosphere and land. A kilogram of seawater consists of a portion of water and a portion of salt. The relative proportions are expressed in the salinity, which is taken for these transport calculations to be (gm salt/kg seawater) or (gm salt/(kg salt + kg freshwater)). Using the salinity measured along a section, we can calculate the freshwater transport across the section. Typical values are order 1 Sv.

Other substance transports (carbon, oxygen, etc etc). If the property is given as a concentration ( gm property/gm seawater), then the transport is integral(concentration*density*velocity) over the area, which yields gm/sec of the substance.

(Figure in class: mass transports in the North Atlantic from Schmitz and McCartney; heat transports for the globe from various sources.)

2. Forcing of general circulation

How do forces work on the ocean's general circulation? Most of them create pressure gradients which cause water to try to flow from high pressure to low pressure. The earth's rotation introduces a Coriolis acceleration which induces flow in the frame of reference of the earth which is to the right of the motion in the northern hemisphere and to the left in the southern hemisphere, if the flow persists for about a day or longer such that it is affected by the rotation. Details for each were given in Hendershott's lectures.
  • What equations do physical oceanographers use to describe the ocean?
    ma=F (vector form; F = pressure gradient, body forces and dissipation and a includes time change of velocity, advection and Coriolis acceleration)
    mass conservation (whatever amount goes into a box must come out)
    equation of state (dependence of density on temperature, salinity and pressure)
    density changes as a function of heating/cooling and evaporation/precipitation, and pressure

    2.a. Wind forcing. As described in full in Hendershott's lectures, the wind acts directly and frictionally on the surface 50 to 100 meters of the ocean, in the "Ekman layer". The net transport in the Ekman layer is to the right of the wind in the northern hemisphere and to the left in the southern hemisphere. This effect has been demonstrated by Ralph and Niiler (1997) using surface drifter data from the the Pacific (drogues at 15 m).

    Figure. Annual average surface wind stress (blue arrows in stress/unit area) and the average flow at 15 m depth (red arrows in cm/sec) which arises directly in response to the winds. The latter are the average velocity based on thousands of satellite-tracked surface drifters after the average flow resulting from the ocean's pressure field (geostrophic flow) is subtracted out. Hence the red arrows are the ageostrophic component of the velocity, and correspond to the Ekman response at 15 m. (Figure from E. Ralph.)

    Westerlies and trades (see example or Hellerman and Rosenstein [1983] figures in lecture handout or other wind products)

    Example of global wind field FNOC monthly winds, December, 1990. Taken from the plot package "ferret"'s examples.

    For a more complete and general description of how the wind drives the general circulation, see section 5 in

    Talley, L. D., G. Fryer, and R. Lumpkin, 1997. Physical oceanography of the tropical Pacific. In Geography of the Pacific Islands, ed. M. Rapaport. Bess Press, Honolulu, HI. In press.

    2.b. Thermohaline forcing. The gross aspects of the salinity and temperature distributions, and the driving force for the slow overturning circulation, are due to surface heating/cooling and surface evaporation/precipitation/ continental runoff. Maps of heat flux and evaporation - precipitation are presented. Components of the heat flux are described (incoming shortwave solar radiation, outgoing longwave radiation, latent heat loss due to evaporation, sensible heat change due to conduction between air and water). Input of fresh water takes place through precipitation and runoff from land. I don't have a net buoyancy flux map for the lecture notes.

    Thermohaline forcing takes several forms.
    (1) cooling/evaporation in a region (cooling is often due to large evaporation), which creates dense water at the sea surface which then overturns in convective cells. These cells are very narrow (order 1 km), and are referred to sometimes as "chimneys", or a whole patch of convective cells might be referred to as a chimney. Flow in the convective cells is "ageostrophic" - that is, not geostrophic, since vertical velocities and vertical length scales are of the same order as in the horizontal.
    (2) Brine rejection resulting from sea ice formation. This releases salt into the water column, which increases its density and can create overturn.
    (3) Any downward flow due to increase of density must be compensated somewhere by upwelling and inflow into the overturning regions. The upwelling must be accompanied by vertical mixing as the water parcels migrate upward. This upwelling is an essential part of the thermohaline circulation and is what forces most of the flow which we call "thermohaline".
    (4) Salt and temperature do not actually mix at exactly the same rates, especially at the molecular scale - temperature mixes much faster. This difference in mixing rates can create layering or overturn - in the ocean, on vertical scales of several to 10's of meters. This is a form of thermohaline forcing.

    Annual mean net heat flux (W/m2)

    Net surface heat flux from Hsiung, 1985. Estimates of global oceanic meridional heat transport. J. Phys. Oceanogr., 15, 1405-1413.
    I have superimposed on the map the directions of meridional heat transport at selected subtropical latitudes, based on direct oceanic measurements.

    ECMWF map of heat flux from Bernard Barnier , using the European Center for Medium Range Weather Forecasting analyses for the years 1986-1988 to compute surface fluxes. Rollowing publication. Fields were made available by Barnier for this map which reproduces a similar map in the following reference:

    Barnier, B., L. Siefridt and P. Marchesiello, 1994. Thermal forcing for a global ocean circulation model using a three- year climatology of ECMWF analyses. J. Marine Systems, 6, 363-380.

    Annual mean net evaporation minus precipitation (cm/yr)

    Annual mean E-P in cm/year constructed from climatology data in DaSilva's online Atlas of Surface Marine Data.

    DaSilva, A. M., C. C. Young and S. Levitus, 1994. Atlas of surface marine data 1994.