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Rossby and Kelvin Waves, Upwelling, and Equatorial circulation

Rossby and Kelvin Waves, Upwelling, and Equatorial circulation. October 15. Rossby Waves. L: measure of length over which U changes; also a measure of how far parcel travels before acted on by Coriolis. If R 0 <<1, ocean responds by wave propagation. f 3. f 2. f 1. C.

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Rossby and Kelvin Waves, Upwelling, and Equatorial circulation

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  1. Rossby and Kelvin Waves, Upwelling, and Equatorial circulation October 15

  2. Rossby Waves L: measure of length over which U changes; also a measure of how far parcel travels before acted on by Coriolis If R0<<1, ocean responds by wave propagation

  3. f3 f2 f1 C Rossby waves exist because of:

  4. ς=0 ς=0 ς<0 ς>0

  5. ς=0 ς=0 ς<0 ς>0 For west propagation: C<0

  6. For east propagation: ς=0 ς=0 C>0

  7. Assume: Then:

  8. At Mid latitudes: C ~ 1-10 cm/s Equator: C ~ 1 m/s Rossby waves and Kelvin eaves communicate information on changes in wind to different part of the basin – Responsible for quick reversal in Somali current – Play a large role in El Nino Equator oceans respond much faster to changes in winds because of greater Rossby waves speed – Adjustment time scale ~ basin width Rossby Wave Speed

  9. Coastal Upwelling • Mid-ocean upwelling – driven by Ekman divergence • Get Ekman divergence at coast

  10. Equatorial Dynamics • Recall… coastal upwelling is driven by Ekman divergence at the coast • Equatorial upwelling is driven by Ekman divergence at the equator

  11. A’ ME τ(x) Equator B’ B f=0 τ(x) ME A

  12. Equator A A’ pgf pgf f<0 f=0 f>0 Pycnocline is lifted at the Equator, pressure gradient force drives equatorial under current

  13. Sea surface slopes up to the West B’ B pgf East – West slope of the pycnocline Surface current driven by wind is confined to the mixed layer

  14. Figure 14.5 in Stewart. Left: Cross-sectional sketch of the thermocline and sea-surface topography along the equator. Right: Eastward pressure gradient in the central Pacific caused by the density structure at left.

  15. Figure 14.1 in Stewart. Average diabatic heating due to rain, absorbed solar and infrared radiation and between 700 and 50 mb in the atmosphere during December, January and February calculated from ECMWF data for 1983-1989. Most of the heating is due to the relaese of latent heat by rain. From Webster (1992).

  16. Figure 14.2 in Stewart. The mean, upper-ocean, thermal structure along the equator in the Pacific from north of New Guinea to Ecuador calculated from data in Levitus (1982).

  17. Figure 14.3 in Stewart. Average currents at 10m calculated from the Modular Ocean Model driven by observed winds and mean heat fluxes from 1981 to 1994. The model, operated by the NOAA National Centers for Environmental Prediction, assimilates observed surface and subsurface temperatures. From Behringer, Ji, and Leetmaa (1998).

  18. Cp Sea surface pycnocline Barotropic Wave • Ocean’s response to changing winds • external (or surface)waves

  19. Cp Sea Surface pycnocline Baroclinic Wave

  20. p increasing Hi Hi p decreasing divergence Lo pgf Cf C Lo convergence pgf is balanced by Cf p increasing Hi v=0 Top View • Coastal Kelvin waves get trapped against horizontal boundary Side View

  21. for baroclinic waves Wave Phase Speed: ~0.5 to 3 m/s for barotropc (external) waves • L: measure of how far a water parcel can travel before it is affected by Coriolis: • f is smallest near the equator and largest near the poles, L increases toward the equator, coastal waves are not trapped at the equator

  22. pgf pgf pgf Divergence Convergence Lo Hi Lo Equator pgf pgf pgf C Equatorial Kelvin Waves • Equator acts like a coast, with water on either side Equatorial Kelvin Waves move only to the East Le ~250 km, C~3 m/s

  23. Figure 14.10 in Stewart. Left: Horizontal currents associated with equatorially trapped waves generated by a bell-shaped displacement of the thermocline. Right: Displacement of the thermocline due to the waves. The figures show that after 20 days, the initial disturbance has separated into an westward propagating Rossby wave (left) and an eastward propagating Kelvin wave (right). From Philander et al. (1984).

  24. Figure 14.4 in Stewart. Cross section of the Equatorial Undercurrent in the Pacific calculated from Modular Ocean Model with assimilated surface data (See §14.5). The section an average from 160°E to 170°E from January 1965 to December 1999. Stippled areas are westward flowing. From Nevin S. Fuckar.

  25. τ(x) τ(x) z=0 surface 80 m pycnocline 300-400 m Eq. under current 180° El Niño Winds relax – pycnocline flattens out

  26. equator Kelvin wave propagates eastward, depressing the pycnocline as it goes

  27. pyc. depressed pyc. uplifted upwelling shuts off 2-3 months – hits the coast of South America, part of it reflects as a RossbyWave, part moves poleward as a coastal Kelvin wave

  28. CKW California Current Rossby Wave Rossby Wave Humbolt Current Coastal Kelvin Waves (CKW) go all the way to Canada and Chile, altering Eastern Boundary Currents and shutting down upwelling

  29. Figure 14.14 in Stewart. Tropical Atmosphere Ocean tao array of moored buoys operated by the NOAA Pacific Marine Environmental Laboratory with help from Japan, Korea, Taiwan, and France. Figure from NOAA Pacific Marine Environmental Laboratory.

  30. Figure 14.6 in Stewart. Correlation coefficient of annual-mean sea-level pressure with pressure at Darwin. ---- Coefficient < - 0.4. From Trenberth and Shea (1987).

  31. Figure 14.7 in Stewart. Normalized Southern Oscillation Index from 1951 to 1999. The normalized index is sea-level pressure anomaly at Tahiti divided by its standard deviation minus sea-level pressure anomaly at Darwin divided by its standard deviation then the difference is divided by the standard deviation of the difference. The means are calculated from 1951 to 1980. Monthly values of the index have been smoothed with a 5-month running mean. Strong El Niño events occurred in 1957–58, 1965–66, 1972–73, 1982–83, 1997–98. Data from NOAA.

  32. Figure 14.8 in Stewart. Anomalies of sea-surface temperature (in °C) during a typical El Niño obtained by averaging data from El Niños between 1950 and 1973. Months are after the onset of the event. From Rasmusson and Carpenter (1982).

  33. Figure 14.11 in Stewart. Sketch of regions receiving enhanced rain (dashed lines) or drought (solid lines) during an El Niño event. (0) indicates that rain changed during the year in which El Niño began, (+) indicates that rain changed during the year after El Niño began. From Ropelewski and Halpert (1987).

  34. Figure 14.12 in Stewart. Changing patterns of convection in the equatorial Pacific during an El Niño, set up a pattern of pressure anomalies in the atmosphere (solid lines) which influence the extratropical atmosphere. From Rasmusson and Wallace (1983).

  35. Figure 14.13 in Stewart. Correlation of yearly averaged rainfall averaged over all Texas each year plotted as a function of the Southern Oscillation Index averaged for the year. From Stewart (1994).

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