1. The figure shows sea surface height (SSH) anomaly at 24 S (southern hemisphere), from a satellite altimeter.

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1 SIO 210 Problem Set 3 November 16, The figure shows sea surface height (SSH) anomaly at 24 S (southern hemisphere), from a satellite altimeter. (a) What is the name of this type of data display?_hovmöller diagram (b) What is the dominant phenomenon that you are seeing in these plots? (name)_rossby waves (c) Which direction does this phenomenon propagate on average? West (d) Using the South Indian plot on the right, what is the approximate phase speed of this phenomenon? Follow a peak or trough to identify how far it travels in how much time. At 24S, 1 degree of longitude is 111km*cos(-24) = km (e) Looking at the left side of the South Pacific plot, what might you expect a dominant frequency in a temporal spectrum of this data to be? We see about 4 peaks and 4 troughs per year, which means a frequency of (f) Given that frequency, what would be the shortest sampling interval that would resolve that phenomenon? (Also, what is the name of this shortest sampling interval?) (g) Any other interesting observations about these plots, something that piques your interest? Troughs and peaks appear to get stronger during and after the 1997/1998 ENSO

2 2. Ekman flow a) What are the two dominant forces that balance in an Ekman layer? Coriolis and Viscous Write down these terms from the actual momentum equations in partial differential form. b) In an Ekman layer in the northern hemisphere, what direction is the verticallyintegrated transport? 90 degrees to the right of the wind direction The mean wind stress (in N/m 2 ) in the eastern and central North Pacific is shown in the figure. c) Indicate on the figure where coastal upwelling could be found. What is the name of the current system where this occurs? California current system d) Indicate on the figure where open ocean upwelling is likely to be found. What is the name of this part of the general circulation? The subpolar gyre e) Suppose the southward wind stress along the North American coast averages 0.1 Newton/m 2. Use the expression for Ekman transport given in class and in the text to compute the corresponding Ekman transport (in m 2 /sec). Recall that this transport is not the full volume transport, but is velocity integrated in the vertical. f) Now compute the net Ekman volume transport along the coast of North America that responds to the southward wind stress. Which direction does it go? Assume for simplicity that the stress is the same value along the coast. Estimate the length of coastline (use a map with latitudes/longitudes) as part of your answer.

3 3. Return to Problem 2 from Problem Set 2, but now knowing that the Earth is rotating, and including Coriolis force. North Atlantic Current Antarctic Circumpolar Current Fig. 1. Potential temperature from the Antarctic to Iceland. (a) Sketch sea surface height (SSH) from the previous problem set, just considering the large scale distribution of temperature in the upper ocean. Show where the sea surface should be relatively high and where it should be relatively low. (You already did this in Problem Set 2.) (b) Using our arrow/tail-of-arrow symbols, indicate where the large-scale surface circulation is eastward and where it is westward. Assume the flow is geostrophic. Please make sure your arrows are in the correct locations relative to the SSH you drew for (a). (c) Label the Antarctic Circumpolar Current. (d) In the Antarctic Circumpolar Current, use the temperature distribution shown to infer the change in the geostrophic flow with depth. Indicate it using arrow/tail-of-arrow symbols. (e) What is the name given to this approach to calculating the change in geostrophic flow with depth? Thermal wind, or geostrophic balance (f) Find a region of the North Atlantic on the figure where the surface flow is broadly eastward. (This is the North Atlantic Current.) Repeat (d) but for this current.

4 4. The wind drives a circulation in the subtropical North Atlantic. The accompanying figure shows the dynamic height (in units that are similar to meters) at the sea surface, from Reid (1994). (a) Mark the Florida Current, the Gulf Stream, the North Atlantic Current, the North Equatorial Current, and the Canary Current on the map. (Pink labels) (b) Sketch (draw) on the map the direction of the prevailing winds that create the subtropical circulation, and include winds that create the Canary Current as well. (Yellow arrows) (c) The Ekman layer is the direct response of the ocean to the wind stress. Sketch the direction of the Ekman transport relative to the wind stress of (b). (green arrows) r ntic Cu a l t A orth rent N Gulf Stream Florida Current Canary Current North Equatorial Current (d) Mark the region on the map where the subtropical circulation is dominated by Sverdrup transport. (blue dashed ellipse)

5 (e) If the net Sverdrup transport at 25 N is 50 Sv (where 1 Sv = 1 x 10 6 m 3 /sec), and if it is distributed over the top 1000 m of the water column, compute the average velocity of the Sverdrup transport. Assume that 1 longitude ~ 100 km at this latitude. (f) If this transport is returned northward in the Gulf Stream, and if it is mostly confined to the upper 1000 m of the water column, compute the average velocity of the Gulf Stream. (Recall the typical width of the Gulf Stream from lecture.) (g) Mark the general region where you would expect to find subducted subtropical waters. What water mass or vertical structure do we associate with this subtropical subduction? (based on the typical distributions lecture) Mode waters (h) Mark the places where you would expect to find deep convection (> 1000 meters deep). What separate water masses are formed in these deep convection regions? (also based on the tyhpical distributions lectures) Labrador and Greenland Sea Water, which contribute to North Atlantic Deep Water formation