ocean 90 assignment 2

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ASSIGNMENT #2: Teleconnection Patterns

Go to the class web site and download the following files to your computer:

exercise2_P1.R

exercise2_P2.R

exercise2_P3.R

exercise2_P4.R

pna_all_DJF_1950-2013.dat

pna_warm_DJF_1950-2013.dat

pna_cold_DJF_1950-2013.dat

nao_all_DJF_1950-2013.dat

nao_warm_DJF_1950-2013.dat

nao_cold_DJF_1950-2013.dat

Next, start up “R” and at the prompt (>>) enter your name in the following way:

name<-“Jane Doe”

Important: Be sure to do this before you run each new program.

This step is very important since it will identify you on the results of your work. If your name does not appear appropriately on the graphical output that you hand-in with your completed assignments, you will receive no credit for this assignment. In addition, if you omit this step, the R-programs for this exercise will not work correctly and you will get an error message.

Print out and hand in all the figures generated by the programs for this assignment.

Points for each problem are given as a guide. Though we will not change these values typically, we reserve the right to do so as we feel appropriate and necessary in grading.

Geostrophic Balance and Atmospheric Winds

As we discussed in class, the pressure gradient force and Coriolis force are generally equal and opposite in the atmosphere (and ocean) which is referred to as geostrophic balance. The resulting winds (and currents) are referred to as geostrophic winds (or geostrophic currents).

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Question 1:

Figure 1 shows idealized maps of high and low pressure in the atmosphere in the northern hemisphere (Figs. 1a and 1b) and in the southern hemisphere (Figs. 1c and 1d). Each circular line in Fig. 1 represents a contour of constant of pressure (i.e. an isobar). In each figure, use arrows to indicate the direction of the geostrophic winds. Use heavy or thicker arrows in places where you expect the winds to be stronger than elsewhere. (12 points)

Figure 1: Contour maps of atmospheric pressure in the northern hemisphere for (a) a high pressure system, and (b) a low pressure system. Each contour is a lines of constant pressure (i.e. an isobar).

Closely spaced contours indicate regions where the pressure gradient is large, while regions where the contours are far apart indicate regions where the pressure gradient is small. Contour maps of atmospheric

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pressure in the southern hemisphere are shown in (c) a high pressure system, and in (d) a low pressure system.

Atmospheric Teleconnection Patterns

As we learned in class, there are preferred and persistent patterns of high and low pressure and winds in the northern hemisphere atmosphere during winter time. The most prominent are the Pacific North American (PNA) pattern in the North Pacific, and the North Atlantic Oscillation (NAO) in the North Atlantic.

Question 2:

Figure 2 shows typical pressure anomalies for January in the atmosphere near the top of the troposphere that are associated with the PNA pattern and the NAO. Recall that the 500 mb geopotential height is the height above the ground at which the atmospheric pressure is 500 mb. At this altitude half the mass of the atmosphere is below and half the mass is above. High and low pressure systems in the atmosphere lead to undulations in the time averaged 500 mb geopotential height. These undulations are referred to as geopotential anomalies which is what is shown in Fig. 2. On each panel in Figure 2, indicate the direction of the geostrophic winds. (4 points)

Figure 2: Maps of January 500mb geopotential height anomalies near the top of the troposphere associated with (a) the PNA pattern, and (b) the NAO. For the purposes of this exercise, you can think of

these as high (H) and low (L) anomalies in atmospheric pressure.

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Question 3:

Read pages 69-103 of the class reader, an article entitled “An Overview of the North Atlantic Oscillation” by James W. Hurrell, Yochanan Kushnir, Geir Ottersen and Martin Visbeck (“The North Atlantic Oscillation: Climatic Significance and Environmental Impact. Geophysical Monograph 134. America Geophysical Union, 2003, p1-35). This article is also available online. (11 points)

(a) During the positive phase of the NAO, what happens to the surface temperature over (i) North America, (ii) Northern Europe and Eurasia, (iii) North Africa and the Middle East?

(b) During the positive phase of the NAO, what happens to the North Atlantic storm track? (c) During the positive phase of the NAO, what happens to rainfall over (i) Greenland and

the Canadian Arctic, (ii) central and southern Europe and the Mediterranean, (iii) Iceland, the British Isles and Scandinavia?

(d) What happens to all of these trends during the negative phase of the NAO?

The Influence of El Niño and La Niña on Atmospheric Teleconnection Patterns

As we have seen in class, El Niño and La Niña can influence the preferred phase of the atmospheric teleconnection patterns.

Question 4:

(a) Run the program “exercise2_P1.R” in R, as you were instructed to do in class and in section. This will load the data for the daily average Pacific North American (PNA) index for the winter months December, January and February (DJF) for the period 1950-2013, and will generate three figures: exercise2_plot1.jpg – the probability density function (PDF) of the PNA index for all winters; exercise2_plot2.jpg – the PDF for the PNA index for El Niño winters only; and exercise2_plot3.jpg – the PDF for the PNA index for La Niña winters only. The data for all winters are called pna_all_wtr, the data for El Niño winters only are called pna_el_wtr, and the data for La Niña winters only are called pna_la_wtr. (i) Using the “mean” command in R (“mean(pna_all_wtr)”), compute the mean of the PNA index for all winters, El Niño winters alone, and La Niña winters alone. Write these values on plot 1, 2 or 3 as appropriate. (ii) Briefly describe how the statistics of the mean wintertime PNA index are different during El Niño and La Niña winters (for

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example, does the PDF differ between the different cases? If so, in what ways?). (7 points)

(b) Now run the program exercise2_P2.R. This will generate two additional figures: exercise2_plot4.jpg – the cumulative probability distribution function of the DFJ PNA index during El Niño winters; and exercise2_plot5.jpg – the cumulative probability distribution function of the DFJ PNA index during La Niña winters. (i) Drawing appropriate horizontal and vertical lines on plot4, estimate the probability of the PNA pattern being in its positive phase during El Niño winters and write this value on plot4. (ii) Drawing appropriate horizontal and vertical lines on plot5, estimate the probability of the PNA pattern being in its positive phase during La Niña winters and write this probability on plot5. (iii) Compare these two probabilities with each other, and compare the overall impression of these results with your complementary analysis in (a). (6 points)

Questions 5:

Let’s now explore if the winter time circulation over the North Atlantic (as described by the North Atlantic Oscillation (NAO)) varies statistically with El Niño and La Niña conditions.

(a) Run the program exercise2_P3.R in R which will load the data for the daily average NAO index for the winter months December, January and February (DJF) for the period 1950- 2013 and will generate three figures: exercise2_plot6.jpg – the probability density function (PDF) of the NAO index for all winters (nao_all_wtr); exercise2_plot7.jpg – the PDF for the NAO index for El Niño winters only (nao_el_wtr); and exercise2_plot8.jpg – the PDF for the NAO index for La Niña winters only (nao_la_wtr). (i) Compute the mean of the NAO index for all winters, El Niño winters alone, and La Niña winters alone, and write these values on the appropriate figures. (ii) Briefly describe if and in what ways the winter time NAO index statistically changes with El Niño and La Niña conditions. (4 points)

(b) Now run the program exercise2_P4.R. This will generate two additional figures: exercise2_plot9.jpg – the cumulative probability density function of the DFJ NAO index during El Niño winters; and exercise2_plot10.jpg – the cumulative probability density function of the DFJ NAO index during La Niña winters. (i) Drawing appropriate horizontal and vertical lines on plot9, calculate the probability of the NAO pattern being in its positive phase during El Niño winters and write the result on plot9. (ii) Drawing appropriate horizontal and vertical lines on plot10, calculate the probability of the NAO pattern being in its positive phase during La Niña winters and write the result on plot10. (iii) Compare these two probabilities with each other and compare the overall impression they give with your complementary analysis in (a).

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Question 6:

Based on your findings in questions 4 and 5, briefly comment on the relative influence of El Niño and La Niña on the sign of the PNA and NAO patterns during winter. For example, do El Niño conditions result in similar changes in the two indices (relative to all conditions)? Are changes stronger for one index than for the other? What about during La Niña? (4 points)