Lab Instructions: El Niño

Signature of ENSO dynamics in the tropical Pacific ocean

The ocean heats and cools the atmosphere right where they meet -- therefore, one indicator of the effect of changes in ocean dynamics upon the atmosphere is through sea surface temperature (SST). Since we are interested in departure of sea surface temperature from the typical annual cycle, we look at SST anomalies. By anomalies, we mean the difference between the SST measured that month (e.g. September of 1997) and the averaged SST for all Septembers for which we have data; in the case of the data below, it is January 1970-September 1998.

What is the pattern of SST anomalies in the tropical Pacific during an El Nino event? Use the viewer to look at an animation of monthly SST anomalies. Take note of the latitudinal and longitudinal range of the map view here. Go to the white box above the SST anomaly map and type in "January 1970 to Sep 1998" and click on the redraw button to the left. You will see a progression of SST anomaly maps drawn, starting from January 1970 and continuing to the present. Concentrate on the largest spatial-scale anomaly patterns that you see. Hit "Stop" on the Netscape browser to stop the animation.

Describe the pattern of SST anomalies across the tropical Pacific. Where are the anomalies the largest? What is the typical range of the anomalies in degrees? What is their amplitude? When during the year do anomalies start to develop? How long do the ENSO events tend to last? Do all the events you observe look the same, or are there differences in the timing, duration and strength of events?

Now consider the regularity of ENSO warm phase events. One way to do so is via a time vs. longitude plot of SST anomalies. Using the viewer, make a time vs. longitude plot for SST anomaly data right on the Equator. Make sure that the viewer is at 0 degrees (the default is 29°S).

Can you pick out the signatures of the main ENSO warm phase events? How much time passes between events? Is this time interval constant, or does it vary?

Finally, let's look at December 1982 - February 1983 averaged sea surface temperature (not anomaly). This is during a recent strong ENSO warm phase event.

Where is SST the warmest? How does the area of the Pacific covered by the warmest SST change during ENSO warm phase events? How does the location of the warmest SST compare to the location of the largest SST anomaly during ENSO events? Keep this comparison in mind as we look at how the atmosphere reacts to ENSO warm phase conditions.

The effect of ENSO on the tropical atmosphere

During warm phase of ENSO, the atmosphere in the tropics is heated via increased SST, so the atmosphere must respond and distribute the extra heating. It does so via enhanced convective activity. One way we can observe changes in convection is via satellite observations of the outgoing longwave radiation (OLR). The OLR measurement tells us the temperature of the surface that the satellite sees. If the atmosphere between the satellite and the Earth's surface is clear, then the satellite essentially sees the OLR from the ocean or land surface. However, if the atmosphere is full of thick clouds, then the satellite sees the top of the clouds. Since the cloud tops may be 5-10 km above the surface, they are much colder than the surface. Therefore, when we see patches of low OLR, we interpret this as the locations of thick thunderclouds.

Now look at the OLR anomaly for December 1982 -February 1983, in the middle of a strong ENSO warm phase event (this is the same period for which you just examined sea surface temperature data).

Where are the lowest OLR anomalies found? Do the patterns of the OLR anomalies more closely resemble those of the sea surface temperatures, or those of the sea surface temperature anomalies? Why do you think this is?

Understanding correlation

Scientists often wish to quantify the association between variables. For example, below you will examine the association between ENSO and crop yields. For this task we will use the correlation statistic. Given two variables, x and y, the correlation (r) is a measure of how well a line drawn through a scatter plot of y vs. x fits the data. It is computed from the following formula:

where and are the mean values of x and y respectively, sx and sy are the standard deviations of the data, and n is the number of data points:

r can take on any value between -1 and 1. If r is positive, then the data are positively correlated. This means that an increase in variable x corresponds to an increase in y, whose magnitude depends on the slope of the line drawn on a plot of y vs. x. If r is negative, then the data are negatively correlated: an increase in variable x corresponds to a decrease in variable y, again with magnitude depending on the slope of the line drawn through the data. If r=0, then there is no relationship between the data y and x: we can't make any prediction about how y should change if we vary x. In practice r almost never exactly equals -1, 0 or 1, but falls somewhere in between. Then we have to decide whether there really is any relationship between y and x. It would help to know something about the problem itself, such as its physics, to interpret and explain the correlation coefficient. The correlation coefficient itself says nothing about causality, however: it merely suggests whether changes in x are associated with changes in y (or the other way around).

Are SST anomalies in the eastern equatorial Pacific associated with sea level pressure anomalies across the tropical Pacific?

We'll investigate this question by computing the correlation between NINO3 and an index of anomalous atmospheric sea level pressure difference between the eastern and western tropical Pacific, called the Southern Oscillation Index. NINO3 is the average SST anomaly over the region 150W to 90W, 5N to 5S. (From the map views of SST anomaly, you can see that this region has the strongest SST anomalies associated with ENSO warm phase events.) The SOI is the difference between the atmospheric sea level pressure anomaly at Tahiti (in the southeastern tropical Pacific), and the atmospheric sea level pressure anomaly at Darwin, Australia (in the western Pacific). Pressure is usually low in the western tropical Pacific, and high in the eastern tropical Pacific. (From lecture, can you explain why, given the pattern of sea surface temperatures across the tropical Pacific?) The SOI tells us when this atmospheric pressure pattern departs from normal conditions, or in other words, when atmospheric sea level pressure is simultaneously lower in the eastern tropical Pacific, and higher in the western tropical Pacific.

Save the data in a place you can easily access (e.g., the Desktop). There are three columns of data. The first is the year: notice the data are averaged for April through March of the following year. The second column is the NINO3 annually-averaged SST anomaly for the corresponding years, and the third column gives like averages of the SOI.

First make a scatter plot of NINO3 vs. SOI. Do you see a negative or positive correlation? Weak or strong? Try to estimate the correlation on a scale from 0 to 1 (0 to -1 for negative correlation).

Compute the correlation between SOI and NINO3 using Excel's =correl() function.

Is the correlation positive or negative? Weak or strong? Your eye was probably pretty accurate at judging the strength of the correlation.

Is the correlation between NINO3 and SOI really different from zero?

If we don't know anything about the physics (or even if we do), we still would like to test the reality of the relationship between NINO3 and SOI. Is it really different from zero? Typically a statistical test is phrased as follows. We obtained a value r for the correlation coefficient between the variables x and y. Suppose instead of the series y, we had a series z of randomly chosen numbers. In this case, what value of correlation coefficient would you expect -- what is the most likely value for the correlation between x and z? We want to know the likelihood that we obtained a correlation as high as r. If the probability that we obtained a correlation as high as r by correlating x and z is low, then we are pretty sure the relation between x and y is significant -- that is, that the relationship we observed is not likely to be due to chance. If the probability is high, however, then we can't be confident that there is a real relationship between x and y.

We took the time series of annual averages of NINO3 SST anomaly for 1961-1990 (30 years) as x, and generated 10,000 random time series of 30 numbers each -- these are our z's. Here is a histogram showing the number of observations of the magnitude of r between 0-0.1, 0.1-0.2, 0.2-0.3, etc. For instance, reading from the histogram, there were 4039 occurrences of |r| between 0 and 0.1. (The bars around r mean "absolute value of".)

What is the median of r (i.e. the value of r where half the data has higher r, and half the data has lower r)? What percentage of the values fall between 0.4 and 0.5? What percentage of values of r is less than 0.1? 0.2? 0.3?...1.0?

Now recall the correlation between SOI and NINO3 that we calculated earlier. What percentage of the correlations between NINO3 and the random time series is less than the correlation between SOI and NINO3? What percentage is greater than the correlation between SOI and NINO3? This percentage is the chance that a random time series will be correlated as well with NINO3 as SOI is correlated with NINO3. How confident are you that the correlation between SOI and NINO3 is real?

Relationships between NINO3 SST anomaly and agricultural yields

The atmosphere has to get rid of the extra heating supplied by the eastern tropical Pacific Ocean during an ENSO warm phase event. It does this in certain preferred patterns, which affect temperatures and precipitation in many places around the world. As a result, weather-sensitive human activities, such as agriculture, can be adversely affected. In this part of the lab, we'll examine how closely Eastern Equatorial Pacific SST anomaly is associated with remotely-located agricultural yields. We'll do so by examining the correlation between NINO3, and selected crop yield time series.

Now consider the following data table which gives annual NINO3 SST anomaly, and crop yield anomalies for rice and maize in India, the U.S. and Peru. The first column gives the year. The second column gives the same NINO3 data as in table 1. The next columns are agricultural yield anomalies (difference from the 30-year mean value). The third column is annual rice harvest in India, the fourth is annual maize harvest in the United States, and the final column is the annual maize harvest for Peru.

Make scatter plots and compute the correlation between NINO3 and

Are the correlations positive or negative? weak or strong? Based on comparison with the correlations obtained for NINO3 SST anomaly with random time series, how confident are you of the reality of these relationships?

Why would SST anomalies in the Pacific be related to crop yield elsewhere?

Given a prediction of a high/low NINO3 anomaly, what advice would you give to farmers in the US, India, and Peru? In all cases, how would you explain why they should listen to you, based on your analysis of the data? Include a sketch to support your answer.

Lab Report Instructions

Write a lab report (as per the Lab Report Format) summarizing the major findings of your investigation.