Wednesday, June 8, 2011

The Importance of El Nino

Switching gears a bit, I wanted to talk a bit about El Nino and why it's such a big deal for us.

When we talk about El Nino (or, as it is usually called these days, the El Nino-Southern Oscillation (ENSO)), we're talking about a periodic shift in the sea-surface temperature pattern over the eastern and central equatorial Pacific.  This in turn affects pressure patterns throughout the world, leading to swings in the weather.  It's a pretty big deal.

But why is it such a big deal?  And how can we see this?  First, sea-surface temperatures have far-reaching impacts on the overall weather pattern.  Remember from my discussion about dewpoint temperatures that water has a much higher heat capacity than air--for the same mass of water and air, it takes more energy to raise the water temperature by one degree Celsius than it takes to raise the air temperature by one degree Celsius.  Now, think of the vast quantites of water we have spread throughout the world's oceans.  If sea-surface temperatures warm or cool by just one degree Celsius, that exchanges a lot of energy with the air.  All that energy goes into reshaping our weather patterns.  So, variations in sea-surface temperatures are crucial energy sources (or sinks!) for the atmosphere.

So, let's analyze variations in sea-surface temperatures.  If we understand how sea-surface temperatures vary in space and time, we can probably get a good idea about how in general our atmosphere might vary in space and time as well.  To do this, I'm going to take a 51 year record of monthly mean sea-surface temperatures across the globe from 1950-2001 (the NCEP reanalysis, if you want to know).  I did this as part of a project with Elizabeth Maroon earlier this year, though many other scientists have used this same technique to derive modes of variability in sea-surface temperatures.  We used a technique to break down the data called Empirical Orthogonal Functions (EOF) analysis (also called Singular Value Decomposition (SVD) or Principle Component Analysis (PCA)).  This uses some matrix algebra on the sea-surface temperature patterns to tell us three things:
  1. Pictures of the dominant spatial patterns (or modes) of the sea-surface temperatures.
  2. How big of a contribution each of those spatial patterns has to the total variability of the sea-surface temperatures.
  3. How each of these spatial patterns varies in time throughout the dataset.
I know, it may seem a bit confusing now.  Hopefully when I start showing pictures things will start making more sense.

I start by doing this analysis on the raw sea-surface temperatures.  The output of the analysis gives pictures of the four dominant spatial patterns of sea-surface temperatures during those 51 years.  These are seen below, with the most dominant pattern to the upper left.
Fig 1 -- Dominant spatial modes from an EOF analysis of SSTs from 1951-2001.  The most dominant mode is to the upper left, with the 2nd most dominant mode to the upper right, 3rd to the lower left.
So these are the patterns of sea-surface temperatures that are most dominant over time.  Let's look at the most dominant one in the upper left corner.  Notice how it indicates warm temperatures in the tropics and colder temperatures toward the poles.  Well, that makes perfect sense--we know it's warmer in the tropics and colder at the poles.  So this EOF analysis is telling us that the dominant pattern of sea-surface temperatures is just the mean state of these sea-surface temperatures--it's always warmer in the tropics and colder in the poles.  We can ask ourselves how much of our sea-surface temperature patterns over time are explained by this simple mean state.  Here's a bar chart showing what percent of the variability of sea-surface temperatures are explained by each mode:
Click on the bar chart to make it bigger if you can't read the labels.  It shows that 70% (.7) of the total variability in sea-surface temperatures can just be explained by that first mode--by knowing that it's warm in the tropics and cold in the poles.  70% of the varibility--that's an awful lot.  But then again, most of the general circulation in our atmosphere is determined by that simple heat gradient, from warm at the equator to cold at the poles. So this makes sense.

All right--so this equator-to-pole difference explains a lot.  But that's kind of easy.  We know that there's more variability than that.  So, what we can do next is take our sea-surface temperatures over 51 years at each point and then subtract the mean value at each point.  This should effectively remove that mean state and let us just look at the remaining modes.  After removing that mean and repeating the EOF analysis, we get these spatial patterns:
Hmm.  Now let's again look at the most dominant mode in the upper left.  This shows an interesting pattern.  It looks like in the northern hemisphere, there's a lot of areas where the temperature is warmer.  In contrast, in the southern hemisphere it looks like that everywhere the ocean is colder.  Remember there is one more thing that this EOF analysis gives us--how each mode varies over time.  Let's look at a plot of how the magnitude of that mode varies over the 1950-2001 period.
Wow...this mode oscillates back an forth between positive and negative values rather frequently and regularly.  If we do a Fourier analysis on this time series, we can figure out just how frequently it completes an oscillation.

Hmm--we see from the Fourier analysis that the periodicity of this mode is almost all at one year intervals.  That means that this mode goes from a positive phase to a negative phase and back again exaclty once every year.

Remember the spatial pattern we're talking about here from the plot above--it was generally warmer in the northern hemisphere and colder in the southern hemisphere.  Combined with the other evidence (like the fact that it oscillates once per year), we can conclude that this represents the seasonal cycle--during June, July and August, it's summer in the northern hemisphere and winter in the southern hemisphere.  Since it takes the ocean a while to absorb and release its large amounts of heat, there's a bit of a delay--sea-surface temperatures actually peak in the fall (which is why hurricane season peaks in the fall, among other things...) and reach a minimum in spring.  However, you can see in the spatial plot above that one hemisphere is generally warm and the other hemisphere is cold.  During the opposite season, this structure flips--it becomes the negative of that spatial pattern.  That's why when we looked at the time series, the magnitude of the pattern oscillated between positive and negative values. It's just the seasonal cycle.

How much of the total variability does the seasonal cycle explain?  Let's return to the first bar chart again before we removed the overall mean--remember here the seasonal cycle is the second most dominant mode.
If we go to the second bar in the bar chart, we can see that the seasonal cycle accounts for only about 8% (.08) of the variability of sea-surface temperatures.  That's not so much compared to the 70% explained by the mean state of warm at the tropics and cold at the poles.  But still--it's enough to strongly contribute to our seasonal differences in weather.

All right, now we've gotten rid of the mean state, so let's get rid of this seasonal cycle, too.  We can do this by subtracting the mean value at each point for each month instead of just the overall mean value.  This means we'll get a sea-surface temperature anomaly relative to the average monthly sea-surface temperature.  If we repeat the EOF analysis on this new set of numbers, we get these spatial patterns:

Now, for any of you who have seem El Nino graphics before, the dominant mode here clearly looks like El Nino.  Warmer than normal sea-surface temperatures are indicated throughout the equitorial Pacific stretching westward from the west coast of South America--the classic El Nino pattern.  However, there also seems to be a sort of anti-El Nino pattern (like a La Nina) of cool temperatures in the same area in the second most dominant mode (the upper right image).  The work I did with Elizabeth Maroon delved a bit more into examining the split in ENSO signal between those modes (and other modes).  But that's beyond what I wanted to discuss here.  The key point is--once you remove the mean state (warm in the tropics and cold in the poles) and the seasonal cycle, then the dominant mode of variability in global sea-surface temperatures is governed by ENSO

How much variability is explained by this ENSO signal?  I'm going to switch bar charts now to the bar chart with ENSO as the dominant mode.  Remember, 70% of the variability was explained by the mean state, and about 8% of the variability was explained by the seasonal cycle.  That leaves 22% of the variability unaccounted for.  Here's a bar chart of the strength of the remaining modes:
Remember I switched the bar chart so now mode 1 is the El Nino mode described above.  Notice that this mode only explains about 3.7% (.037) of the remaining variability in sea-surface temperatures.  Since it turns out that the second mode also strongly tracks ENSO and that explains about 2.5%, we can reasonably infer that overall the ENSO pattern explains about 6.2% of the remaining variability of ocean sea-surface temperatures.  That's 6.2% of the remaining 22%--or about 1.36% of the total variability of sea-surface temperatures.  That's really small, particularly when compared to the seasonal cycle and definitely when compared to the mean state.  Yet ENSO is so important for variations in the ocean and in our weather and climate.  Pretty incredible.

If you want further proof that this mode represents ENSO, here's a chart that compares it to an actual ENSO index.  The top graph shows the official ENSO 3.4 index from 1950-2001, which is commonly used to describe the strength of an El Nino of La Nina event over time.  Below it in bold red is the variation in the strength of the El Nino mode over time.  The two match almost exactly.  The light blue line shows the trace of the negative of that second, anti-El Nino mode over time.  It, too correlates strongly with the actual ENSO signal in the panel above.
So what's my point with all of this?  We often talk about how important the ENSO variability is for determining monthly or seasonal climate forecasts.  We hear all the time about how, "Oh, it's going to be wetter because this is a La Nina year..." or "It's going to be hot because it's an El Nino year...".  But, really, how important is ENSO?

On one hand, it's not so important--we saw that only a little over 1% of the total variability of sea-surface temperatures can be explained by ENSO modes.  That's such a small amount of the variability.

On the other hand, once we remove the mean state of sea-surface temperatures and the known, predictable seasonal cycle, the ENSO modes are the dominant mode of variability in sea-surface temperatures!  Since we can do a decent job of predicting the mean state of the sea-surface temperatures and also have a good grasp of the seasonal cycle, the next thing we need to get a handle on to increase predictability is ENSO.  But we still don't have a good idea of how to predict ENSO.  And so, even this little effect that only accounts for 1% of the variability of the system stands in the way of our being able to make better long-term predictions.  In that respect, ENSO is very, very important.

As always, email me or post a comment if you have any questions.

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