teleconnections. background… …on correlations… consider a simple function of time, such as the...
Post on 20-Dec-2015
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Teleconnections
Background…
…on correlations…
• Consider a simple function of time, such as the daily T(t)
• Construct a new time series consisting of T(t-n hours)
• Compute the correlation between series.
Background…
• Result?
• At n=0 there is a correlation of 1.0
• As n increases the correlation drops off.
• Eventually at some ncrit, the correlation will be so small as to imply that the two series are independent.– This is often used as a definition of
independence of two time series.
Background…
• So the correlation gives us a measure of whether physical quantities are related in some way. – In the above example we measure
correlations in time.– Might be useful in forecasting.
• Use the current T to forecast T in one hour.
Background…
• Suppose we now take two time series at different locations and form the correlation.
• In some situations, we may get high positive and negative correlation values.– Will depend on field examined (surface
pressure, 500 mb height etc.) and how the time series is “massaged”.
procedure…
• Basic example…
• Take the 500 mb height field for, say, the NH.
• Form time averages.– The averaging period WILL make a
difference!– Daily? Weekly? Monthly?
procedure…
• If we choose one location/grid point at random, we can compute the correlation between the time-varying heights there with the time-varying heights at any other grid point.
• We can do this for EVERY other grid point.
• We can contour the result.– Wallace & Gutzler (WG) show examples.
procedure…
procedure…
• Some of these plots/maps may show nothing.
• How do we find something interesting?– Choose a point, and compute correlations
with all other points (correlating tme series).– The largest value we will get is 1.0 with the
base point.– Thus – search for the largest negative value.
procedure…
– Suppose the largest negative correlation is -0.86.
– Assign that value to the base point.– Repeat for ALL points.– Plot.– WG Fig 7 shows this.
procedure…
Based on SLPBased on SLP…a “max” value of -0.86 becomes 86 on the plot.
procedure…
Based on 500mb height
procedure…
• These plots give us a clue of where to look – unless we already know!
• In WG, they appeared to know – see section 2.
• The results in section 2 are based on limited analyses.
• The results presented by WG are based on analysis of hemispheric datasets.
Results from 500 mb analyses
• EA
Results from 500 mb analyses
• Strong north-south signature but with downstream effects too
• 500 mb differences
Results from 500 mb analyses
+ -
Results from 500 mb analyses
Results from 500 mb analyses
• PNA
Results from 500 mb analyses
500 mb difference field
Results from 500 mb analyses
SLP difference field
Results from 500 mb analyses
• Net results…
Results from 700 mb analyses
Overall
• Convincing evidence that teleconnections exist
• PNA, NAO have been much studied
• Obs indicate “equivalent barotropic” structure.
• Thus a barotropic model will tell us a lot about the dynamics!