teleconnections. background… …on correlations… consider a simple function of time, such as the...

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!