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 n crit, 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…

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 –Assign that value to the base point. –Repeat for ALL points. –Plot. –WG Fig 7 shows this.

procedure… Based on SLP Based on SLP…a “max” value of 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 + -

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!