1. Christina Bonfanti University of Miami- RSMAS MPO 524

2. * How does the Arctic Oscillation and El Nino/Southern Oscillation interact to affect weather over the United States?

3. Winter ENSO trends Expect to see some correlation between wetter/dryer or hotter/colder anomalies Time scale is pretty yearly Oscillation period very variable on its own 2-7 years

4. Much shorter “mean” cycle of about 60 days Negative phase well linked to colder eastern USA winters

5. * Collected monthly mean temperature and moisture totals from seven cities across the country over 60 years * 1950-2010 * Multivariate data * Removed the annual cycle * Standardized the Data * Naked Eyeball test * Quite messy * Correlations * Ruled out FFT’s for this particular study * Empirical Orthogonal Functions (EOF’s) analysis * Ran on all variables, not just between two

6. * EOF analysis * Uses PCA * Unlike a linear regression, it doesn’t know if data are independent or dependent * Goal is to find a coordinate system that maximizes variance of each variable in the dataset * SVD constructs the correlation matrix * For multivariate data, data must be standardized (phew!) and the covariant matrix becomes the correlation matrix * Find eignevalues/vectors of correlation matrix * Then calculate principle components * Calculate orthogonal eigenvalues/vectors to obtain PC’s (eigenvalues) and EOF’s (eigenvectors) * Based on the eigenvalues/eigenvectors, can see which variables eigenvalues contribute most to which principle component(s) * Matlab gave us pca and princomp!

10. * Checked to make sure correlation between standardized values and non-standardized were same * They were * Simply looking at correlation between ENSO/AO and Temp/Moist * Why such low correlation values when we know that ENSO and AO both have an impact on temperature and moisture in the USA?

11. * EOF will take all three data variables and create new principle components, a linear combo of the original variables, each orthogonal to each other, to form an orthogonal basis for the space data * Graphs * The first principal component is a single axis in space. Project each observation on that axis and the resulting values form a new variable. The variance of this variable is the maximum among all possible choices of the first axis * The second principal component is another axis in space, perpendicular to the first. * Each point is an observation with coordinates indicting the “score” for each PC * Reading: points nearer to left edge have lowest score for PC1 * They’re scaled with respect to the maximum score value and coefficient length * Notice later when I compress data that there are less of these data points since less observations

12. * Did a matlab EOF analysis/SVD decomposition to see which principle components drive which variables * Look at Austin temperature that had negative correlation with ENSO and positive with AO

13. * Projected observations on axis of Principle Components to obtain a newly defined variable * Direction/length indicate how each variable contributes to PC’s and PC1 is able to distinguish between AO and Temp variable from the ENSO variable

15. * Didn’t understand why something we know that impacts the country wasn’t showing up * Idea: look at seasonal aspect (winter and summer) * Recall from ENSO and AO trends that even the cities with which we expect to have biggest impact have highest correlation values!

18. * AO in same direction and both influence PC1 and PC2 but ENSO only influences PC1 and hardly PC2 * Recall ENSO has negative correlation with Moist and AO has a positive higher correlation * Could explain why they’re in same direction? Yes except not sure about when they are in 3 different quadrants. BUT even then, they agreed in direction for PC1. INTERESTING.

19. * All three variables contributed to PC1 and PC2 * All positively contributed to PC2 * Again recall that ENSO has a negative correlation and AO has a positive correlation

20. * Same behavior as before except unlike Seattle that had all vectors influence both PC’s, AO and temp don’t contribute to PC1 that much

21. * Summer anomalies for Colorado Springs * Small positive correlation to both AO and ENSO and produced this * I think most interesting feature is the lack of ENSO contributing to PC2 at all

22. * Need to look at the seasonal versus monthly data * Even if AO is a more monthly period, ENSO doesn’t * Observed that AO and ENSO vectors never in same quadrant except on case with Chicago yearly moisture * Observed that AO and ENSO vectors are rarely in same direction * EOF’s are a good way to start understanding which components drive the three variables * Both negatively and positively * Still question on how both AO and ENSO’s peaks influence (or don’t) the temperatures and moisture totals of certain US regions * Especially Colorado Springs…

23. * Bet if looked at ENSO on a yearly timescale, even more time than seasonal, correlation values will increase * Explore to see if there is possibly a time lag * ENSO and AO on two different time scales * Literature suggests that there are teleconnections between the two * Impact of the Arctic Oscillation on ENSO- precipitation teleconnections across the eastern USA by Dagmar Budikova, Illinois State University, Normal, IL * Other methods of Analysis such as a linear regression

24. * http://en.wikipedia.org/wiki/Arctic_oscillation http://en.wikipedia.org/wiki/Arctic_oscillation * Wikle, Christopher K. "Spatio-temporal methods in climatology." Encyclopedia of Life Support Systems (EOLSS) (2002). * http://web.unbc.ca/~ytang/Chapter4.pdf * http://www.srh.noaa.gov/tbw/?n=tampabayelninop age http://www.srh.noaa.gov/tbw/?n=tampabayelninop age * http://www.martinsaphug.com/learn/maps- 2/united-states-and-canada/ http://www.martinsaphug.com/learn/maps- 2/united-states-and-canada/ * http://www.wunderground.com/blog/JeffMasters/u nusually-cold-spring-in-europe-and-the-southeast- us-due-to-the-arct http://www.wunderground.com/blog/JeffMasters/u nusually-cold-spring-in-europe-and-the-southeast- us-due-to-the-arct * https://ams.confex.com/ams/89annual/techprogra m/paper_145842.htm https://ams.confex.com/ams/89annual/techprogra m/paper_145842.htm * http://www.mathworks.com/help/stats/princomp. html http://www.mathworks.com/help/stats/princomp. html