Christina Bonfanti

University of Miami- RSMAS

MPO 524

*Analyzing Effects of ENSO and AO on Monthly Moisture and Temperature Anomalies in 7 US Cities

*The Question

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

*Quick Introduction

• 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

*More Quick Introduction

• Much shorter “mean” cycle of about 60 days

• Negative phase well linked to colder eastern USA winters

*The Methods

*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

*The Methods

*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!

*The Results

*The Results

*The Results

*The Results

*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?

*The Results

*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

*The Results

* 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

*The Results

* 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

*The Results

*The Results

*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!

*The Results

*The Results

*The Results

* 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.

*The Results

* 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

*The Results

*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

*The Results

* 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

*The Conclusions

*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…

*The Expansions

*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

*The References

*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=tampabayelninopage

*http://www.martinsaphug.com/learn/maps-2/united-states-and-canada/

*http://www.wunderground.com/blog/JeffMasters/unusually-cold-spring-in-europe-and-the-southeast-us-due-to-the-arct

*https://ams.confex.com/ams/89annual/techprogram/paper_145842.htm

*http://www.mathworks.com/help/stats/princomp.html