Christina Bonfanti University of Miami- RSMAS MPO 524.
-
Upload
corey-barber -
Category
Documents
-
view
219 -
download
0
Transcript of Christina Bonfanti University of Miami- RSMAS MPO 524.
![Page 1: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/1.jpg)
Christina Bonfanti
University of Miami- RSMAS
MPO 524
*Analyzing Effects of ENSO and AO on Monthly Moisture and Temperature Anomalies in 7 US Cities
![Page 2: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/2.jpg)
*The Question
*How does the Arctic Oscillation and El Nino/Southern Oscillation interact to affect weather over the United States?
![Page 3: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/3.jpg)
*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
![Page 4: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/4.jpg)
*More Quick Introduction
• Much shorter “mean” cycle of about 60 days
• Negative phase well linked to colder eastern USA winters
![Page 5: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/5.jpg)
*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
![Page 6: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/6.jpg)
*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!
![Page 7: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/7.jpg)
*The Results
![Page 8: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/8.jpg)
*The Results
![Page 9: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/9.jpg)
*The Results
![Page 10: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/10.jpg)
*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?
![Page 11: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/11.jpg)
*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
![Page 12: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/12.jpg)
*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
![Page 13: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/13.jpg)
*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
![Page 14: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/14.jpg)
*The Results
![Page 15: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/15.jpg)
*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!
![Page 16: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/16.jpg)
*The Results
![Page 17: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/17.jpg)
*The Results
![Page 18: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/18.jpg)
*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.
![Page 19: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/19.jpg)
*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
![Page 20: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/20.jpg)
*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
![Page 21: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/21.jpg)
*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
![Page 22: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/22.jpg)
*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…
![Page 23: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/23.jpg)
*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
![Page 24: Christina Bonfanti University of Miami- RSMAS MPO 524.](https://reader036.fdocuments.net/reader036/viewer/2022062423/5697bfab1a28abf838c9aeae/html5/thumbnails/24.jpg)
*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