Identifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps

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Identifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps. Freja Hunt, Joel Hirschi and Bablu Sinha National Oceanography Center, Southampton, UK 8 th April 2011 EGU General Assembly Vienna . Correlation Maps. Wallace & Gutzler 1981 - PowerPoint PPT Presentation

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<p>Slide 1</p> <p>Identifying Teleconnection Patterns from Point Correlation Maps using Self Organizing MapsFreja Hunt, Joel Hirschi and Bablu SinhaNational Oceanography Center, Southampton, UK</p> <p>8th April 2011 EGU General Assembly Vienna </p> <p> Combines well established point correlation</p> <p> Recently introduced self organizing maps</p> <p> Background and how works</p> <p> Idealized scenario =&gt; benefit of method</p> <p> Gridded temperature data</p> <p>1Correlation MapsWallace &amp; Gutzler 1981Correlate a grid point with every other grid point on the map for all grid points</p> <p>Identifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p> base point =&gt; correlating time series Base point near Greenland</p> <p> Shows NAO</p> <p> Highlights related areas</p> <p>2Self Organizing Maps (SOMs)What is a SOM?An unsupervised non-linear neural networkFinds representative patterns in the dataResults are arranged topologicallySimilar results are close together, different results are far apartExamples of SOMs in teleconnectionsLeloup et al 2008 ENSO, Johnson et al 2008 NAOSimple example</p> <p>Identifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p> 2nd part patterns in large data sets</p> <p> Unique arranged topologically </p> <p> Already used for teleconnections</p> <p> ENSO IPCC</p> <p> NAO continuum Explain SOM methodology simple example3Current data from a moored buoy in Loch Shieldaig, Scotland</p> <p>Actual data willbe shown in RED</p> <p>SOM data willbe shown in BLUEData courtesy of the British Oceanographic Data CentreIdentifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja HuntHow do Self Organizing Maps work?</p> <p> Current data from a moored buoy in Scotland</p> <p> Current rose frequency of current direction</p> <p> individual data points</p> <p> Actual red, SOM blue</p> <p>4</p> <p>InitializationHow many patterns?</p> <p>Starting patterns</p> <p>Identifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja HuntHow do Self Organizing Maps work?</p> <p> 3 stages in making SOM 1st initialization</p> <p> Decide no of patterns, determines level of detail</p> <p> Define some starting patterns here random</p> <p> Training phase</p> <p>5How do SOMs work?Locate SOM pattern most similar to data patternPresent each data pattern to SOMLocate BMUUpdate BMU learning rateUpdate neighbors - neighborhood functionLearning rate and neighborhood function reduce over time</p> <p>BMUIdentifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p> SOM pattern most similar to data point</p> <p> Best matching unit BMU6How do SOMs work?Update BMU to more closely resemble the data patternPresent each data pattern to SOMLocate BMUUpdate BMU learning rateUpdate neighbors - neighborhood functionLearning rate and neighborhood function reduce over time</p> <p>BMUIdentifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p> Update BMU =&gt; data point</p> <p> Amount depends on learning rate7How do SOMs work?Update neighboring SOM patterns Present each data pattern to SOMLocate BMUUpdate BMU learning rateUpdate neighbors - neighborhood functionLearning rate and neighborhood function reduce over time</p> <p>Neighborhood functionIdentifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p> define neighborhood around BMU</p> <p> update patterns a little bit =&gt; data point</p> <p> step caused the arrangement of patterns8</p> <p>How do SOMs work?Present each data pattern to SOMLocate BMUUpdate BMU learning rateUpdate neighbors - neighborhood functionLearning rate and neighborhood function reduce over timeIteratively present each data pattern to SOM</p> <p>Identifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p> Repeat each data point</p> <p> Find BMU &amp; neighborhood</p> <p> Update patterns</p> <p> Next data point, so on9ComparisonCompare original data patterns with SOM patterns</p> <p> For each data pattern find its BMU</p> <p>Add up number of times each SOM pattern is BMU to get hitsFrequency of occurrence </p> <p>Identifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja HuntHow do Self Organizing Maps work?</p> <p> Last step</p> <p> Where find out something about orig data</p> <p> Find BMU for each data point</p> <p> Number of times each SOM patterns is BMU is number of hits it gets</p> <p> Reflect frequency each pattern occurs in orig data set10Identifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja HuntPercentage frequency occurrence of each SOM pattern in the original data </p> <p>How do Self Organizing Maps work?</p> <p> End up with this</p> <p> Each pattern has frequency</p> <p>Similar patterns close together</p> <p> Compare SOM to rose</p> <p> All current types represented</p> <p> greater range of patterns occur more often</p> <p> This SOM method, now applied to corr maps &amp; advantages11Correlation Map SOMsGridded data setPoint correlation maps for each grid pointnx by ny correlation mapsPresent correlation maps to SOM rather than raw dataAdvantages:Correlation maps already highlight related regionsSOM summarizes patternsNo requirement for orthogonality</p> <p>Identifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p> Point corr maps 4 every grid point</p> <p> Large no of maps =&gt; difficult to extract info from so much data</p> <p> SOM comes in</p> <p> not rely on SOM to find relationships in raw data =&gt; already highlighted by maps</p> <p> SOM just summarizes patterns</p> <p> Better than EOFs no ortho &amp; no mirror</p> <p> Idealized example to demonstrate method12Idealized Self Organizing MapsRectangular domainSimple north-south oscillationPlus east-west oscillation in northern halfAdd noiseConstruct point correlation maps for each grid pointPresent to 4 x 4 SOMAlso SOM from raw dataIdentifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p> Data rectangular domain: N-S, E-W between -1 &amp; 1 diff noise inc</p> <p> Corr maps made</p> <p> 4 x 4 SOM</p> <p> SOM using raw data for comparison13Idealized SOMN-S oscillation, + E-W oscillation, no noise</p> <p>Red = positiveBlue = negativeGreen = zeroIdentifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p> No added noise</p> <p> Left corr map</p> <p> Right raw map</p> <p> nos = frequencies</p> <p> corr 3 patterns, n-s &amp; e-w</p> <p> freqs right half maps one half other</p> <p> raw SOM hits all over</p> <p> not underlying relationships, but stages in combined oscillation</p> <p> both useful, but corr better at summarizing underlying relationships14Idealized SOMN-S oscillation, + E-W oscillation, + white noise </p> <p>Red = positiveBlue = negativeGreen = zeroIdentifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p> white noise range 2 to -2 </p> <p> orig data between 1 &amp; -1</p> <p> cor left raw right</p> <p> raw more affected by noise =&gt; corr maps filter noise</p> <p> similar patterns picked out, cor relationships, raw stages</p> <p> 6 &amp; -6 corr SOM indecipherable</p> <p> noise spreads hits clustering</p> <p>15Idealized SOMN-S oscillation, + E-W oscillation, + random walk</p> <p>Red = positiveBlue = negativeGreen = zeroIdentifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p> Random walk</p> <p> a varies size of next step is 0.1</p> <p> contrast</p> <p> SOM patterns clear &amp; up to 0.25</p> <p> extract patterns under heavy noise =&gt; advantage of cor maps underlying relationships</p> <p> Give example real temperature data</p> <p>16</p> <p>Temperature SOM20 x 40 SOM - NCEP/NCAR monthly 2m temperature anomalies1.1948 to 11.2008</p> <p>Identifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja HuntENSO TypeNAO Type</p> <p> NCEP/NCAR 2m monthly temperature anomalies</p> <p> 20 x 30 SOM each cor map represented by a hexagon</p> <p> color determined by distance to neighbor</p> <p> cluster of patterns, boundaries between them</p> <p> black hex = hits</p> <p> top 9 patterns in terms of hits</p> <p> so occurred most often in cor maps</p> <p>17</p> <p>18ConclusionsCorrelation maps + SOMs effectively identify and summarize teleconnectionsAdvantage over raw data as relationships already definedAdvantage over EOFs as no orthogonalityFlexible method use comparison stage in many different ways to get different insights into large datasetsValidating model behaviorIdentifying Teleconnection Patterns from Point Correlation Maps using Self Organizing Maps Freja Hunt</p> <p>Point 1</p> <p> adv raw data as saw in idealized, more robust &amp; pick out relationships</p> <p> Adv EOFs more flexibility in patterns detected lead by data</p> <p> Power in comparison stage</p> <p> Used to test model representations of teleconnections and lead to better seasonal forecasts and prediction of climate variability.19</p>