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Self-Organizing Maps (SOMs): Proposed RMIP Diagnosis

Self-Organizing Maps (SOMs): Proposed RMIP Diagnosis. W. J. Gutowski, Jr. Iowa State University. with thanks to: H. Wei , F. Otieno , Z. Pan, R. W. Arritt, E. S. Takle. RMIP (December 2001). Outline. Background Example 1: Precipitation simulation versus observations

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Self-Organizing Maps (SOMs): Proposed RMIP Diagnosis

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  1. Self-Organizing Maps (SOMs):Proposed RMIP Diagnosis W. J. Gutowski, Jr. Iowa State University with thanks to: H. Wei, F. Otieno, Z. Pan, R. W. Arritt, E. S. Takle RMIP (December 2001)

  2. Outline • Background • Example 1: Precipitation simulation versus observations • Example 2: RMIP sea-level pressure behavior • Summary RMIP (December 2001)

  3. Self-Organizing Maps: Background • Set of maps • Show characteristic data structures • Trained to distribution of data • Give 2-D projection of higher order • map space • Are approximately continuous • Basis in Artificial Neural Nets

  4. SOM set: Sea-level pressure

  5. Initial - Random Distribution

  6. Apply input sequence of maps: example

  7. Compare sample to ... … existing set

  8. Find closest map ...(here - smallest RMS difference) … and it nudge toward sample

  9. Nudge also a surrounding region ... … that decreases with iteration

  10. Nudge also a surrounding region ... … that decreases with iteration

  11. Nudge also a surrounding region ... … that decreases with iteration

  12. SOM map (0,2) - 1 Iteration

  13. SOM map (0,2) - 10 Iterations

  14. SOM map (0,2) - 30 Iterations

  15. SOM map (0,2) - 100 Iterations

  16. SOM map (0,2) - 1,000 Iterations

  17. SOM map (0,2) - 10,000 Iterations

  18. SOM map (0,2) - 50,000 Iterations

  19. SOM map (0,2) - 100,000 Iterations

  20. SOM map (0,2) - 150,000 Iteration

  21. Outline • Background • Example 1: Precipitation simulation versus observations • Example 2: RMIP sea-level pressure behavior • Summary RMIP (December 2001)

  22. Simulations

  23. Simulation Domain

  24. SOM: RegCM2 & VEMAP Precipitation

  25. SOM: RegCM2 & VEMAP Precipitation 1 2

  26. SOM: Major Dimensions 1 “warm” 2 “cold” 0 [mm/mo] 100 200

  27. RegCM2

  28. VEMAP

  29. SOM: RegCM2 & VEMAP Precipitation

  30. SOM: RegCM2 & VEMAP Precipitation

  31. SOM Trajectories RegCM VEMAP J-J-A

  32. SOM Trajectories RegCM VEMAP J-J-A RegCM D-J-F VEMAP D-J-F

  33. SOM: Lowest two rows 0 [mm/mo] 100 200

  34. Trajectory Separation by Month

  35. Outline • Background • Example 1: Precipitation simulation versus observations • Example 2: RMIP sea-level pressure behavior • Summary RMIP (December 2001)

  36. RMIP Sea-level Pressure • Input: • ISU MM5 simulation • Sampled daily at 12 UTC • 18 months  549 samples • Unadjusted (e.g., no filtering, scaling, etc.)

  37. SOM set: Mean Sq. Error vs. Iterations

  38. SOM set: Sea-level pressure

  39. “Nearest map” Frequency 5 4 3 2 1 0 Even distribution  0.04 0 1 2 3

  40. Mean Squared Error of Fit - All Days 5 4 3 2 1 0 [hPa2] 0 1 2 3

  41. “Nearest map” Frequency - Summer 5 4 3 2 1 0 0 1 2 3

  42. “Nearest map” Frequency - Fall 5 4 3 2 1 0 0 1 2 3

  43. “Nearest map” Frequency - Winter 5 4 3 2 1 0 0 1 2 3

  44. “Nearest map” Frequency - Spring 5 4 3 2 1 0 0 1 2 3

  45. Summer High Frequency Map

  46. Fall High Frequency Map

  47. Winter High Frequency Map

  48. Spring High Frequency Map

  49. SOM set: Lead/Lag Transitions?

  50. Frequency of Maps that Lead: 90 Days

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