1. Atmospheric Science Department University of Missouri - Columbia A Procrustes Shape Analysis Verification Tool Steve Lack Sakis Micheas Neil Fox Chris Wikle

2. Atmospheric Science Department University of Missouri - Columbia Methodology Procrustes Scheme –In Greek mythology, Damastes, was a thief who often went by the name Procrustes and offered travelers a bed to rest –The twist was he would “fit” the travelers to the bed…stretching them if they were too short and cutting their limbs off if they were too tall Journal of Hydrology article forthcoming Micheas et al.

3. Atmospheric Science Department University of Missouri - Columbia Methodology So in this context we will fit forecast cells to truth cells by shifting location, resizing the object, and rotating them if necessary Origin use is in biology (anatomy) for lining up jaw bones (landmarks) or other structure for classification Works with gridded data of any dimensions for spatial objects, originally designed for ensembles

4. Atmospheric Science Department University of Missouri - Columbia Methodology Define a penalty function –Takes into account max,mean,min intensity, location fitting –May be user defined (apply weights) –The lower the penalty the better the forecast

5. Atmospheric Science Department University of Missouri - Columbia Advantages Reduction of dimensionality for speed (less than 1 minute to run on a fair sized domain) Takes into account shape information with intensity data Can alter the penalty function to get more meaningful data Error decomposition User defined thresholds

6. Atmospheric Science Department University of Missouri - Columbia Shortcomings Memory issue when running a large domain with a lot of identifiable cells –Can break down domain however The total penalty function adds error components that may not of the same magnitude –Can refine these in the future Relative comparison (interpretation)

7. Atmospheric Science Department University of Missouri - Columbia Results Entire domain penalty was calculated by using 0.10” (memory issue) Minimum size of cell set to 10 pixels Divided domain into NE,NW,SE,SW quadrants Recalculated penalties based on 0.01” again minimum size set to 10 pixels

8. Atmospheric Science Department University of Missouri - Columbia 13 May 2005 – WRF4NCAR

9. Atmospheric Science Department University of Missouri - Columbia 13 May 2005 – Stage 2

10. Atmospheric Science Department University of Missouri - Columbia Fits – WRF4NCAR

11. Atmospheric Science Department University of Missouri - Columbia Total Penalties – Entire Domain WRF4NCARWRF4NCEPWRF2CAPS RSS (1*10^3)5.91515.44874.8603 SStot (1*10^3)1.75312.30831.9005 # Cells (Truth = 17) 266139 Tot Error (1*10^5) 2.66075.78582.8416

12. Atmospheric Science Department University of Missouri - Columbia Error Decomposition – Entire Domain WRF4NCARWRF4NCEPWRF2CAPS Min Intensity244 Mean Intensity8926268259079.9 Max Intensity252122054630002702100 Translation4.671122.66911.596 Rotation000 Dilation42829077367001176000

13. Atmospheric Science Department University of Missouri - Columbia NW Domain- 13 May 2005 (clockwise NCAR, NCEP, CAPS, Stage 2)

14. Atmospheric Science Department University of Missouri - Columbia Total Penalties – NW Domain WRF4NCARWRF4NCEPWRF2CAPS RSS (1*10^3)5.82555.75835.34 SStot (1*10^3)3.46593.87123.4335 # Cells (Truth = 39) 503337 Tot Error (1*10^4) 0.961531.84171.1106

15. Atmospheric Science Department University of Missouri - Columbia Error Decomposition – NW Domain WRF4NCARWRF4NCEPWRF2CAPS Min Intensity000 Mean Intensity104.78297.67148.31 Max Intensity3685123615618 Translation32.48813.96915.15 Rotation000 Dilation797540691740758880

16. Atmospheric Science Department University of Missouri - Columbia 1 June 2005 – WRF4NCAR

17. Atmospheric Science Department University of Missouri - Columbia Stage 2

18. Atmospheric Science Department University of Missouri - Columbia Total Penalties WRF4NCARWRF4NCEPWRF2CAPS RSS (1*10^3)4.34583.86314.7510 SStot (1*10^3)1.77612.31131.8553 # Cells (Truth = 48) 5910949 Tot Error (1*10^5) 3.84233.42303.4501

19. Atmospheric Science Department University of Missouri - Columbia Error Decomposition WRF4NCARWRF4NCEPWRF2CAPS Min Intensity181311 Mean Intensity161511239414009 Max Intensity363710326030326240 Translation5.57818.1396.3785 Rotation0.000100 Dilation108500019455001316600

20. Atmospheric Science Department University of Missouri - Columbia NW Domain- 01 June 2005 (clockwise NCAR, NCEP, CAPS, Stage 2)

21. Atmospheric Science Department University of Missouri - Columbia Total Penalties – NW Domain WRF4NCARWRF4NCEPWRF2CAPS RSS (1*10^4)1.18381.62531.4684 SStot (1*10^3)2.92213.98072.9628 # Cells (Truth =30) 535058 Tot Error (1*10^4) 1.75423.88732.3150

22. Atmospheric Science Department University of Missouri - Columbia Error Decomposition – NW Domain WRF4NCARWRF4NCEPWRF2CAPS Min Intensity000 Mean Intensity184.91425.3760.646 Max Intensity5519221948405 Translation59.10712.88330.551 Rotation000 Dilation3217400357250827400

23. Atmospheric Science Department University of Missouri - Columbia Conclusions A lot of weight is given to intensity forecasts as well as position/shape June 1 forecast are all handled equally well by the models WRF4NCAR handles intensity the best for May 13 although WRF2CAPS is close on position WRF4NCEP underestimates intensity in most cases

24. Atmospheric Science Department University of Missouri - Columbia Acknowledgements Stat Group: Sakis Micheas, Chris Wikle, Yong Song, Kent Peng Rains Group: George Limpert and Neil Fox Award # ATM-0434213