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

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.

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

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

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

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)

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

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

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

Atmospheric Science Department University of Missouri - Columbia Fits – WRF4NCAR

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

Atmospheric Science Department University of Missouri - Columbia Error Decomposition – Entire Domain WRF4NCARWRF4NCEPWRF2CAPS Min Intensity244 Mean Intensity Max Intensity Translation Rotation000 Dilation

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

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

Atmospheric Science Department University of Missouri - Columbia Error Decomposition – NW Domain WRF4NCARWRF4NCEPWRF2CAPS Min Intensity000 Mean Intensity Max Intensity Translation Rotation000 Dilation

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

Atmospheric Science Department University of Missouri - Columbia Stage 2

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

Atmospheric Science Department University of Missouri - Columbia Error Decomposition WRF4NCARWRF4NCEPWRF2CAPS Min Intensity Mean Intensity Max Intensity Translation Rotation Dilation

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

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

Atmospheric Science Department University of Missouri - Columbia Error Decomposition – NW Domain WRF4NCARWRF4NCEPWRF2CAPS Min Intensity000 Mean Intensity Max Intensity Translation Rotation000 Dilation

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

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