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Rethinking Global Precipitation Data Representation

This presentation discusses the challenges of accurately representing data products on a global scale, particularly in high-latitudes and polar regions. The speaker explores different map projections and their distortions, emphasizing the need for a standardized mapping approach.

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Rethinking Global Precipitation Data Representation

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  1. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Global Precipitation:a time to rethink the representationof data products? Chris Kidd UMD/ESSIC & NASA/GSFC

  2. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Background The fundamental problem is that no map from the sphere to the plane can accurately represent both angles (and thus shapes) and areas. In general, area-preserving map projections are preferred for statistical applications, because they behave well with respect to integration, while angle-preserving (conformal) map projections are preferred for navigation. Ideally we need area-preserving map projections

  3. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Why? • Latitude/longitude (CED) grids are typically the de facto standard for global visualisation - to date, distortion has not been seen as critical since most products are 60°N-60°S; however, we must address mapping at higher latitudes - critically, Polar regions are data-rich! i) Most low-Earth orbiting-observations are equal-area ii) ground observations (e.g. radar) are essentially equal area iii) remapping introduces additional errors into estimates

  4. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Lat/lon grid • Mapping is easy: lat/lon→x/y conversion simple (!?) • Visualisation easy: locating regions, etc • Interpretation okay: near the Equator reasonably equal area, less so mid-latitudes, but certainly not at high-latitudes • Treatment of higher latitude inconsistent; grid boxes represent smaller areas; improved number of observations but fewer samples/grid box; area smoothing/replication... . • Equal-area pseudo lat/lon grids exist (e.g. Gall-Peters, but these compress the latitudinal range.

  5. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center ‘Standard’ Lat/Lon or CED grid

  6. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Lat/lon scale distortion 75N 0.259 60N 0.500 45N 0.707 30N 0.866 Equator 1.000 30S 0.866 45S 0.707 60S 0.500 75S 0.259 Scale relative to the Equator (=1.00)

  7. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Lat/lon swath distortion

  8. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Lat/lon swath distortion (Gall-Peters) Equal-area, but greater distortion in the higher latitutes.

  9. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Representing high latitudes • GPM = Global Precipitation Measurement, therefore necessary to provide, represent and present precipitation on a global basis. • Lat/lon grid inappropriate for polar regions, therefore some sort of polar mapping required. • Mapping should become the de facto standard (i.e. one that everyone should use)

  10. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Polar projections • Azimuthal Equidistant - preserves distances • Lambert Azimuthal Equal Area - preserves areas • Gnomonic - all great circles become straight lines • Stereographic - conformal, equal angle • Universal Polar Stereographic (UPS) - a specific Stereographic Projection for use with UTM (Universal Transverse Mercator) system • Orthographic - infinite perspective projection • Near-Sided Perspective - finite perspective projection

  11. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Polar mapping examples: Orthographic Equal area, ‘distorted’ at low latitudes Azimuthal Not equal area, less ‘distorted’ at low latitudes

  12. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Polar mapping examples: SSMIS F18 10th November 2011 Orthographic Equal area, distorted in low latitudes Azimuthal Not equal area, less distorted in low latitudes

  13. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center The answer: There isn’t one! There are many… Ultimately, it depends upon what degree of distortion you (developer & user) are prepared to accept

  14. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Equal distance along latitude centres *90° 60° 30° 0° 30° 60° *90°

  15. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Equal degrees of distortion *90° 76° 60° 41° 0° 41° 60° 76° *90°

  16. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Polar & Equatorial regions Region of overlap +ve: Relatively simple mapping -ve: Large distortions at edges

  17. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Local “true” equal-area mapping Lighter = more distortion

  18. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Local “true” equal-area mapping As above, but clipped

  19. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Local “true” equal-area mapping +ve: controls degree of distortion overlap region - advection -ve: less easy to interpret

  20. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Local “true” equal-area mapping Plotted with SSMIS orbit

  21. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Global-IR remapped (8-10 October 2012)

  22. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Gaussian Grids N48 grid 208 km N128 grid 78 km N640 grid 15 km +ve: essentially equal area globally & existing usage -ve: computatively awkward; point vs area

  23. 6th IPWG meeting, 15-19 October 2012 São José dos Campos, Brazil Goddard Space Flight Center Summary No single projection is suitable for mapping global precipitation, so: • Lat/lon grid for whole Earth (i.e. 90°N-90°S) • Polar grid based upon Longitude (bearing) and Latitude (distance), or ‘weighted’ Latitude • Polar grid limited to polewards of ‘x’ latitude. • Local equal-area mapping • Gaussian grids (or other ‘model’ grids)

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