1. Cloud-top Relief Spatial Displacement Adjustments of GOES-R Images Shayesteh Mahani CREST & CE Dept. at the City College (CCNY) of the City University of New York (CUNY) Co-Is: Johnny Luo, William Rossow, Reza Khanbilvardi, and Kibre Tesfagiorgis, CREST, CCNY/CUNY NOAA-Collaborators: Robert Rabin, NOAA/NSSL, UW-Madison/CIMSS Andrew Heidinger and Robert Kuligowski, NESDIS-STAR, NOAA Satellite Science Week, April 30 – May 04, 2012, Kansas City

2. Objectives Estimate Cloud-Top Height (CTH) using 3-D principals and vertical height-temperature profile; Enhance the quality of high resolution GOES-R infrared (IR) data by adjusting pixel based cloud-top relief Spatial Displacements (SD). Introduction Cloud VIS and IR images posses SD associated with CTH that is a function of satellite height, satellite-cloud view angle, sun zenith angle, and earth curvature. Stereo-graphical (3-D) principle using corresponding & simultaneous cloud IR data from GOES-E and -W, are applied to estimate CTH and its associated SD for adjustment. The 3-D based technique and the GOES-R Algorithm Theoretical Basis Document (ATBD) will be evaluated against CTH from CALIPSO as a reference to examine if the combined method can improve CTH output.

3. Major Tasks & Accomplishments 1.Derive the geometric relationship between cloud-top height and pixel-based spatial displacement for GOES-R (accomplished); 2.Derive the relationship between CTH, X-parallax of SD, and IR- CTBT, utilizing 3-D principals from scan-synchronous GOES-E and -W IR Images and optimize the parameters of the relationship using the SCE (Shuffled Complex Evolution) calibration Model to estimate CTH and adjust SD (90% accomplished); 3.Understand which IR channels, and/or combination(s) of which IR channels work better to estimate CTH and to adjust CTSD for a given cloud type, region, and season (Year-2); 4.Evaluate the CTH estimates and the CTH from GOES-R ATBD algorithm against the CALIPSO-CTH product (Year-2);

4. Major Tasks & Future Work 5.Modify/update the number and value of the optimized model parameters of the CTH-CTBT or CTBT-SD relationships for seasonal, topography, land type, and storm type variability, (Years-2 & 3); 6.Investigate improvement of CTH estimates by incorporating the proposed technique into ATBD model and evaluating the new CTH product against CALIPSO-CTH (Year-3); OUTLINE Geometry of the relationship between CTH and pixel-based SD Relationship between CTH and CTBT and CTH-based X-parallax, Deriving the relationship between CTH, SD and IR-CTBT utilizing corresponding pairs of scan-synchronous and simultaneous GOES-E (13) and -W (11) as proxy for GOES-R Images. Validation & Results.

5. Satellite Spatial Displacement related to Cloud-Top Height

6.  =  (h, ,  ) Geometric Relationship between Cloud Top Height and its related SD. Cloud-Top Relief Spatial Displacement (BC or  depends on Height of Cloud (h), Distance from Satellite (  and Satellite Height (H). Cloud-Top Height-Displacement Relationship   = Satellite View Angle = Angular Displacement  = Angular Distance h = Cloud-Top Height H = Satellite Height O S A h C N   B R  H S O B C C'  N O' B' B LxLx  LxLx  LyLy BB dL y = R   (rd) (km)  i (rd) = [h c (H+R) Sin(d i )] /{R[(H+R) Cos(d i ) – (R+ h c )]} dL x = R  λ (rd) (km)

7. h = 20 km h = 19 km h = 18 km h = 17 km h = 16 km h = 15 km h = 14 km h = 13 km h = 12 km h = 11 km h = 10 km h = 9 km h = 8 km h = 7 km h = 6 km h = 5 km h = 4 km h = 3 km h = 2 km h = 1 km 0 5 10 15 20 25 30 35 40 45 50 55 60 65 50 45 40 35 30 25 20 15 10 5 0 Spatial Displacement (km) Longitudinal or Latitudinal Distance from a Geostationary Satellite (Degrees) Cloud Top Relief SD for GOES Images Cloud-Top Height (km) Relationship between Cloud Distance from Satellite, Cloud-Top Height and related Spatial Displacement

8. Stereoscopic Parallax Related to CTH dp is the X- or Stereoscopic Parallax Associated with h c, Cloud-Top Height, between GOES-E and -W Images of a Cloud Element. R = 6370 km (Radius of Earth) H s = 36000 km IF: h c = 10 km dp = 16.0 km GOES-W hchc GOES-E 60° X HsHs (75W) (135W) R dp Earth C

9. 250 215 215 K 250 K 265 225 265 225K 265K Latitude (Pixel numbers) Longitude (Pixel Numbers) Comparison between x-parallaxes related to 2, cold (blue) and warm (red), temperatures between IR cloud-top BT of corresponding pairs of GOES-E (solid line) and GOES- W (dotted line) IR Images, over Southeastern U.S. (left) and Colorado (right). Dependency of SD & CTH / BT Latitude (Pixel numbers) Longitude (Pixel Numbers) GOES-E (13) BTGOES-W (11) BT

10. XX Earth GOES-W (135W) GOES-E (75W) BT E BT W 10 20 30 40 50 10 20 30 GOES-E Cloud-Top Brightness Temperature 10 20 30 40 50 10 20 30 hchc hchc X Y RR Ground-Based Radar Rainfall 10 20 30 X Y 10 20 30 40 50 Cloud-Top Relief Spatial Displacement (Pixel Size = 2 km) GOES-W Cloud-Top Brightness Temperature

11. Designing a 3-pieces piecewise line with 6 parameters for T b -Height/SD relationship. Optimized parameters are estimated based on minimizing X-parallax between a pair of simultaneous GOES-E and -W IR images using 3-D principle and Shuffled Complex Evolution algorithm (SCE-UA). 3-Piece Line (6 Parameters) 6 parameters of a 3-pieces Linear Profile Designing Fitted Piecewise Cloud-top BT-Height Relationship Line Parameters Optimized Values h0h0 2.6 km T1T1 242 K T2T2 225 K l1l1 0.15 km/K l2l2 0.105 km/K l3l3 0.14 km/K

12. Longitude (Degrees, West) Latitude (Degrees, North) CTH (km) Cloud-Top Height (CTH) 2-D and 3-D Maps Estimated Cloud-Top Height 3-D cloud-top height map Estimated cloud-top height and their related contours (right) in the forms of 2-D and 3-D maps.

13. Cloud-top IR Brightness Temperature (K) Original GOES-E (13) IR-BTOriginal GOES-W (11) IR-BT Spatial Adjusted GOES-E IR-BTSpatial Adjusted GOES-W IR-BT Cloud-top GOES-E & -W IR-BT Before and After Spatial Adjustment

14. Before Spatial AdjustmentAfter Spatial Adjustment Longitude (Degrees, West) Latitude (Degrees, North) - 45 - 30 - 15 0 15 30 45 Difference Cloud-Top Brightness Temperature (  Kelvin) Longitude (Degrees, West) Latitude (Degrees, North) Comparison between differences of GOES-E (13) and GOES-W (11) cloud-top BT before (left) and after (right) adjusting cloud-top relief spatial displacement. Difference of GOES-E and GOES-W IR-BT Before & After Spatial Adjustment Before Adjustment After Adjustment minimum-32-15 maximum2317

15. GOES-W IR Brightness Temperature (K) GOES-E IR Brightness Temperature (K) Corr. = 0.95 RMSE = 4.65 Pixel based GOES-11 (-W) IR cloud-top BT versus GOES-13 (-E) IR before (left) and after (right) adjustment of cloud-top relief spatial displacement. GOES-W IR-BT vs. GOES-E Before and After Spatial Adjustment Before Spatial Adjustment GOES-W IR Brightness Temperature (K) GOES-E IR Brightness Temperature (K) Corr. = 0.987 RMSE = 2.45 After Spatial Adjustment

16. Cloud-top IR Brightness Temperature (K) Original GOES-E (13) IR-BTOriginal GOES-W (11) IR-BT Spatial Adjusted GOES-E IR-BTSpatial Adjusted GOES-W IR-BT Cloud-top GOES-E & -W IR-BT Before and After Spatial Adjustment for Validation

17. GOES-W IR Brightness Temperature (K) GOES-E IR Brightness Temperature (K) Corr. = 0.96 RMSE = 5.7 Pixel based GOES-11 (-W) IR cloud-top BT versus GOES-13 (-E) IR before (left) and after (right) adjustment of cloud-top relief spatial displacement using the derived CTH-IRBT for an independent study case, for validation. GOES-W IR-BT vs. GOES-E Before and After Spatial Adjustment, Validation Before Spatial Adjustment GOES-W IR Brightness Temperature (K) GOES-E IR Brightness Temperature (K) Corr. = 0.98 RMSE = 4.1 After Spatial Adjustment

18. Future Tasks Evaluate the CTH estimates against CALIPSO-CTH (year 2); Investigate if the piecewise line model can be enhanced by increasing the number of parameters (pieces of lines) (Year 2); Test the model using other GOES thermal IR bands to investigate which IR frequency is more sensitive to cloud-top height, which will be used to improve CTH estimates (Year 2); Investigate and enhance Comparing the CTH estimates with the CTH from GOES-R ATBD algorithm and the CALIPSO-CTH product (Year 2); Investigate the impacts of seasonal, geographical, topography, storm types, and climate variability on model parameters and modify model for each (Year 3); Incorporate the 3-D based model into GOES-R ATBD model and evaluate the new CTH product against CALIPSO-CTH (Year 3);