Cloud-top Relief Spatial Displacement Adjustments

of GOES-R ImagesShayesteh 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

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.

Major Tasks & Accomplishments1. 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);

Major Tasks & Future Work5. 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.

BUSSTOP 200

Satellite

Spatial Displacement related to Cloud-Top Height

= (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

hC N

B

R

H

S

O

B

C

C'll

N

O'

B'B Lx

Lxf

Ly

fB

dLy = R (rd) (km)

li(rd) = [hc (H+R) Sin(dli)] /{R[(H+R) Cos(dli) – (R+ hc)]}

dLx = R λ (rd) (km)

h = 20 kmh = 19 kmh = 18 kmh = 17 kmh = 16 kmh = 15 kmh = 14 kmh = 13 kmh = 12 kmh = 11 kmh = 10 kmh = 9 kmh = 8 kmh = 7 kmh = 6 kmh = 5 kmh = 4 kmh = 3 kmh = 2 kmh = 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

Spa t

ial D

isp l

acem

e nt (

km)

Longitudinal or Latitudinal Distance from a Geostationary Satellite (Degrees)

Cloud Top Relief SD for GOES Images

Clo

u d-T

op H

eig h

t (km

)

Relationship between Cloud Distance from Satellite, Cloud-Top Height and related Spatial Displacement

Stereoscopic Parallax Related to CTH

dp is the X- or Stereoscopic

Parallax Associated with hc,

Cloud-Top Height, between GOES-E and -W Images of a Cloud Element.

R = 6370 km (Radius of

Earth) Hs = 36000 km

IF: hc = 10 km

dp = 16.0 km

GOES-W

hc

GOES-E

60° X

Hs

(75W

)

(135W)

Rdp

Earth

C

250

250

215

215

215

215 K250 K

265

225

225

265

225K265K

Latit

ude

(Pix

el n

umbe

rs)

Longitude (Pixel Numbers)Comparison between x-parallaxes related to 2, cold (blue) and warm (red), temperaturesbetween 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 La

titud

e (P

ixel

num

bers

)

Longitude (Pixel Numbers)

GOES-E (13) BT GOES-W (11) BT

X

Earth

GOES-W(135W)

GOES-E(75W)

BTE BTW

10 20 30 40 50

10

20

30

GOES-E Cloud-TopBrightness Temperature

10 20 30 40 50

10

20

30

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-TopBrightness Temperature

Designing a 3-pieces piecewise line with 6 parameters for Tb-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

ParametersOptimized

Values

h0 2.6 km

T1 242 K

T2 225 K

l1 0.15 km/K

l2 0.105 km/K

l3 0.14 km/K

Longitude (Degrees, W

est)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.

Clo

ud-to

p IR

Brig

htne

ss T

empe

ratu

re (K

)

Original GOES-E (13) IR-BT Original GOES-W (11) IR-BT

Spatial Adjusted GOES-E IR-BT Spatial Adjusted GOES-W IR-BT

Cloud-top GOES-E & -W IR-BT Before and After Spatial Adjustment

Before Spatial Adjustment After Spatial Adjustment

Longitude (Degrees, West)

Latit

ude

(De g

rees

, Nor

t h)

- 45 - 30 - 15 0 15 30 45Difference Cloud-Top Brightness Temperature (Kelvin)

Longitude (Degrees, West)

Latit

ude

(De g

rees

, Nor

t h)

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

maximum 23 17

GO

ES

-W IR

Brig

htne

ss T

empe

ratu

re (K

)

GOES-E IR Brightness Temperature (K)

Corr. = 0.95RMSE = 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

GO

ES

-W IR

Brig

htne

ss T

empe

ratu

re (K

)

GOES-E IR Brightness Temperature (K)

Corr. = 0.987RMSE = 2.45

After Spatial Adjustment

Clo

ud-to

p IR

Brig

htne

ss T

empe

ratu

re (K

)

Original GOES-E (13) IR-BT Original GOES-W (11) IR-BT

Spatial Adjusted GOES-E IR-BT Spatial Adjusted GOES-W IR-BT

Cloud-top GOES-E & -W IR-BT Before and After Spatial Adjustment for Validation

GO

ES

-W IR

Brig

htne

ss T

empe

ratu

re (K

)

GOES-E IR Brightness Temperature (K)

Corr. = 0.96RMSE = 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

GO

ES

-W IR

Brig

htne

ss T

empe

ratu

re (K

)

GOES-E IR Brightness Temperature (K)

Corr. = 0.98RMSE = 4.1

After Spatial Adjustment

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);