ATMS Optimal Striping Filters

X. Zou1, Y. Ma1 and F. Weng2

May 13, 2014

1Department of EOAS, Florida State University

STAR JPSS Annual Meeting, May 12-16, 2014

2Center for Satellite Applications and Research, NOAA

Outline

• ATMS TDR/SDR Striping Issues

• User Complains

Qin, Z., X. Zou and F. Weng, 2013: Analysis of ATMS and AMSU striping noise from their earth scene observations. J. Geophy. Res., 118, 13,214-13,229.

• Requirements for Characterization and Correction • AMSU-A/MHS/AMSU-B

• ATMS Striping (TVAC, Pitchover Data, Earth Scene ...) • De-striping Methodology

• Optimal Striping Filters for Radiances

• Optimal Striping Filters for Calibration Counts

PCA Decomposition for ATMS Channel 10

30N

20N

10N

EQ

10S

20S

30S156E 168E 180 168W 156W

30N

20N

10N

EQ

10S

20S

30S156E 168E 180 168W 156W

30N

20N

10N

EQ

10S

20S

30S156E 168E 180 168W 156W

30N

20N

10N

EQ

10S

20S

30S156E 168E 180 168W 156W

202.0

202.8

203.6

204.4

205.2

206.0

206.8

207.6

208.4

209.2

210.0

202.0

202.8

203.6

204.4

205.2

206.0

206.8

207.6

208.4

209.2

210.0

-1.8

-1.5

-1.2

-0.9

-0.6

-0.3

0.0

0.3

0.6

0.9

1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Tb obs.

The 2nd component

The 1st component

The 3rd component

re1

ru1

re2

ru2 re3

ru3

PC mode A =

rejruj

j=1

96

∑

The ATMS data can then be expressed as in PCA:

PC coefficient

A =

TB1,1 TB1,2 L TB1, j L TB1,K

TB2,1 TB2,2 L TB2, j L TB2,K

M OTBk ,1 TBk , j TBk ,K

M OTB96,1 TB96,K

K -total number of scanlines

The First Three IMFs of ATMS Ch10 Obs.

Scanline

The 1st IMF

The 3rd IMF

The 2nd IMF

Scanline

e 48,

1 u1,

j (K

)

The 1st PC Component at Nadir

Frequency (s-1)

Pow

er S

pect

rum

Den

sity

Original data

After taking away the three IMFs

The Optimal Striping Filters: Mathematical Formula

u1,k = α n

n=−N

N

∑ u1,k+n , α n = α−n

rm = α n

n=0

N

∑ cos(2π f ∆t)

u1,k = Cme

− i2πmkK

m=0

K−1

∑ u1,k = Cme

− i2πmkK

m=0

K−1

∑

(k = 1,2,L , K ) u1,k{ }

The first PC coefficient

The filtered first PC coefficient

uk ,1

eemd = uk ,1 − IMFm(k)m=1

L

∑

minαnJ = min (

k=1

K

∑ α nn=−N

N

∑ u1,k+n − u1,keemd )2

α nn=−N

N

∑ = 1, α n = α−n

Tb,k ,i

destriping = e1,i α nn=−N

N

∑ u1,k+n + ej ,iu j ,kj=2

96

∑

i = 1,2,L ,96

where

k = 1,2,L , K

represents scan position

represents scan line

Cm = rmCm , f = m

K∆t, ∆t = 8

3s

Power Spectrum Density of the First Seven IMFs and Residuals of ATMS Brightness Temperatures

Am

plitu

de

ATMS Ch1 ATMS Ch9 ATMS Ch22

The total number of IMFs removed are two for channels 1-2 and three for channels 3-22.

Decision:

Scanline (n)

Cos

t Fun

ctio

n (J

)

Frequency (f, unit: s-1)

Filter Span (N)

Wei

ghtin

g Fu

nctio

n (α

n)

Pow

er S

pect

rum

Den

sity

The Optimal Striping Filters: Numerical Results

This is a set of optimal filters for ATMS radiances designed to

smooth out the striping noise but not to alter lower frequency

weather signals.

J = (

k=1

K

∑ α nn=−N

N

∑ u1,k+n − u1,keemd )2

J = (

k=1

K

∑ α nn=−N

N

∑ u1,k+n − u1,keemd )2

rm = α n

n=0

N

∑ cos(2π f ∆t)

Variation of Cost Function J with Filter Span

J = (

k=1

K

∑ α nn=−N

N

∑ u1,k+n − u1,keemd )2

Cos

t Fun

ctio

n (J

)

Filter Span (N)

Cos

t Fun

ctio

n (J

)

Filter Span (N)

Cos

t Fun

ctio

n (J

)

Filter Span (N)

Cos

t Fun

ctio

n (J

)

Filter Span (N)

Optimal Weighting Coefficients

J = (

k=1

K

∑ α nn=−N

N

∑ u1,k+n − u1,keemd )2

Scanline (n)

Wei

ghtin

g Fu

nctio

n (α

n)

Scanline (n)

Wei

ghtin

g Fu

nctio

n (α

n)

Scanline (n)

Wei

ghtin

g Fu

nctio

n (α

n)

Scanline (n)

Wei

ghtin

g Fu

nctio

n (α

n)

Response Functions of the Optimal Striping Filters

rm = α n

n=0

N

∑ cos(2π f ∆t)

Frequency (f, unit: s-1)

Pow

er S

pect

rum

Den

sity

Frequency (f, unit: s-1)

Pow

er S

pect

rum

Den

sity

Frequency (f, unit: s-1)

Pow

er S

pect

rum

Den

sity

Frequency (f, unit: s-1)

Pow

er S

pect

rum

Den

sity

Ch1 Ch9 Ch22

Striping noise Spectrum removed by the optimal striping filters

without with without

with

Global O-B Spectrum with and without Applying the Optimal Striping Filter

Before After

Before minus After

Global O-B Distributions of ATMS Channel 8

Striping noise

Pitch-Over Maneuver Data with and without Optimal Filtering

without with without with

ATMS Channel 1 ATMS Channel 9

Striping Index (SI)

Valong =1N

1M

Tb (k, j)− 1M

Tb (k, j)k=1

M

∑

2

k=1

M

∑

j=1

N

∑

SI =

Valong

Vcross

Along-track variance

Cross-track variance

Vcross =1M

1N

Tb (k, j)− 1N

Tb (k, j)j=1

N

∑

2

j=1

N

∑

k=1

M

∑

Striping Index (SI) of Pitch-Over Maneuver Data

Channel

SI

VC

T V

DT

Variance of down-track (VDT), variance of cross-track (VCT), and striping index (SI) before (red) and after (blue) applying

the optimal striping filter.

SI is significantly reduced to one for ATMS all channels.

Summary

• Twenty two optimal striping filters are developed for 22 ATMS channels

• Two months of de-striping ATMS data are being produced for NWP impact test

Future Plan

Similar optimal striping filters will be developed for calibration counts, and impact of striping noise on

NEDT will be quantified.