Use of Apodization to Improve Quality
of Radiometric Measurements from
Interferometric Sounders
(2/11/02)
Acknowledgements:
This work is the result of a student project performed at Rose-Hulman
Institute that was sponsored by ITT Aerospace/Communications Div.
Sponsor: J. Predina (ITT Industries)
Student Members: K. Gibbs, B. Dames, Z. Kissel, B. Brosmer, T. Clancy,
K. Galamback, R. Smith & C. Zawistoski
ITT INDUSTRIES - ROSE-HULMAN INSTITUTE
ILS Knowledge
& Apodization
What Spectral Instrument Line Shape (ILS) Uncertainty Can
Be Tolerated for Advanced Sounding Missions?
• CrIS Phase 1 Studies
Systematic
Study Allowed
Evaluation of ILS
Uncertainty for
Each CrIS Band
Determine if
Sensitivity to ILS
Uncertainty
Could be
Reduced by Use
of Hamming or
Blackman-Harris
Apodization
– Concluded that CrIS EDR performance begins to degrade if ILS
uncertainty grows larger than 1.5%
– Based upon measures of rms temperature and moisture
retrieval errors
– Impact upon radiometric bias error and NEdN not evaluated
• More Recent Studies Have Refined Our Knowledge of this
Effect to include:
–
–
–
–
–
Impact upon radiometric bias error
Impact upon NEdN
Specific impacts in each CrIS band (LW, MW & SW)
Scene type effects (land/ocean, cloudy/cloud free)
Sensitivity of various apodization techniques to ILS uncertainty
• Unapodized
• Hamming
• Blackman-Harris
Section 1 - 2
ILS Knowledge
& Apodization
Unapodized Window
Hamming Window
1
1
CrIS LW
Dynamic Range
2000:1
.1
Magnitude
.1
Magnitude
Unapodized
- Standard Format
- Highest Spectral
Crosstalk
- Highest
Uncertainty With
ILS Variation
Apodizations Compared During this Study?
.01
CrIS LW
Dynamic Range
2000:1
.01
.001
.001
1
Hamming
- Lower Spectral
Crosstalk
- Some Adjacent
Channel Correlation
.0001
700
705
710
715
720
Wavenumber
725
.0001
730
705
710
715
720
725
730
Wavenumber (cm -1)
Blackmann Window
1
Magnitude
.1
Blackman
- Lowest Spectral Crosstalk
- High Adjacent Channel
Correlation
- Fastest EDR Forward
Model Execution
700
(cm -1)
CrIS LW
Dynamic Range
2000:1
.01
.001
.0001
700
705
710
715
Wavenumber (cm -1)
Section 1 - 3
720
725
730
Example
Illustrates
Spectral
Response for
700 cm-1
Channel
Center
ILS Knowledge
& Apodization
Concerns Relate to Sensor Spectral Response Uncertainty
(Variation of the ILS Shape, FWHM)
• Overlay Plot of Two Unapodized Spectral Responses
Differing by only 1% Spectral Resolution
Unapodized Window
1
1% Uncertainty
of Spectral Resolution
Maximum
Sidelobe Level
Replaces Null
Response Only
30 cm-1 from
Channel Center
Magnitude
.1
.01
.001
.0001
700
705
710
715
Wavenumber
720
725
(cm -1 )
Section 1 - 4
Sidelobe
Suppression
Below CrIS Noise
Floor Is Not
Achieved
730
Error Magnitude
Contributed by
Each Sidelobe Bin
Is Large Relative
to Noise Floor
Interferometer Optical Band Pass Filter Edges
Interact With an Unapodized Spectral Response
ILS Knowledge
& Apodization
1
10
650 cm-1
1095 cm-1
CrIS Sensor
Long Wave Band
Optical Response
0
10
Transmission
-1
10
-2
10
Filter Edges That
Interact Strongly
with Spectral
Sidelobes
-3
10
-4
10
-5
10
0
500
1000
1500
2000
2500
Wavenumber (cm-1)
Section 1 - 5
3000
3500
4000
ILS Knowledge
& Apodization
Resultant Error Due to 2% ILS Uncertainty
With Ideal Optical Filter 650 cm-1 to 1095 cm-1
Requirement
(all sensor
error sources)
Temperature
Bias Error
(197 scene ensemble)
Noise Equivalent
Radiance
NEdN
(197 scene ensemble)
Section 1 - 6
ILS Knowledge
& Apodization
Can the Use Of Apodization Reduce Sensitivity to
ILS and Optical BPF Uncertainties?
• Sources of Error
Uncertainty in
Any One Source
Leads to
Significant Error
– Mismatch of sensor ILS with ILS used in forward radiometric
transmittance model
– Uncertainty in the optical filter cutoff wavenumber
– Unmodeled scene effects (solar reflection, etc)
• Potential Benefits of Apodization
Elimination of
Error in the
Unapodized Case
Requires More
Precise
Knowledge Over
a Broader Range
of Wavenumbers
– Significantly less precision of hardware components to
achieve a given level of performance
– Better independence of radiance measurements at one
wavenumber to any uncertainties from any radiance source
at other wavenumbers
– Trace gas model errors
– Imprecisely modeled solar reflection from surface or cloud
• Trade Study Evaluations
– Impact on radiometric bias error
– Impact on NEdN
Section 1 - 7
ILS Knowledge
& Apodization
481 Data Files Depicting Upwelling Infrared Signatures of
Earth Scenes Used During the Analysis
• Generation of Test Scenes
Methodology of
Synthesizing
Test Scenes
Test Scenes
Were Previously
Developed
During the CrIS
Phase 1 Effort
Test Scenes
Were Previously
Developed
During the CrIS
Phase 1 Effort
– 481 temperature/moisture profiles randomly selected from
NOAA88 data set
– 197 cloud free profiles over land
– 284 cloud free profiles over ocean
– NOAA88 provided surface emissivity used for each profile
• Converted Temperature/moisture Profiles Into Radiance
– Used Atmospheric Environmental Research Inc. supplied
OSS forward model code developed during CrIS Phase 1
– Spectral resolution of earth scene radiance model
• LW = 0.04 cm-1
• MW = 0.08 cm-1
• SW = 0.16 cm-1
• Added Cloud Content (additional set of 481 data files)
– “Optically thick” clouds added
– Cloud fraction and cloud height data bases supplied by
P. Wylie (U. of Wisconsin) and T. VonderHaar (STC METSAT
@ Colorado State)
Section 1 - 8
ILS Knowledge
& Apodization
Methodology
Ideal ILS
Earth
Scene
Radiance
• Unapodized
• Hamming
• Blackman-Harris
X
+
Σ
-
X
K = 284 Ocean/cloud free
K = 197 Land/cloud free
K = 284 Ocean/cloudy
K = 197 Ocean/cloudy
Repeat Calculation
of Error for Each
Earth Scene
Distorted
ILS
Integrate
over
wavenumber
Radiance
Error
2%, 1% & 0.25%
Bin Width Distortion
Evaluated
Repeat Calculation of Error
for Each Channel Center
in all 3 CrIS Bands
(1305 Channels)
Section 1 - 9
Compute Statistics
• Mean (bias)
• STD (NEdN)
• % Error bias
ILS Knowledge
& Apodization
Typical Radiance Error Plots Generated
(Unapodized ILS with 1% Excessive Bin Width)
Radiometric
Bias Error
NEdN
% Radiometric
Bias Error
Relative to
287 K BB
Section 1 - 10
ILS Knowledge
& Apodization
Comparison of Apodization Effect
(Long Wave Band, Land Surface, Cloud Free)
Unapodized
Case with
1% ILS
Uncertainty
Bias Errors Drop
as Much as 8
Times Using
Hamming
Window
Blackman-Harris
Yields Even More
Improvement
Section 1 - 11
ILS Knowledge
& Apodization
Comparison of Apodization Effect
(Mid Wave Band, Land Surface, Cloud Free)
Unapodized
Case with
1% ILS
Uncertainty
Bias Errors Drop
as Much as 4
Times Using
Hamming
Window
Blackman-Harris
Yields No
Improvement Over
Hamming
Section 1 - 12