Analysis of Nonlinearity Correction

for CrIS SDR

April 25, 2012

Chunming Wang NGAS

Comparisons Between V32 and V33 Engineering Packets

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Expected Linearity Improvement Using v33 Engineering Packet Parameters is Confirmed

• Detailed analyses of residual nonlinearity were performed using the Golden Days data and data from April 15, 2012

– Convergence of statistics were examined

– Distribution of scene brightness temperature, FOV to FOV differences in brightness temperatures were examined

• Stratification of statistics using mean brightness temperature for each FOR provided valuable information on linearity of the detectors

– Change in the magnitude of nonlinearity as a function of mean brightness temperature relative to ICT were analyzed

– Sensitivity of brightness temperature to small radiance variation for low temperature scene were taken into consideration

• Expected improvement in linearity using v33 parameters is confirmed– Independent processing of RDR using NGAS off-line code provided additional

confirmation

Updated Parameters Substantially Improves Linearity of CrIS SDR

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IDPS Generated SDR Products for April 15 Were Used in the Analyses

February 24 April 15

• Standard IDPS SDR products showed stable quality– No obvious anomalous radiances were detected; small data gap is due to delay in

data delivery to NGAS

– Expected warming in Northern hemisphere and cooling in Southern hemisphere were visible

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Differences in Brightness Temperatures of LWIR FOVs from FOR Mean Were Reduced

February 24 April 15

• Ensemble averages of brightness temperature difference of each FOV to the FOR mean were substantially reduced

– All Earth scenes were used without rejection by variation in brightness temperatures among 9 FOVs

– Standard deviations of the differences due to geometric effects were unchanged

FOV5 FOV5

Side FOVs Side FOVs

Corner FOVs Corner FOVs

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Meam Differences in Brightness Temperatures Among MWIR FOVs Were Greatly Reduced

• Substantial improvement for FOV7 and FOV8 were observed– FOV7 and FOV8 are now in family with the rest of FOVs

– Residual differences are at similar magnitude as the difference between FOV9 and FOV6 which were shown to be basically linear during TVAC tests

February 24 April 15

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Statistics of SWIR FOVs Were Unchanged Due to Identical Processing Parameters

February 24 April 15

• The brightness differences from FOV to FOV were substantial– In-depth analysis of the distribution of these differences show the detectors are

basically linear

– Brightness temperature differences seem to be linked to geometry

Analyses Methodology

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Key Issues Concerning the Analysis Methodology Were Investigated

• Convergence of statistics is achieved using one day of data – One or two orbits data may not be sufficient

– Convergence in average brightness temperature is slower than average differences from FOR mean

• Effect of scene brightness relative to ICT is taken into consideration– When scene brightness if very close to that of ICT nonlinearity effect is minimized

– At very low temperature scene brightness temperature is sensitive to radiance uncertainty

• Separation of nonlinearity from other sources of errors– Identify signatures of nonlinearity

– Independent processing of RDR using NGAS off-line code provided additional confirmation

Confidence in Conclusion is Gained by the Validation of Methodology

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Using Spectrally Averaged Channel Brightness Temperature Reduces Effects of ILS Errors

• Spectral resampling helps reduce effects of spectral calibration uncertainties

– Averaging in brightness temperatures space is preferred because of the flatness of Earth scene spectra in brightness temperature

• Nonlinearity is an effect on the broad spectrum

– Overall nonlinearity is a function of the radiance energy over the entire band

– Spectral resampling does not affect dynamic range of spectra

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Convergence of Brightness Difference Requires Averaging Over 3 Orbits of Data

• Convergence of mean brightness temperature is slow due to bi-modal distribution of radiances

– Mean brightness temperatures for all FOV changes simultaneously

– It requires more than 3 orbits of data to bring the average FOV to FOV difference to within 10% of its final value

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Convergence of Brightness Difference Requires Averaging Over 3 Orbits of Data

• Convergence for MWIR seems faster than LWIR band

– More than 2 orbits of data is required to bring the average FOV 2 FOV differences in brightness temperature to within 10% of its final value

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Brightness Temperature Error Due to Nonlinearity Depends on Scene Brightness

BT Range, smoothed channels

BT RangeDesignatedWindow channels

ICT TemperatureMin,Max

Mean BT

• Earth scene spectrum has different brightness temperature for all channels

• Warmest channels carry most of photon energy

– A subset of window channels is selected for each band to represent the brightness of the scenes

– Average of all FOVs is used to classify the brightness of a scene

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Each Earth Scene (FOR) is Classified into one of 50 Groups According to Its Brightness

• Bi-modal distribution of the Earth scene brightness is consistent with channel brightness statistics

– Large number of Earth scenes are warmer than ICT

– Since Earth scene spectrum is not constant in brightness the total energy is lower than black body at the same brightness

• ICT temperature varies over a very small range

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FOV-to-FOV Brightness Temperature Differences Depend on Scene Temperature

High Temperature Scenes Low Temperature Scenes

LWIR

MWIR

SWIR

FOV6-FOV9

FOV6-FOV9

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Examination of the Joint Probability Distribution Reveals Scene Dependence of BT Differences

February 24LWIR932.5 cm-1

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BT DifferenceFrom FORMean

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Wider Spread of Distributions in BT Difference for Cooler Scene is Due to Higher Sensitivity

• Constant perturbation in radiance space leads to larger changes in brightness temperature for cooler scenes

– Wider spread of difference in brightness temperature among FOVs is due in part of this sensitivity

• Very warm scenes are also more likely to be cloud free

– Cloud free scene may be more uniform than cloudy scenes

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Examination of Joint Probability Distribution for MWIR FOV Helps Us Recognize Nonlinearity

Nonlinear FOV

Linear FOV

February 24,2012MWIR1275 cm-1

Large Difference Away

from Calibration Points

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Correction with v33 Engineering Parameters Nearly Completely Removed Nonlinearity

April, 152012MWIR1275 cm-1

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Residual Nonlinearity for LWIR Are Significantly Reduced for FOV9 with v33 Parameters

April 15LWIR932.5 cm-1

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Examination of the Joint Probability Distribution Shows SWIR Detectors Are Mostly Linear

February 24SWIR2535 cm-1

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Statistical Results for SWIR Band Are Highly Consistent for Two Focus Days

April 15SWIR2535 cm-1

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Empirical Data from Two Days Seem to Suggest Geometric Trend in BT Bias for SWIR

• Brightness temperature biases seem to be linked to the position of the FOVs

– Both days of data show the similar trend

• More in-depth analyses are needed to determine the cause of these biases

– Analyses of DS and ICT raw spectra are needed

FOV2FOV1 FOV3

FOV5FOV4 FOV6

FOV8FOV7 FOV9

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Conclusion

• Residual nonlinearity for all detectors are very small– Joint probability distribution of the Earth scene brightness and brightness

difference is very useful in identifying nonlinearity

– SWIR detectors are all linear

• SWIR band FOV-to-FOV biases may be caused by non-uniformity of the calibration targets

– More analyses are on-going

• Methodology can be used to monitor nonlinearity