Analysis of Nonlinearity Correction for CrIS SDR April 25, 2012 Chunming Wang NGAS Comparisons Between V32 and V33 Engineering Packets

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 2 Updated Parameters Substantially Improves Linearity of CrIS SDR

IDPS Generated SDR Products for April 15 Were Used in the Analyses 3 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

Differences in Brightness Temperatures of LWIR FOVs from FOR Mean Were Reduced 4 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 Side FOVs Corner FOVs

Meam Differences in Brightness Temperatures Among MWIR FOVs Were Greatly Reduced 5 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

Statistics of SWIR FOVs Were Unchanged Due to Identical Processing Parameters 6 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

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 8 Confidence in Conclusion is Gained by the Validation of Methodology

Using Spectrally Averaged Channel Brightness Temperature Reduces Effects of ILS Errors 9 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

Convergence of Brightness Difference Requires Averaging Over 3 Orbits of Data 10 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 Convergence of Spectra Convergence of Distribution of Difference to FOR mean Convergence of Distribution of Earth Scene Brightness

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 11 Convergence of Spectra Convergence of Distribution of Difference to FOR mean Convergence of Distribution of Earth Scene Brightness

Brightness Temperature Error Due to Nonlinearity Depends on Scene Brightness 12 BT Range, smoothed channels BT Range Designated Window channels ICT Temperature Min,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

Each Earth Scene (FOR) is Classified into one of 50 Groups According to Its Brightness 13 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

FOV-to-FOV Brightness Temperature Differences Depend on Scene Temperature 14 High Temperature ScenesLow Temperature Scenes LWIR MWIR SWIR FOV6-FOV9

Examination of the Joint Probability Distribution Reveals Scene Dependence of BT Differences 15 February 24 LWIR cm -1 Scene Brightness BT Difference From FOR Mean

Wider Spread of Distributions in BT Difference for Cooler Scene is Due to Higher Sensitivity 16 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

Examination of Joint Probability Distribution for MWIR FOV Helps Us Recognize Nonlinearity 17 Nonlinear FOV Linear FOV February 24, 2012 MWIR 1275 cm -1 Large Difference Away from Calibration Points

Correction with v33 Engineering Parameters Nearly Completely Removed Nonlinearity 18 April, MWIR 1275 cm -1

Residual Nonlinearity for LWIR Are Significantly Reduced for FOV9 with v33 Parameters 19 April 15 LWIR cm -1

Examination of the Joint Probability Distribution Shows SWIR Detectors Are Mostly Linear 20 February 24 SWIR 2535 cm -1

Statistical Results for SWIR Band Are Highly Consistent for Two Focus Days 21 April 15 SWIR 2535 cm -1

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 22 FOV2FOV1FOV3 FOV5FOV4FOV6 FOV8FOV7FOV9

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 23