In this step, collocated data are transformed to allow their direct comparison. This includes modifying the spectral, temporal and spatial characteristics of the observations, which requires knowledge of the instruments’ characteristics. The outputs of this step are the best estimates of the channel radiances, together with estimates of their uncertainty.
Figure 7: Step 2 of Generic Data Flow, showing inputs and outputs
2.a Convert Radiance
2.a.i. Purpose
Convert observations from both instruments to a common definition of radiance to allow direct comparison.
2.a.ii. General Options
2.a.ii.v0.1.
The instruments’ observations are converted from Level 1.5/1b/1c data to radiances, using pre-defined, published algorithms specific for each instrument.
2.a.iii. Infrared GEO-LEO inter-satellite/inter-sensor Class
2.a.iii.v0.1
Perform comparison in radiance units: mW/m^{2}/st/cm^{-1}.
2.b Spectral Matching
2.b.i. Purpose
Firstly, we must identify which channel sets provide sufficient common information to allow meaningful inter-calibration. These are then transformed into comparable pseudo channels, accounting for the deficiencies in channel matches.
2.b.ii. General Options
2.b.ii.v0.1.
The Spectral Response Functions (SRFs) must be defined for all channels. The observations of channels identified as comparable are then co-averaged using pre-determined weightings to give pseudo channel radiances. A Radiative Transfer Model can be used to account for any differences in the pseudo channels’ characteristics. The uncertainty due to spectral mismatches is then estimated for each channel.
2.b.iii. Infrared GEO-LEO inter-satellite/inter-sensor Class
For hyper-spectral instruments, all SRFs are first transformed to a common spectral grid. The LEO hyperspectral channels are then convolved with the GEO channels’ SRFs to create synthetic radiances in pseudo-channels, accounting for the spectral sampling and stability in an error budget.
Equation 5:
R_{GEO} = \frac{\int_\nu R_\nu \Phi_\nu d\nu}{\int_\nu \Phi_\nu d\nu}
where R_{GEO} is the simulated GEO radiance, R_\nu is LEO radiance at wave number \nu, and \Phi_\nu is GEO spectral response at wave number \nu.
In general LEO hyperspectral sounders do not provide complete spectral coverage of the GEO channels either by design (e.g. gaps between detector bands), or by subsequent hardware failure (e.g. broken or noisy channels). The radiances in these gap channels shall be accounted by one of the following techniques:
2.b.iii.v0.5
Gunshor [2007] matches the pre-computed radiance at the beginning and end of the gap. The ratio between the AIRS radiance and simulated radiance is computed at the last channel before a gap and the first channel after the gap, and is linearly interpolated to the channels within the gap. The missing AIRS radiances are then estimated as the simulated radiances multiplied with the ratio linearly interpolated to the missing channel.
2.b.iii.v0.6
This is the recommended option. Tahara and Kato [2009] define virtual channels named gap channels to fill the spectral gaps and introduce the spectral compensation method by constrained optimization. The gap channels to fill the AIRS spectral gaps (AIRS gap channels) are defined by 0.5 cm^{-1} intervals, and are characterized by a unique SRF, whose shape is a Gaussian curve with a sigma of 0.5 cm^{-1}. The gap channels to extend the IASI spectral region (IASI gap channels) are defined by the same intervals (0.25 cm^{-1}) and SRFs as the IASI level 1c channels. The radiances of the missing channels are calculated by regression analysis using radiative transfer simulated radiances with respect to the eight atmospheric model profiles as explanatory variables.
Equation 7:
\log I_{i}^{calc} = c_0 + \sum_{k=1}^{K} c_{k}\log I_{i,k}^{sim} ,\ \ (i=hyper\ and\ gap\ channels)
where I_{i}^{calc} is the calculated radiance of the hyper channel i, I_{i,k}^{sim} is the simulated radiance of the hyper channel i with respect to the atmospheric model profile k, c_{k} are regression coefficients, and K is the number of the atmospheric model profiles. Equation 7 introduces logarithm radiances as response and explanatory variables in order to increase fitting accuracy and avoid calculation of negative radiance. The regression coefficients c_{k} are independent of the hyper channels, and are generated for each observing position of the hyper sounder. c_{k} are obtained by the least-square method applying a set of validly observed radiances I_{i}^{obs} in place of I_{i}^{calc} to Equation 7,
Equation 8:
{c_k} = argmin\sum_{i=exist(I_{i}^{obs})}\{\log I_{i}^{obs}-(c_0 + \sum_{k} c_k \log I_{i,k}^{sim})\}^2
Once the regression coefficients c_{k} are computed, the radiances of the missing channels can be calculated by Equation 7. It might be possible to apply the observed radiances of all hyper channels to Equation 8 to compute c_{k} and then calculate the radiances of all missing channels at once. However, this yields a large fitting error in practice. In inter-calibration application, the coefficients c_{k} are computed for each broadband channel spectral region. Equation 7 and Equation 8 use the simulated radiances I_{i,k}^{sim}. For the radiance simulation, this study uses the following eight atmospheric model profiles:
- U.S. standard without cloud,
- U.S. standard with opaque cloud with tops at 500 hPa altitude,
- U.S. standard with opaque cloud with tops at 200 hPa altitude,
- Tropical without cloud,
- Tropical with opaque cloud with tops at 500 hPa altitude,
- Tropical with opaque cloud with tops at 200 hPa altitude,
- Mid-latitude summer without cloud,
- Mid-latitude winter without cloud.
These profiles include not only clear weather conditions but also cloudy conditions because Equation 7 should be applicable under any weather conditions. As for radiative transfer code, the line-by-line code LBLRTM (Clought et al., 1995) version 11.1 is used with the HITRAN2004 spectroscopy line parameter database (Rothman et al., 2003) including the AER updates version 2.0 (AER Web page). The emissivities of the surface and clouds are assumed to be one. The benefit of this spectral compensation method is that it does not use radiative transfer computation in inter-calibration operation. This not only speeds up the computation but also prevents super channel radiance computation from introducing biases contained in radiative transfer code and atmospheric state fields.