a. Instruments

For detailed descriptions of the AIRS, IASI, and GOES imager instruments, the reader is referred to other references (Blumstein et al. 2004; Chahine et al. 2006; Klaes et al. 2007; Schmit et al. 2001). Summarized in Table 1 are the instrument characteristics. The simulated AIRS and IASI spectra, as well as the GOES imagers spectral response functions (SRFs), are given in Fig. 2.

AIRS is a grating IR sounder that disperses the radiation from the earth scene onto 17 linear arrays of Hg–Cd–Te detectors on a focal plane with 2378 IR channels. AIRS views the ground through a cross-track rotary scan mirror that provides ±49.5° ground coverage every 2.67-s scan cycle. A total of 90 ground footprints is observed for each scan with each footprint containing all 2378 spectral samples. The AIRS IR spatial resolution is 13.5 km from the nominal altitude of 705.3 km with a 1330 ascending node. The on-orbit calibration of AIRS involves radiometric and spectral calibrations. Routine IR radiometric calibration data are taken while the scan mirror rotates from −49.5° (relative to nadir) through 180° (antinadir position) to +49.5°. These data consist of four independent views of cold space and one view of the onboard blackbody, and are used to derive the radiometric gain (slope) and offset (intercept). The nonlinearity correction is performed by using the prelaunch calibration data. The selected atmospheric spectral features with simulated upwelling radiances are compared with AIRS to diagnose possible shifts of each feature relative to the nominal grating model. The AIRS version 5 data are used in this study.

IASI on MetOp-A is a Michelson interferometer that measures infrared radiation emitted from the earth in the infrared spectra between wavelengths of 3.6 and 15.5 μm (Blumstein et al. 2004). IASI is in a sun-synchronous polar orbit at 819 km with a 0930 equator cross in a descending node. The IASI observations are obtained by a step scanning mirror covering ±47.85° range in 30 steps in every 8.0-s scan cycle, with 3.3° for each step (normal mode). At each step, the field of regard (FOR) includes 2 × 2 1.25° fields of view (FOVs) with a pixel resolution of 12 km at nadir, each positioned in the cross- and along-track directions located at ±0.825°. The measured interferograms are processed by an onboard digital processing subsystem in order to reduce the data transmission rate, which performs the inverse Fourier transform, the radiometric calibration (based on the measurements of cold and warm reference targets, i.e., deep space and an onboard blackbody), and nonlinearity corrections. The ground processing includes radiometric postcalibration, spectral calibration, and apodization, which produces resampled, apodized, and calibrated spectra with 8461 spectral samples, that is, IASI level-1C radiance products.

The GOES-11 and GOES-12 imagers are five-channel imaging radiometers, including one visible channel (0.65 μm), one shortwave IR channel (3.9 μm), and three longwave IR channels (6.7, 10.7, and 12.0 μm for GOES-11; 6.5, 10.7, and 13.3 μm for GOES-12). Compared to the GOES-11 imager, the GOES-12 imager has a spectral channel centered at 13.3 μm, replacing the previous 12.0-μm channel. The GOES-12 imager also includes a spectrally modified 6.5-μm channel with an improved spatial resolution from 8 to 4 km at the subsatellite point. As a trade-off, the GOES-12 13.3-μm channel’s spatial resolution is approximately 8 km in the north–south direction, the same as that of the 6.7-μm channel of GOES-11 (Table 1). In other words, the detectors used for the GOES-12 13.3-μm and GOES-11 10.7-μm channels have an instantaneous geometric field of view (IGFOV) of 224 μrad, resulting in a subsatellite pixel of 8 km on a side, while the detectors for the other three IR channels have an IGFOV of 112 μrad, corresponding to a square 4-km pixel at the subsatellite point. Because of the combination of scan rate (20° s⁻¹) and detector sample rate (5460 samples per second for the IR channels and 21 840 samples per second for the visible channel), each sample step corresponds to an angle of 16 μrad for the visible channel and 64 μrad for the IR channels along a scan line. In other words, the GOES imager oversamples the infrared IGFOVs of 4 and 8 km along a scan line by factors of 1.75 and 3.5, respectively. During the instrument’s operation, the infrared channels are frequently calibrated based on space-view and onboard blackbody view observations, providing an absolute calibration accuracy of better than 1.0 K with 0.3-K relative precision (Boeing 2006).

b. Method

Three major steps are involved for the intercomparison of the AIRS and IASI radiances using geostationary imagers as transfer radiometers, including 1) spectral convolution, 2) spatial and temporal collocation for AIRS/IASI and the GOES imagers’ observations, and 3) statistical calculations. These three steps are described in this section.

1) Spectral convolution

The objective of spectral convolution is to integrate the hyperspectral radiance spectrum to match the broadband GOES imager SRF and make it comparable with the GOES imager observations. Given the hyperspectral radiance R(ν) at each wavenumber ν, it can be convolved with the GOES imager SRF S(v) to generate the IASI- or AIRS-simulated GOES imager infrared channel radiance L as

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where ν₁ and ν₂ are the spectral bandpass limits. The GOES imager SRFs can be obtained online (http://cimss.ssec.wisc.edu/goes/calibration/).

A major issue in spectral convolution for AIRS is estimating the missing spectral radiance values either by design or due to dead or unstable detectors. A common practice is to replace these radiance values with simulated atmospheric spectra, the so-called AIRS gap-filling technique (Gunshor et al. 2009; Tobin. et al. 2006). The GSICS intercalibration algorithm uses the method proposed by Tahara and Kato (2008). In their method, the atmospheric spectra for eight different atmospheric profiles (including both cloudy and clear-sky conditions) are simulated by the Line-by-Line Radiative Transfer Model (LBLRTM). The relationship between the simulated and observed radiances for the AIRS good channels is then established by solving a linear least squares problem. The radiance values of missing AIRS channels are then predicated based on this relationship. The accuracy of the gap-filling method has been reviewed by Tahara and Kato (2008). It shows that the gap-filling method has minimal effects (smaller than 0.001 K) on the channels where the AIRS individual channels are missing due to the dead or unstable detectors, but yields significant improvements in the spectral regions that AIRS does not fully cover. It is known that only the GOES-12 water vapor channel suffers from the uncertainties due to the AIRS spectral gap filling (see Fig. 2).

2) Spatial and temporal collocation

In the second step, the AIRS and IASI measurements are collocated to the GOES observations in space, time, and view geometry. The strategy is to find the geostationary satellite measurements that fall inside the pixels of the polar-orbiting satellites by minimizing the observational time and view geometry differences. First, the time difference between IASI–AIRS and geostationary observations is constrained to less than 300 s in this study. The sensitivity test performed in this study—as well as those done by others (Gunshor et al. 2009; Wang et al. 2009)—indicates that, given a relatively uniform scene, tightening the time collocation criterion reduces both the standard deviation of the IASI–AIRS − GOES brightness temperature (BT) differences and the number of collocations, but does not significantly impact the mean value of the BT differences. The 300-s time window is chosen as a compromise to keep a sufficient number of samples and also reduce the effects caused by instrument observational time difference.

Two identical satellite instruments sensing the same target at the same time should obtain the same measurements only if they have identical lines of sight, that is, if their zenith angles from the target are the same and their relative azimuth angles equal zero. Within the infrared spectrum, where AIRS and IASI cover, a similar view zenith angle means a similar geometric pathlength, which implies a similar optical pathlength. Since the secant of the zenith angle is approximately proportional to the optical pathlength, the relative difference between the secant of the two zenith angles from geostationary and polar-orbiting satellites can be used to limit the optical path difference, which is expressed as |cos(geo_zen)/cos(leo_zen)-1|, where geo_zen and leo_zen represent the view zenith angles of the geostationary and polar-orbiting satellites, respectively. The criterion of this parameter is set to 0.01 or less in this study. This requirement allows 8.07° of zenith angle difference at nadir and 0.327° at 60° zenith angle, respectively.

A minimal relative azimuth angle is required for visible and near-infrared channels due to scene bidirectional reflectance characteristics. For infrared window channels and absorptive channels, if the scene and atmosphere are highly inhomogeneous (e.g., when clouds exist), longwave emission may be anisotropic. To reduce the azimuth angle effects, the comparison is limited to uniform scenes, and also excludes the shortwave IR channels.

A spatially uniform environment surrounding the collocated measurements is desirable to compensate for minor violations of collocation and coincidental criteria as well as to reduce the uncertainties caused by azimuth angle differences and navigation errors. In our implementation, the collocation environment is defined as 3 times the FOVs of the polar-orbiting instruments, as shown in Fig. 3. The environment uniformity is measured by the standard deviation of radiance relative to the mean radiance, expressed as

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where σ_env and L_env are the standard deviation and mean of the environment radiance, respectively. In addition, for each collocated AIRS/IASI–GOES FOV, the ratio of the standard deviation and the mean of the GOES radiances is also required to be less than 0.01:

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where σ_fov and L_fov are the standard deviation and mean of the GOES radiances within the collocated AIRS/IASI–GOES FOV, respectively.

3) Statistical calculation

For each collocated AIRS/IASI–GOES FOV, the brightness temperatures (BTs) are computed from the IASI–AIRS-convolved radiance and the mean of GOES radiances, respectively. The BT differences between AIRS–IASI and the GOES imager are derived. Given hundreds of collocations for each day, the mean BT difference is calculated, which represents the GOES observation bias relative to AIRS and IASI. The double differences between the AIRS and IASI radiances relative to the GOES imagers in terms of BTs is defined as

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where BT_AIRS, BT_IASI, and BT_GOES are the BT values from AIRS, IASI, and the GOES imagers, respectively, for one collocation pair. Note that the subscript of “mean” indicates an average over a day. To cancel out the impacts of the transfer radiometers, the transfer radiometer itself must be stable during the AIRS/IASI–GOES collocation. In other words, since AIRS and IASI pass over the geostationary satellite nadirs two times each day at a fixed local time (i.e., 0130–1330 and 0930–2130), any diurnal calibration difference of the GOES imagers can introduce systematic errors into the final results. It is well known that the computed calibration slopes for the GOES imager infrared channels exhibit anomalous dips during the approximate 6 h centered on satellite midnight, which is believed to be interference by stray radiation from solar-heated structural components that reaches the imager detectors during the blackbody look (Johnson and Weinreb 1996). While corrections have been made for the GOES radiance data, our analysis still indicates that this calibration problem exists for the GOES midnight observations as compared with the observations from other time periods. Thus, this study is limited to daytime data only.

c. Uncertainty analysis

In general, two types of errors can be introduced into the bias statistics: 1) those introduced by random processes and 2) systematic biases. The purpose of this study is to identify the systematic radiometric difference between AIRS and IASI within the spectral channels of the GOES imagers. To detect the systematic errors related to the AIRS and IASI measurements, it is expected that the method is able to avoid possible systematic errors from other sources and minimize random errors through the collocation and convolution. The remainder of the random errors can be further reduced to a negligible level by averaging enough samples.

The possible sources of random errors are 1) the instrument radiometric noise levels of AIRS, IASI, and the GOES imagers; 2) view zenith angle and azimuth angle differences; 3) collocation uncertainties due to each instrument’s navigation errors; 4) the observational time difference; 5) other errors related to scene nonuniformity and instrument footprint size difference; and 6) the spectral gap-filling errors (only for the GOES-12 water vapor channel). The instrument noise of AIRS, IASI, and the GOES imagers has a Gaussian distribution. Spectral convolution should filter out the AIRS and IASI instrument noise. The average of the daily samples further reduces the noise of the GOES imagers as well as other IASI and AIRS instrument noise. The bias related to the spectral gap filling is only a concern for the GOES-12 water vapor channel (6.5 μm), due to its relatively large spectral gap. Recall that the predicated relationship used to calculate the AIRS spectral-gap radiances is generated by solving a least squares problem. A sensitivity test based on different atmospheric profiles indicates that errors caused by the spectral gap filling are dependent on the collocation environment and thus are random rather than systematic. Given hundreds of collocated samples each day in different collocation environment, the average will minimize this error. The collocation uncertainties due to each instrument’s navigation errors and the differences in instrument footprint size are minimized with the help of collocation criteria and the uniformity of the collocated FOV and environment, as well as taking the average. Figure 4 gives the GOES − AIRS BT difference distribution with respect to the observational time and zenith angle differences, the relative azimuth angle between AIRS and GOES, as well as the collocated FOV scene uniformity for GOES-12 channel 6 data taken during the daytime of 3 July 2007. Figure 4 clearly shows that the BT differences are randomly distributed along their mean value with the zenith angle, azimuth angle, and observational time differences as well as scene uniformity. In other words, the mean BT difference does not depend on these parameters.

The factors that may cause the systematic biases but are not related to AIRS and IASI are the calibration bias of each GOES imager, for example, diurnal and seasonal calibration bias, instrument sudden-change-induced bias, and SRF-uncertainty-caused bias. As we discussed above, the day–night calibration bias is avoided by choosing daytime observations only. The GOES diurnal calibration variation during the daytime has been examined by binning the collocation data according to the observation time. We did not observe any calibration variation pattern for a 4-h time window during the daytime period. In other words, given a 4-h time window from 0930 to 1330 (local time at satellite subpoints), the calibration of the GOES imagers is stable so that no systematic calibration bias is introduced. Through a double-difference method, other calibration biases of the GOES imagers are expected to be canceled out. Therefore, we believe that the final results from the double differences are mainly related to the systematic bias due to the AIRS–IASI measurement difference.

a. Intercalibration capabilities

As discussed above, the AIRS and IASI hyperspectral radiances are often used to assess the calibration accuracy of geostationary imagers (Gunshor et al. 2009; Wang et al. 2009). Here, we believe that these intercalibration results can also be used to quantify the AIRS and IASI radiance difference. Since this comparison involves four sensors (i.e., AIRS, IASI, and the GOES-11 and -12 imagers), the intercalibration results can be cross validated through different pairs of instruments to facilitate the root cause analysis for the bias. Examples are presented below to demonstrate these capabilities.

The first example begins with GOES-12 channel 6 (13.3 μm), shown in Fig. 5c. The time series plot of the GOES − AIRS BT difference (indicated by the red dots) depicts a sudden change around 2 July 2007 (jump from −2.5 to −1.0 K). After that, the BT difference remained relatively constant (∼−1.0 K) till it gradually decreased after April 2008. However, the comparison of these two sensors cannot determine which instrument, either AIRS or the GOES-12 imager, caused the cold bias. In other words, additional information is needed to identify the root cause of the bias. The GOES and IASI intercalibration (represented by the blue dots) time series indicates the same features, which confirms that this cold bias is caused by the GOES-12 imager. Further investigation indicates that the GOES-12 imager experienced a decontamination procedure from 2 to 4 July 2007, where certain internal components were warmed up in an attempt to drive off contaminants (mainly water ice). This instrument change apparently impacted the GOES-12 calibration accuracy, which was confirmed by both IASI and AIRS. It is of particular interests that the double-difference time series (shown as the black dots in Figs. 5c) removed the sudden change and the later gradual decrease of the bias, and remained constant during the entire time period. This suggests the excellent calibration of IASI and AIRS because both can track the GOES imager calibration bias well. The same feature can also be found for GOES-12 channel 3 (6.5 μm) (Fig. 5a).

Figure 6a, for GOES-11 channel 3 (6.7 μm), serves as another example to show this capability. There are pronounced fluctuations along the GOES–AIRS and GOES–IASI BT time series (represented by the red and blue dots), indicating that they are caused by the GOES-11 imager change. We found that the detector patch temperature of GOES-11 was raised from 91 to 99 K in the summertime and lowered from 99 to 91 K in the wintertime, as indicated by the blue arrows in Fig. 6a. Since the patch is on the north-facing side of the satellite, it runs warmer in the summertime. The float patch temperature often causes a variable instrument noise. As a trade-off, the patch temperature is raised in summer in order to keep the stable (constant) patch temperature. It is expected that the GOES calibration accuracy should not be impacted by this patch temperature change. However, both IASI and AIRS successfully track the calibration accuracy change caused by the patch temperature change. More interestingly, the IASI and AIRS double differences were not impacted and remained consistent before and after the GOES-11 patch temperature change. The above discussion further demonstrates that systematic errors related to the calibration accuracy of the transfer radiometer calibration are canceled out through the double-difference calculations. These results have been encouraging enough to merit further investigation of the IASI and AIRS radiance difference through the double differences.

The 10.7-μm channels of the GOES-12 and -11 imagers are presented as a final example, given in Figs. 5b and 6b. As indicated by Fig. 2, these two channels have the same spectral coverage. The double differences for these two channels, which are used to quantify the AIRS–IASI difference, should give similar results within their uncertainties regardless of which transfer radiometer is chosen. To make it clear, we summarize the statistics of the double differences (shown in Figs. 5 and 6) in Table 2. The double-difference results for GOES-11 and -12 channel 4 (the mean and 95% confidence level) are consistent to each other within the uncertainties. Note that the standard deviation of GOES-12 is larger than that of GOES-11 because the collocations for GOES-12 occurred more over land and hence contained more inhomogeneous scenes than GOES-11. The above example confirms the effectiveness of the double-difference method, which is not sensitive to the transfer radiometer.

In summary, the above discussion demonstrates that the variations in the GOES − AIRS and GOES − IASI BT differences can well track the relative consistency between AIRS and IASI in spite of sudden changes or gradual variations of the GOES imager calibration accuracy. In the discussion that follows, we thus focus on the AIRS and IASI radiance differences revealed by the double differences.

b. IASI and AIRS difference

The statistics of the double differences, which are used to characterize the IASI and AIRS radiance differences in terms of BT within the GOES imager spectral channels, are summarized in Table 2. Histograms of the double differences, shown as the gray bars in Fig. 7, are overlaid with fitted Gaussian distributions. The reduced chi-squared statistic χ_υ²(=χ²/υ) where χ² is the chi-squared statistics and υ the degrees of freedom) can be used to describe the goodness of fit of the computed values to the data. As noted by Bevington and Robinson (2003), ideally, a value of χ_υ² = 1 implies the best fit of the given data. Values of χ_υ² much larger than 1 result from large deviations from the assumed distribution and may indicate poor measurements, incorrect assignment of uncertainties, or an incorrect choice of the probability function. The calculated χ_υ² values range from 1.53 to 2.83 (given in Fig. 7), indicating that the distributions of the double differences approximate a normal or Gaussian distribution in practice. Therefore, it is possible to use the Student’s t test to estimate the 95% confidence interval of those differences using

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where t_0.025 is the Student’s t test’s critical point for a large sample number and is equal to 1.96, σ is the standard deviation of the double differences, and N is the sample number. The null hypothesis is that the differences in the mean values of both the GOES − AIRS and GOES − IASI BT differences are zero (or that the mean values are equal). The formula given above for the error estimation is, however, only correct if the individual data points are unrelated, or statistically independent. As described in Santer et al. (2000), a common and relatively simple method can be used to correct the autocorrelation effects by determining the effective sample size N_eff:

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where R₁ is the lag-1 autocorrelation coefficient and N is the sample number from the data. The adjusted 95% confidence level based on the above method is given in Table 2.

At the 95% confidence level, the mean values of the IASI–AIRS brightness temperature differences are −0.0641 ± 0.0074 K, −0.0432 ± 0.0114 K, and −0.0095 ± 0.0151 K for the GOES-11 6.7-, 10.7-, and 12.0-μm channels, and −0.0490 ± 0.0100 K, −0.0419 ± 0.0224 K, and −0.0884 ± 0.0160 K for the GOES-12 6.5-, 10.7-, and 13.3-μm channels. Note that the results from the GOES-12 6.5-μm channel should be viewed with caution due to the spectral gap filling. AIRS and IASI have the best agreement within GOES-11 12.0-μm channel (channel 5; i.e., −0.0095 ± 0.0151 K). For the CO₂ absorption channel (GOES-12 channel 6 at 13.3 μm), AIRS and IASI have a relatively larger cold bias (−0.0884 ± 0.0160 K) than do the other channels. Generally speaking, the radiance differences between AIRS and IASI within the GOES imager channels is less than 0.1 K while AIRS is slightly warmer than IASI.

Note that the largest uncertainty value is found for the GOES-12 10.7-μm channel while the two water vapor channels have the smallest values, which is due to scene inhomogeneity as discussed above. This suggests that the preciseness of the double-difference method is impacted by scene uniformity, which is a key factor in controlling the uncertainties caused by the minor violations of the collocation and concurrence, as well as the view geometry difference.

To characterize the IASI − AIRS BT difference variation with time, we also calculate the linear trend of the double-difference time series, as well as one sigma uncertainty with autocorrelation correction, given in Table 2. Except for the two water vapor channels, there is no statistically significant trend because the uncertainty is larger than or comparable to the trend value. More interestingly, small seasonal variations can be found from the double-difference time series of GOES-12 channels 3 and 4, as well as GOES-11 channel 3. However, the statistical period in this study is too short, so it cannot determine statistically significant trends for the IASI and AIRS BT differences, as well as the seasonal variations. We will extend the time series and revisit this issue in the future.

Figures 8 and 9 present the time series of the standard deviation of the BT difference and mean GOES BT for the GOES–AIRS and GOES–IASI collocations for GOES-12 and -11, which provide information about random errors and scene temperatures. The standard deviations of both GOES–AIRS and GOES–IASI BT differences are stable with time, indicating that the random errors do not vary much during the time period. The time series of the GOES mean BT show that the AIRS and IASI comparison is performed for relatively warm scenes, that is, ∼290 K for the window channels, ∼220 K for the water vapor channels, and ∼270 K for the CO₂ channel. These values are also relatively constant with time in this study.

It is not possible, from this study, to address the absolute calibration accuracy for both the AIRS and IASI instruments by means of intersatellite comparison results. However, the small relative difference between AIRS and IASI disclosed from this study provides useful information for climate-related studies using the IASI and AIRS data.

c. Discussion

It is not a novel approach to indirectly compare two sensors through a third transfer target using the double-difference technique. For example, Wu et al. (2008) conducted an intercomparison of the two Moderate Resolution Imaging Spectroradiometers (MODISs) on board Terra and Aqua using the Advanced Very High Resolution Radiometer (AVHRR) on board the NOAA-KLM series of satellites as a transfer radiometer. Strow et al. (2008) employed radiative transfer calculations using global model output to indirectly compare AIRS and IASI at the finest scale. Aumann and Pagano (2008) chose the Real Time Global Sea Surface Temperature (RTGSST) from the National Centers for Environmental Prediction in the tropical ocean as a transfer target, and then used the double differences between AIRS − RTGSST and IASI − RTGSST to investigate the AIRS and IASI radiance difference at 2616 cm⁻¹. This study demonstrates that the relatively stable GOES imager can be used as a transfer radiometer to indirectly compare two polar-orbiting sensors. However, in order to fully cancel the calibration bias of the transfer radiometer, the following conditions must be met. First, the transfer radiometer must be stable during the time period when two polar-orbiting satellites pass overhead. Second, coincident observations of two polar-orbiting instruments with the transfer radiometer are expected to be sampled in similar atmospheric conditions, which can avoid the calibration bias related to a specific atmospheric environment. The GOES mean BTs for AIRS–GOES and IASI–GOES collocated observations in Figs. 8 and 9 have similar values, and their time series remain constant during the study period, suggesting that the GOES–IASI and GOES–AIRS collocations are sampled in the same environmental conditions. The advantages of using geostationary imagers as transfer radiometers include 1) a large number of coincident collocations, 2) various spectral coverage patterns, 3) the capability of making comparisons in the tropical regions, and 4) cross validation by switching different geostationary imagers. We believe that the double-difference method proposed in this study allows for checking the AIRS and IASI calibration accuracy and stability over a long period of time.

For the AIRS and IASI radiance difference, Strow et al. (2008) used the double-difference method to compare AIRS and IASI at the finest scale by choosing radiative transfer calculations as a transfer target. Tobin et al. (2008) directly compared AIRS and IASI at the finest spectral scale based on the SNO observations. They both found that AIRS and IASI agree on the order of 0.1 K, while AIRS is slightly warmer than IASI. Aumann and Pagano (2008) chose RTGSST as a transfer target. The double-difference statistics between AIRS and the RTGSST and IASI and the RTGSST also reveal a ∼0.02 K difference, and indicate that AIRS is slightly warmer than IASI. Our analysis is consistent with their findings, though it is confined at the spectral regions covered by the GOES imagers.