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Corresponding author: R. Chen, I.M. System Group at NOAA/NESDIS/Center for Satellite Applications and Research, 5825 University Research Ct #1500, College Park, MD 20740, USA. (firstname.lastname@example.org)
 The 30 years of observations from the High-Resolution Infrared Radiation Sounder (HIRS) longwave CO2 channels aboard the NOAA series of satellites are being used to detect climatological changes of cloud. However, the intersatellite radiance discrepancies in the channels need to be removed for the development of a consistent cloud series using HIRS data. By analyzing the intersatellite radiance comparisons at simultaneous-nadir-overpass locations for HIRS longwave CO2 channels onboard the NOAA and MetOp series of satellites, this study optimizes the spectral response functions (SRF) for each HIRS to generate a more consistent long-term set of observations. Intersatellite radiance biases as large as 5% are found for these channels; the spectral differences and spectral uncertainties are shown to be the main causes. To estimate the radiance change for a specific channel due to SRF difference and uncertainty, a linear model is developed to correlate the radiance change for the channel being analyzed with the spectral radiances in the eight selected HIRS channels. The hyperspectral measurements from the Infrared Atmospheric Sounding Interferometer on the MetOp satellite are used to simulate HIRS observations and estimate the parameters of the linear models. The linear models are applied to the NOAA and MetOp HIRS data at simultaneous-nadir-overpass locations to estimate the intersatellite radiance differences due to the SRF differences and uncertainties. The intersatellite mean radiance biases are minimized toward zero with residual maximum uncertainty less than 1% after the SRF differences and uncertainties are mitigated. Using the MetOp Infrared Atmospheric Sounding Interferometer as a reference, the optimized SRFs for every NOAA HIRS are found by effectively minimizing the root-mean-square values of the intersatellite radiance differences. The optimized shifts of the SRF can be as large as 3 cm−1.
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 Climate monitoring is very important for understanding climate change and mitigating related risks. The passive and active radiance measurements from satellite platforms can be used for global estimation of atmosphere, land, and ice properties (temperature, precipitation, ice coverage, etc.), which are key parameters for climate monitoring. The long-term observations from past and current weather/environmental satellites are widely used to develop climate data records (CDRs) [National Research Council, 2004] because they have significant temporal and global coverage. CDR development has very stringent quality requirements on the data from different satellite platforms. The accuracy and consistency in the satellite level-1b radiance data are fundamental because they affect satellite products and applications at all levels. However, intersatellite discrepancies are a common problem for the level-1b radiance data from different weather/environmental satellites because of the differences and uncertainties in the calibration systems. Several programs have been initialized to ensure as much as possible consistent accuracy among past and current satellite platforms; these include the Global Space-based Inter-calibration System by the World Meteorological Organization and the Climate Data Record Program by the National Climate Data Center. With support from the Climate Data Record Program, this study aims at improving the consistency of the 30+ years of High-resolution Infrared Radiation Sounder (HIRS) observations from the National Oceanic and Atmospheric Administration (NOAA) weather satellites and helping to build a CDR of cloud parameters using HIRS data.
 The NOAA series of polar satellites have been used operationally in the past 30 years for weather observations. NOAA-6, launched in 1979, starts the NOAA satellite series, and NOAA-19 is the latest. Each NOAA satellite carries a HIRS for determining atmospheric temperature and humidity profiles. The MetOp satellites launched by the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) also carry a HIRS. The 30+ years of HIRS observations from the NOAA and MetOp satellites are being used in climate studies [Bates et al., 1996; Wylie and Menzel, 1999; Shi et al., 2008]. Wylie et al.  used the long-wave CO2 channels of HIRS (702 cm−1, 716.5 cm−1, 731.7 cm−1, and 748.8 cm−1) to develop a 22 year cloud climatology. Previous studies have shown that consistency in the HIRS observations from different satellites is an essential ingredient for the climate studies. However, significant discrepancies have been found in the HIRS radiance measurements between different satellites [Cao et al., 2005; Shi et al., 2008, Cao et al., 2009]. The intersatellite spectral differences and uncertainties have been shown to be the major causes for the intersatellite radiance biases of HIRS long-wave CO2 channels [Cao et al., 2009; Chen and Cao2012]. HIRS spectral differences between satellites are evident in the prelaunch measured spectral response functions (SRF). In addition, uncertainties or errors in HIRS SRF measurements due to other factors (e.g., the ambient environment differences between prelaunch measurement and satellite orbit) can contribute to the HIRS channel spectral discrepancies. The measurement from hyperspectral instruments has been widely used to correct the biases found in regular sounder and imager spectral measurements [Tobin et al., 2006; Cao et al., 2009; Doelling et al., 2012]. Cao et al.  used the Infrared Atmospheric Sounding Interferometer (IASI) observations from MetOp-A to calculate the HIRS radiances; they showed that the true SRF-induced intersatellite biases can be separated from SRF prelaunch measurement uncertainties or errors. Chen and Cao  developed a comprehensive orbital analysis method to analyze collocated IASI and HIRS data from MetOp-A and found that the SRF error is the most important cause for the radiance biases of the HIRS long-wave CO2 channels (e.g., 0.5 cm−1 SRF error can cause a bias larger than 0.5 K). The radiometric and spectral recalibration parameters from their study make the MetOp HIRS data traceable to IASI data with uncertainties less than 0.1 K for the four long-wave CO2 channels. However, the spectral recalibration of HIRS long-wave CO2 channels has never been studied for the earlier NOAA satellites because there are no available simultaneous hyperspectral measurements. A major challenge is to develop relationships that convert radiance discrepancies into appropriate spectral parameters. Chen and Cao  performed a preliminary analysis of the intersatellite HIRS radiance discrepancies for the NOAA series of satellites and reported initial progress for the spectral recalibration of HIRS channel 4. They used one orbit of IASI hyperspectral measurements and MetOp HIRS SRFs to develop an experimental relationship between the radiance change and SRF shift for all HIRS channel 4. However, the accuracy of this simple relationship is questionable because each HIRS has different SRFs and results from one-orbit of data may not be reliable for all four seasons. Moreover, the impact of SRF differences is not separated from that of SRF uncertainties. Therefore, further study is needed to provide a more reliable spectral recalibration for all four long-wave CO2 channels onboard the NOAA satellites.
 Thus, following up on Chen and Cao , this study aims to ensure consistency and reduce uncertainty in the HIRS longwave CO2 channel (channels 4, 5, 6, and 7) observations from the 30+ years of NOAA satellites. The HIRS measurements between the successive NOAA satellites (referred as a satellite pair hereafter) are compared at simultaneous-nadir-overpass (SNO) locations to build a time series of the intersatellite HIRS biases. The IASI measurements from MetOp-A [Chen and Cao, 2011] are used as a reference to analyze the time series of intersatellite biases. This study focuses on the spectral causes (i.e., SRF differences and uncertainties) for intersatellite HIRS biases because of their major contribution in the HIRS longwave CO2 channels, as suggested in previous studies [Cao et al., 2009; Chen and Cao, 2012]. Cao et al.  reported that the impact of SRF uncertainties can be effectively demonstrated by shifting HIRS SRFs. For a given SRF shift or SRF difference, the corresponding radiance change is determined by the top-of-atmosphere (TOA) spectrum. Because the TOA spectrum changes as location and time changes, the SRF-induced HIRS biases generally show scene-temperature dependencies and seasonal variations [Cao et al., 2009; Shi at al., 2008]. Chen and Cao  showed that optimized SRF shifts can effectively reduce the scene-temperature dependencies and seasonal variations of the MetOp-A HIRS biases relative to IASI (i.e., mean biases toward zero with residual uncertainties less than 0.1 K). The collocated TOA spectra measured by hyperspectral infrared instruments (e.g., IASI) are used to estimate the HIRS radiance changes caused by a given SRF shift [Chen and Cao, 2012]. However, there are no collocated hyperspectral measurements before NOAA-15. To estimate SRF-induced HIRS biases for the earlier NOAA satellites, this study uses HIRS radiance measurements in the selected channels as a replacement for TOA spectra measured by hyperspectral instruments. The physical reason for the replacement is that HIRS radiance measurements in the selected channels and TOA spectra are correlated because both are determined by surface temperature and atmospheric temperature, humidity, and CO2 profiles. Linear models are developed to estimate the radiance change for a specific channel as a function of the spectral radiances in eight selected HIRS channels. One year of sampled hyperspectral measurements from the IASI on MetOp-A are used to simulate HIRS observations for each NOAA satellite and to estimate the coefficients of the linear models. The resulting linear models are applied to historical HIRS data for the spectral calibration. The spectral recalibration process consists of three steps: deducting the impact of prelaunch measured SRF differences from the intersatellite radiance differences, estimating the intermediate SRF shifts corresponding to the remaining intersatellite radiance differences, and using MetOp-A IASI as a reference to determine the final optimized SRF for each NOAA HIRS. Each HIRS is directly calibrated with respect to MetOp-A IASI measurements at SNO locations for satellites from NOAA-15 onwards. For the pre-MetOp satellites before NOAA-15, the spectral recalibration of each HIRS depends on the intersatellite calibration for each NOAA satellite pair and uses the recalibrated HIRS from the later satellite as a reference (which is traceable back to MetOp-A IASI along the consecutive satellite pair chain). The resulting recalibrated SRFs generate more consistent long-term measurements from the HIRS longwave CO2 channels on the NOAA satellite series.
 Section 'Data and Methodologies' of this study introduces the HIRS data from the NOAA and MetOp satellite series, discusses HIRS operational calibration, describes the SNO methods for collocating HIRS observations between different satellites, and explains how to use IASI hyperspectral measurements to simulate the HIRS measurements. In section 'Analysis of SNO Data', the intersatellite bias of HIRS CO2 channels 4–7 for NOAA and MetOp satellite series are shown in a time series and the spectral differences are verified as the major cause for the large intersatellite radiance discrepancies. Then, linear models are developed to estimate the HIRS radiance changes for specific channels using SRF differences/uncertainties and spectral radiances in eight selected HIRS channels. Finally, based on the three-step spectral recalibration procedure introduced above, the SRFs of the longwave HIRS CO2 channels 4–7 are recalibrated for NOAA-9 to NOAA-19. Section 'Impact of the Spectral Recalibration on Climate Studies of Clouds' discusses the impact of calibration corrections on trends of cloud properties. Section 'Conclusions and Future Studies' summarizes the results and discusses future studies.
2 Data and Methodologies
 This study uses HIRS level-1b data from the NOAA and MetOp series of satellites and IASI level-1c data from MetOp satellite. The data are archived at NOAA's Comprehensive Large Array-data Stewardship System. IASI hyperspectral measurements are convolved with HIRS spectral response functions to simulate HIRS observations and to study the impact of spectral differences. HIRS measurements from consecutive NOAA satellites are spatially and temporally matched for intersatellite comparisons at SNO locations [Cao et al., 2004, 2011].
 The High-Resolution Infrared Radiation Sounder, on board the NOAA and EUMETSAT polar orbiting satellites, measures scene radiance measurements in 1 visible and 19 infrared channels. The HIRS instantaneous field-of-view is 10 km at nadir for HIRS-4 and 20 km for HIRS-3 and HIRS-2. Satellites before NOAA-15 carried HIRS-2; NOAA-15 through NOAA-17 carry HIRS-3, and NOAA-18, NOAA-19, and MetOp-A, MetOp-B carry HIRS-4. The long-wave CO2 channels of HIRS (channels 4, 5, 6, and 7) are investigated in this study to improve intersatellite consistency for use in a long-term cloud study. IASI is onboard the EUMETSAT MetOp-A and -B satellites, which also carry HIRS/4. The IASI provides hyperspectral measurements of scene radiance in the spectral range of 645–2760 cm−1 with 0.25 cm−1 spectral sampling interval, 0.5 cm−1 spectral resolution, and 10 km nadir instantaneous field-of-view size. The relative radiometric accuracy of IASI is estimated to be around 0.1 K in previous studies [Cao et al., 2009; Strow et al., 2008].
 Figure 1 shows the typical IASI-measured brightness temperatures over the HIRS long-wave CO2 spectral range along with the prelaunch measured SRFs from NOAA-9 to NOAA-19 (referred as from N9 to N19 in this study) and MetOp-A satellite (referred as M2 in this study). Central wave number (CWN) is derived from the SRF by splitting the area under the SRF into two equal halves. In Figure 1 and Table 1, the SRF shapes and central wave numbers (CWN) of HIRS channel 4–7 exhibit some differences between satellite platforms. Table 1 shows the CWNs of the HIRS CO2 channels on the NOAA and MetOp satellites. CWN differences between consecutive NOAA polar satellites can be as large as 3 cm−1. In Figure 1, the IASI measured TOA brightness temperatures show some obvious spectral structure including the Q-branch near 720 cm−1. Thus, SRF differences between HIRS instruments contribute to intersatellite HIRS biases because different SRFs measure different parts of TOA spectrum. As discussed in the previous section, in addition to SRF differences found in prelaunch measurements (referred to as SRF differences hereafter), uncertainties and errors in the prelaunch SRF measurements (referred to as SRF uncertainties hereafter) also contribute to intersatellite HIRS channel radiance biases. In this study, the IASI hyperspectral data are used to simulate HIRS observations and study the contributions from both SRF differences and uncertainties.
Table 1. Center Wave Number (in cm−1) of HIRS Channels 4, 5, 6, and 7 for Different Satellites
 To simulate the radiance measurements for HIRS channels 4–7, hyperspectral IASI measurements are convolved with HIRS SRFs. This method has been used in the previous studies to simulate HIRS measurements with IASI [Chen and Cao, 2011, 2012; Cao et al., 2009]. The simulated HIRS radiance for channel n, Ln, is derived as follows:
where Fn(v) is the HIRS SRF in channel n, R(v) is the IASI-measured spectra radiance, vn1 and vn2 define the wave number range of the HIRS SRF in channel n.
 Simultaneous-nadir-overpass methodology is used to find collocated events between consecutive NOAA satellites, which include NOAA-9, -10, -11, -12, -14, -15, -16, -17, -18, and -19. Because there is no temporal overlap between NOAA-8 and NOAA-9, NOAA-6, -7, and -8 are not included in this study. The intersatellite calibration of these three early NOAA satellites will be added in future studies that include geostationary satellite measurements. Figure 2 demonstrates the NOAA intersatellite calibration process. For the satellites before NOAA-18, the HIRS measurements from successive NOAA satellites are compared at SNO locations that happen frequently between morning and afternoon polar orbiting satellites. NOAA-18 and NOAA-19 are both afternoon polar satellites and their SNO events many not happen for several months, therefore the HIRS measurements from NOAA-18 and NOAA-19 are compared with recalibrated MetOp-A (M2) HIRS [Chen and Cao, 2012] at SNO locations directly. In this study, intersatellite comparisons of HIRS radiances are carried out for 10 satellite pairs, including N9/N10, N10/N11, N11/N12, N12/N14, N14/N15, N15/N16, N16/N17, N17/N18, N18/M2, and N19/M2. For each satellite pair, an intersatellite SRF shift (referred to as intermediate SRF shift hereafter) is calculated to minimize the root-mean-square values of intersatellite radiance differences. After NOAA-15, HIRS measurements are compared with the IASI-simulated HIRS measurements directly to recalibrate the HIRS SRF. Before NOAA-15, the final SRF shifts are calculated by adding the intermediate SRF shifts of all the prior satellite pairs (as shown in Figure 2).
 Because all NOAA/MetOp satellites fly in Sun synchronous orbits, the SNO events between these satellites happen over polar regions during the normal operational periods. SNO events from both southern and northern polar regions are included in this study. The data matching and processing follows the methods described in Cao et al. . For each SNO event, the collocated data are averaged in a nadir window consisting of 10 cross-track pixels and 11 scans. Shifting one HIRS data set relative to the other by a variable number of pixels in both the column and row directions further optimizes the pixel-by-pixel match up; this radiance correlation between the data sets compensates for possible large and systematic geolocation errors. The standard deviations of intersatellite radiance differences within a nadir window are generally less than 0.5 K for the HIRS long-wave CO2 channels [Cao et al. 2005]. The intersatellite HIRS biases within a nadir window are averaged for each SNO event. Using data from all SNO events, mean values and standard deviations of intersatellite HIRS biases are calculated. To reduce uncertainties, the absolute deviation of HIRS bias for an SNO event is empirically required to be less than three times of the standard deviation; less than 7% of the SNO events are filtered out by this criterion. Comparison of HIRS measurements at SNO locations between consecutive satellites establishes a time series of intersatellite biases of HIRS long-wave CO2 channels for the NOAA and MetOp-A satellites, which is displayed and analyzed in the following sections.
3 Analysis of SNO Data
3.1 Intersatellite Biases for HIRS Channels 4, 5, 6, and 7
 Figure 3 shows the time series of intersatellite biases of HIRS long-wave CO2 channels for NOAA satellite series (from NOAA-9 to NOAA-19), where solid lines come from South Pole SNOs and dashed lines from North Pole SNOs. The intersatellite HIRS biases have a clear seasonal variation and show different patterns between the two polar regions. The most likely reason is that the HIRS radiance biases caused by spectral issues generally have some dependence on scene temperature [Cao et al., 2009; Shi et al., 2008; Chen and Cao, 2011]. Figure 3 shows there are obvious intersatellite discrepancies for HIRS channels 4, 5, and 7. For example, NOAA-14 HIRS channel 4 radiances at SNO locations in Figure 3a could be nearly 4% (around 1.8 K for a typical polar scene brightness temperature of 215 K) larger than those for NOAA 15, NOAA-18 HIRS channel 5 in Figure 3b could be nearly 4% (around 1.9 K for a typical polar scene brightness temperature of 215 K) less than those for MetOp-A, and NOAA-16 HIRS channel 7 in Figure 3d could be nearly 2% (around 1.0 K for a typical polar scene brightness temperature of 237 K) larger than those for NOAA-17. Figure 3c shows that the intersatellite radiance differences of HIRS channel 6 are generally within 1% (around 0.5 K for a typical polar scene brightness temperature of 232 K), which is much less than those of channels 4, 5, and 7. Because HIRS long-wave CO2 channels 4, 5, 6, and 7 all share the same radiometric calibration system, spectral causes for the intersatellite radiance differences (instead of radiometric causes) are more likely given that HIRS channel 6 shows much smaller intersatellite discrepancies than the other three channels. Figure 1 shows that the HIRS channel 6 is located in a relatively flat region of the brightness temperature spectrum, while there are obvious slopes in the spectrum for HIRS channels 4, 5, and 7. Cao et al.  used IASI data simulated HIRS radiances for the long-wave CO2 channels and suggested that the temperature-dependent intersatellite HIRS biases are likely caused by intersatellite SRF differences.
 In Figure 1, the HIRS on different satellites generally show some differences in prelaunch measured SRF. As discussed in the previous sections, both the SRF differences and the SRF uncertainties contribute to the channel spectral differences between satellites and affect the intersatellite radiance biases. As such, the intersatellite difference of exact on-orbit HIRS SRF consists of differences caused by the prelaunch measured SRF including measurement uncertainty, which is summarized in equations ((2)) and ((3)).
where SRF is the true SRF on orbit DSRF is the prelaunch measured SRF, which may have errors, SRF _ u represents the SRF uncertainty, DSRF is the real on-orbit intersatellite SRF difference, DSRF _ p is the intersatellite difference of prelaunch measured SRF, and DSRF _ u is spectral difference contributed by SRF uncertainties. The impacts of DSRF _ p and DSRF _ u are separated and analyzed in the following sections.
3.2 The Impact of Intersatellite Spectral Response Function Differences
 As shown in Figure 1 and equation ((1)), the simulated HIRS radiance measurement is the convolution of the radiance spectra with the HIRS SRF. Therefore, the impact of DSRF _ p on intersatellite radiance bias is dependent on TOA spectra. Because the NOAA satellite series does not carry any hyperspectral instrument, the TOA spectral measurements for the SNO collocations are not available. However, as an infrared sounding instrument, the HIRS measurements in the CO2 and water vapor channels are determined by surface temperature as well as atmospheric temperature and humidity profiles. This is also true for the TOA spectrum. Thus, the HIRS radiance measurements for all CO2 and water vapor channels are expected to be useful for estimating the radiance bias contributed by DSRF _ p. In this study we use HIRS channels 2, 3, 4, 5, 6, 7, 8, and 12 for estimating the radiance bias contributed by DSRF _ p. HIRS channels 2–7 are CO2 channels, channel 8 is a window channel, and channel 12 is a water vapor channel. These HIRS channels are selected because they are within or close to the spectral range of the CO2 channels or water vapor channels, for which we intend to perform intersatellite calibration. To estimate the HIRS channel radiance biases between two satellites due to SRF differences, the following linear model is developed:
where m and n are the satellite numbers (from 9 to 19), i (4, 5, 6, and 7) and j (2, 3, 4, 5, 6, 7, 8, 12) are the HIRS channel numbers, is the intersatellite radiance bias of channel i between satellite m and satellite n, which is contributed by DSRF _ p, and Rj is the HIRS radiance measurement of channel j from satellite n. To derive the coefficients and constants , IASI measurements from MetOp-A are used to simulate HIRS measurements based on equation ((1)). The fifth MetOp orbit of the first day of each month in 2009 is used for the simulation. Only IASI pixels located south of 70°S or north of 70°N are used to restrict geographical coverage to the SNO events between NOAA satellites. As shown in equation ((1)), SRFs of the HIRS channels from satellites m and n are convolved with the hyperspectral measurements from each IASI pixel to simulate HIRS radiance measurements for channels i and j, including , , and . Then the coefficients and constants can be estimated based on the linear regression between and .
 The coefficients and constants are derived for all 10 satellite pairs shown in Figure 3. Table 2 lists the coefficients for estimating the radiance bias contributed by DSRF _ p between NOAA-19 and MetOp-A. To validate the coefficients in Table 2, sampled IASI data from year 2010 are selected to simulate HIRS measurements using the same method. The ninth MetOp orbits of the 18th day of each month are used for validation purpose. As before, the and are calculated for each IASI pixel from the sampled year 2010 data. Then the estimations of are made using equation ((4)) and the coefficients in Table 2. Figure 4 compares the simulated true intersatellite HIRS radiance bias contributed by DSRF _ p using IASI and the estimated intersatellite HIRS radiance bias using the linear model. The estimated intersatellite HIRS biases contributed by DSRF _ p are in high agreement with the true values for the four HIRS channels; the errors are generally within 0.1%t. A few outliers for channel 7 are possibly from the IASI pixels with unusual weather or surface conditions for which the model accuracy decreases. The coefficients and constants for other satellite pairs generally show similar performance (the errors are generally within 0.1 %) in estimating the intersatellite HIRS biases contributed by DSRF _ p.
Table 2. Coefficients for Estimating the Radiance Bias Contributed by DSRF _ p Between NOAA-19 and MetOp-A. aj is the Linear Coefficient for Channel j and c is the Constant
 The linear model of equation ((4)) is applied to the data shown in Figure 3 to estimate the intersatellite HIRS biases due to DSRF _ p for the 10 satellite pairs, which are then subtracted from the total intersatellite HIRS bias shown in Figure 3. Figure 5 shows the remaining intersatellite radiance biases after the subtraction. The intersatellite radiance biases are significantly changed in many cases (e.g., N18/M2 for channel 4, N17/N18 for channel 5 and channel 7) after the impact of DSRF _ p is taken into account. However, the changes for channel 6 are noticeably less, confirming it is less sensitive to spectral change than the other channels. For channels 4, 5, and 7, after removing the impact of DSRF _ p, the biases are reduced for some satellite pairs (e.g., N18/M2, N16/N17, N14/N15), but are increased for some other intersatellite pairs (e.g., N12/N14, N11/N12, N10/N11). Overall, in Figure 5, there are still obvious intersatellite biases (e.g., larger than 1%) for HIRS channels 4, 5, and 7; channel 6 biases are well behaved (less than 1%). Figure 5 suggests that the HIRS SRFs (prelaunch measured) contain uncertainties (SRF _ u) that could cause significant intersatellite channel radiance biases. To further investigate the remaining intersatellite biases in Figure 5 for HIRS channel 4, 5, and 7, the impact of DSRF _ u on the HIRS intersatellite biases of these three channels is investigated in the following section.
3.3 The Impact of Spectral Response Function Uncertainties
 The impact of SRF uncertainties (SRF _ u) on HIRS radiance observations may be studied by shifting the prelaunch measured SRF. The impact on HIRS radiance observation of shifting SRFs is determined by the amount of SRF shift and the TOA radiance spectra. As discussed in the previous section, HIRS observations at CO2 and water vapor channels can be used to estimate the radiance change for a given spectral change. We assume the following linear model to predict the HIRS radiance change caused by a given SRF shift using the spectral radiances in the seven CO2 channels and one water vapor channel.
where m is the satellite number (from NOAA-9 to NOAA-19, and MetOp), i (4, 5, and 7) and j (2, 3, 4, 5, 6, 7, 8, 12) is the HIRS channel number, is the radiance change of HIRS channel i for satellite NOAA-m, is the HIRS radiance measurement of channel j for satellite m, and ΔSRF is the SRF shift. To derive the coefficients and constants , IASI data over the polar regions from the fifth MetOp orbit of the first day of each month in year 2009 is selected to simulate the HIRS measurements. SRFs of the HIRS channels are shifted 1 cm−1 up and down before they are convolved with the TOA spectral measurements from each selected MetOp IASI pixel. To run the regression using equation ((5)), the radiance difference between the two simulations is considered as , and the relative SRF shift of 2 cm−1 between the two simulations is considered as ΔSRF. Then the coefficients and constants are estimated based on the linear regression between and .
 The coefficients and constants used for estimating MetOp HIRS radiance changes caused by SRF shifts are listed in Table 3. To validate the coefficients in Table 3, the IASI data over polar region from the ninth MetOp orbits of the 18th day of each month in year 2010 are selected to simulate HIRS measurements using the same methods. To calculate the MetOp HIRS radiance changes () for shifting SRF by −3 cm−1, −1.5 cm−1, 1.5 cm−1, and 3.0 cm−1, the shifted SRFs are convolved with the selected IASI spectra measurements. Estimations of are made using equation ((5)) and the coefficients in Table 3 for the four selected values of SRF shift. Figure 6 compares the IASI-simulated MetOp HIRS radiance changes and the linear model estimated MetOp HIRS radiance changes for different SRF shift values. The estimation of MetOp HIRS radiance changes are in high accuracy for the three HIRS channels (channels 4, 5, and 7); the errors are generally within 0.2% for 1.5 cm−1 SRF shift and within 0.5% for 3 cm−1 SRF shift. The errors in Figure 6 (branching, slope, etc.) are probably caused by the linear assumption of the model. The coefficients and constants for other satellites show a similar performance (the errors are generally within 0.2 % for 1.5 cm−1 SRF shift and within 0.5% for 3 cm−1 SRF shift) in estimating the HIRS radiance change caused by SRF shift.
Table 3. Coefficients for Estimating MetOp-A HIRS (Referred as M2) Radiance Change Caused by Shifting SRFa
aβj is the linear coefficient for channel j and c is the constant.
 To investigate the remaining intersatellite biases in Figure 5 for HIRS channels 4, 5, and 7, coefficients and constant for each HIRS on the 10 NOAA satellites are used to estimate the HIRS radiance changes associated with a certain value of SRF shift. An intersatellite SRF shift, which effectively represents the impact of SRF uncertainties and minimizes the root mean square value of the intersatellite radiance biases, is estimated for the data shown in Figure 5 using equation ((5)) and the derived coefficients. This “intermediate SRF shift” must build on the successive satellite intermediate SRF shifts to form the “final SRF shift,” which is then traceable to MetOp IASI; this is discussed in the next section. Figure 7 shows the intersatellite HIRS biases for HIRS channels 4, 5, and 7 after the SRFs are shifted to minimize root mean square value of the intersatellite biases; now both SRF differences and SRF uncertainties have been accounted for. Channel 6 is not studied in this section because its intersatellite radiance discrepancies are relatively small (within 1%).
 In Figure 7, after effectively shifting the SRFs, the intersatellite mean radiance biases are significantly reduced for HIRS channels 4, 5, and 7 with residual maximum uncertainty of less than 1%, which is comparable with that for channel 6. Figure 8 shows the intermediate SRF shifts for channels 4, 5, and 7 for each of the 10 HIRS, which minimize the root-mean-square values of the intersatellite radiance bias with the overlapping HIRS. The blue bar represents data from the North Pole and red bar represents data from the South Pole. The SRF shifts for North Pole HIRS data are generally consistent with those for the South Pole. The intermediate SRF shifts for the two polar regions are used for the calculation of final HIRS SRF shift in the following sections.
3.4 Spectral Recalibration of NOAA HIRS Concurrent With MetOp IASI
 Simultaneous-nadir-overpass events can be found between MetOp-A and NOAA-15, -16, -17, -18, and -19. Because of the high spectral resolution, MetOp-A IASI measurements provide an ideal reference for recalibration of the HIRS SRFs for these satellites. To simulate the NOAA HIRS observations, the hyperspectral MetOp-A IASI measurements at SNO locations are convolved with HIRS SRFs. Figure 9 shows the SNO comparisons between NOAA HIRS measurements and the simultaneous IASI simulations, where columns 1 and 2 show South Pole results and columns 3 and 4 show North Pole results; columns 1 and 3 use the operational SRFs (prelaunch measurement) and columns 2 and 4 use the SRFs after the optimized shifts (for channels 4, 5, and 7—the SRF of channel 6 is not changed in this study). The NOAA-16 HIRS biases relative to IASI have the same trend (differences are generally within a few tenths of a percent) as the NOAA-16 HIRS biases relative to AIRS shown in a previous study [Wang et al., 2007]. HIRS radiance biases relative to IASI for channels 4, 5, and 7 using the operational SRFs can be as large as 1% or 2% and highly variable (e.g., South Pole, NOAA-15 and NOAA-18). After the HIRS SRFs are shifted to minimize the root-mean-square differences between HIRS and IASI, the residual uncertainties are within 1% and mean biases are significantly reduced toward zero. The remaining biases for channels 4, 5, and 7 are generally comparable and consistent with that for channel 6, which is not sensitive to spectral error. In Figure 9, HIRS channel 6 shows warm biases relative to IASI for all involved satellites, which may be caused by radiometric calibration errors and need to be further investigated in a future study.
3.5 Spectral Recalibration for Earlier NOAA HIRS not Concurrent With MetOP IASI
 For the NOAA satellites before NOAA-15, there are no SNO events with MetOp-A. As shown in Figure 2 and equation ((6)), the final SRF shift for each HIRS on these earlier NOAA satellites can be estimated by adding the intermediate SRF shift to the final SRF shift of the following satellite.
where n and i is the NOAA satellite number, is the optimized on-orbit CWN, is the prelaunch measured CWN, is the final optimized SRF shift for NOAA-n satellite, is the intermediate effective SRF shift for NOAA-n satellite to minimize its bias with the following satellite. The final SRF shifts for the historical HIRS are shown in Figure 10 (from N9 to N14), ranging between 0 and 3 cm−1. In equation ((6)), from NOAA-14 backward to NOAA-9, each HIRS uses the recalibrated HIRS of the following satellite as its reference. Because NOAA-15 HIRS is calibrated using MetOp-A IASI, the spectral recalibrations for each of these historical HIRS are traceable to IASI.
 Because the spectral recalibration depends on the direct comparison with IASI for NOAA-15 onward and depends on the intersatellite HIRS comparisons for the satellites before NOAA-15, it would be useful to inspect the consistency between the two methods. Both methods for recalibration are possible for NOAA-15 through -19. Figure 11 shows the results. The single intermediate SRF shift for NOAA-18 HIRS and NOAA-19 HIRS is determined from direct comparison with the recalibrated MetOp-A HIRS, which is traceable to IASI with an uncertainty less than 0.1 K [Chen and Cao, 2012]; this intermediate SRF shift is found to be close to the final SRF shift (from direct comparison with IASI) for these two satellites. For NOAA-15, -16, and -17, the accumulated intermediate SRF shifts from HIRS intercomparisons are found to be within 0.3 cm−1 of the final SRF shift (determined by direct IASI comparison). These results suggest a good consistency between the two methods.
4 Impact of the Spectral Recalibration on Climate Studies of Clouds
 The World Meteorological Organization's Global Climate Observing System (GCOS)  defines the requirements for the essential climate variables, which include cloud top pressure (CTP). Our study uses CTP to demonstrate the impact of the HIRS spectral recalibrations on the long-term cloud trends. In GCOS, the accuracy requirement for CTP is less than 50 hPa and the stability requirement of CTP is less than 15 hPa. HIRS channels 4 and 5 are the two most important channels for the CO2-slicing method retrieving CTP. Based on a previous study [Gross et al., 2004], 1 cm−1 SRF accuracy in HIRS channels 4 and 5, which is equivalent to 1.5 K brightness temperature accuracy, is approximately needed for the CO2-slicing method to meet the 50 hPa accuracy requirement. If we assume the sensitivity of the CTP to SRF shift is linear, 0.3 cm−1 SRF stability (equivalent to 0.5 K in brightness temperature) is approximately needed to meet the 15 hPa stability requirement. Our results show that the HIRS SRF traceable to IASI are accomplished with SRF corrections comparable to or larger than 1 cm−1 for many cases (e.g., HIRS channels 4 and 5 on N15, N18, and N19). This suggests that the SRF corrections made in this study are very important for the HIRS CTP estimates to meet the 50 hPa accuracy requirement. The original intersatellite HIRS radiance biases were as large as 3 to 4% (e.g., N14/N15 and N16/N17 for channel 4, N17/N18 and N18/M2 for channel 5) or about 1.5 to 2 K brightness temperature at typical polar scene temperatures. These intersatellite biases cause instabilities 3 to 4 times larger than the 15 hPa GCOS requirement for CTP trends. Our SRF recalibration reduces the mean intersatellite HIRS biases toward zero with the residual uncertainty less than 1%, meeting the GCOS requirements.
5 Conclusions and Future Studies
 To ensure the consistency and reduce the uncertainties for the climate studies of clouds using NOAA HIRS data, this study explores the intersatellite calibration of HIRS measurements from the NOAA satellite series. The spectral differences and spectral uncertainties are shown to be the most probable cause for the large intersatellite radiance biases of channels 4, 5, and 7. To quantitatively recalibrate the SRFs for HIRS longwave CO2 channels on the NOAA satellites series, the impacts of SRF uncertainties and SRF differences are separated and analyzed. A linear model is developed to correlate the radiance change and the spectral radiances in the eight selected HIRS channels. The hyperspectral measurements from the IASI on MetOp-A satellite are used to simulate HIRS observations and estimate the coefficients for the linear models. It is found that intersatellite radiance biases remain for HIRS channels 4, 5, and 7 even after taking into account the intersatellite differences in prelaunch measured SRFs. Using the MetOp-A IASI as a reference, the SRFs of the HIRS on NOAA-9 through -19 are recalibrated based on the optimized SRF shifts with CWN changes ranges between 0 and 3 cm−1. Shifting the SRFs effectively minimized the intersatellite mean radiance biases toward zero for HIRS channels 4, 5, and 7 with residual maximum uncertainty of less than 1%.
 This study established IASI as an on-orbit infrared calibration standard and made HIRS calibration traceable to IASI with small uncertainties. This will ensure the calibration consistency and quality for long-term climate studies, reduce the uncertainties of critical climate trends, and therefore facilitate construction of long-term climate records to support NOAA's strategic goal of predicting and assessing climate change. The linear regression models presented in this study represent a new approach that utilizes the relationships derived from a state-of-the-art hyperspectral infrared instrument to recalibrate current and earlier infrared instruments. Due to the absence of SNO events between NOAA-8 and NOAA-9, the spectral recalibration for the satellites before NOAA-9 is not investigated in this study. Future work using geostationary sensors with SNOs that include the satellites before NOAA-9 is needed to complete the time series.
 The authors wish to thank the anonymous reviewers of this manuscript for their constructive comments and suggestions. Thanks are extended to Pubu Ciren, Likun Wang, and the GSICS program for early processing and verification of the historical NOAA HIRS data. This work is partially funded by the Center for Satellite Applications and Research and the Climate Data Record Program by the National Climate Data Center at NOAA/National Environmental Satellite, Data, and Information Service.The manuscript contents are solely the opinions of the authors and do not constitute a statement of policy, decision, or position on behalf of NOAA or the U.S. government.