Nonlinearity correction (NL) is critical for the quantitative applications of observations from space, particularly for those weak signal measurements in atmospheric absorption spectral regions like hyperspectral soundings in infrared band (i.e. outcomes of GIIRS). In traditional, such a NL processing is implemented according to some prelaunch tests which are inaccurate in theory with a unique onboard blackbody. Fortunately, this manuscript is well written to describe a novel method for NL correction, where the NL parameter μ is firstly determined from in-lab testing and further utilized together with an iterative algorithm to ensure both the linearity and the NL coefficients to be estimated optimally, and some more preliminary assessments are also provided. Meanwhile, the proposed NL method is theoretically suitable for both infrared and microwave sensors. Therefore, this article is recommended to be accepted for publication in AMT with a few minor improvements as given by the following comments.

Minor comments:

1. The NL parameter μ is originally proposed and applied in microwave sensors. Please supply some more detailed explanations about its feasibility for infrared ones (i.e. GIIRS).
2. In section 4, three influencing factors, i.e. SRF variation under in-orbit condition, non-ideal onboard BB source and the amplification effect of NL coefficient upon linearity one in the traditional method, are briefly discussed. It is recommended to add the corresponding subtitles to make these issues more clearly for readers.
3. In figure 2, three labelled information in parallelograms need to be given in a more accurate manner. For example, these parallelograms may be deleted directly.

The manuscript deals with the problem of nonlinear correction in hyperspectral infrared sounders of GIIRS. The authors attempt to provide a new nonlinear correction method based on the NL parameter estimation from the pre-launch radiometric calibration tests. However, the authors seem do not understand the cause of nonlinearity in infrared sounders, so the correction methods provided are not clear in logic. The final calibration results after nonlinear correction are not in accord with the calibration characteristics of similar instruments. In addition, the English writing and illustrations are terrible. I recommend that this manuscript be rejected for publication. I also recommend that the editor find other experts who are familiar with infrared sounder radiometric calibration to review this manuscript again. (e.g. Robert Knuteson, David Tobin, and Joe Taylor from University of Wisconsin–Madison, Dorothee Coppens from EUMETSAT, Laura Le Barbier from CNES).

My comments:

1. line 15~17 in abstract, “the NL parameter μ independent of different working conditions (namely the thermal fields from environmental components) can be achieved from laboratory results before launch and directly utilized for in-orbit calibration.” The author needs to explain why the nonlinear coefficient is not affected by the temperature field. I don't find any discussion of this assertion in the paper.
2. line 17~19, “to overcome the inaccurate linear coefficient from two-point calibration influencing the NL correction, an iteration algorithm is established to make both the linear and the NL coefficients to be converged to their stable values with the relative errors less than 0.5% and 1%” Nonlinear correction should be done before radiometric calibration, how to ensure the applicability of iteration coefficient? The nonlinear response of CrIS is only 0.13%, and the remaining 1% nonlinear coefficient is still too large.
3. line 21~23, “the final calibration accuracy for both all the detectors and all the channels with the proposed NL correction method is validated to be around 0.2-0.3K at an ordinary reference temperature of 305K.” The radiometric calibration deviation after nonlinear correction should meet the calibration accuracy requirements at a series of blackbody temperatures, rather than just one temperature point, especially the temperature is close to the onboard blackbody temperature, and the deviation without nonlinear correction is inherently small, so this conclusion is not convincing.
4. line 23~25, “in the classical method, the relative error of NL parameter immediately transmitting to that of linear one in theory which will introduce some additional errors around 0.1-0.2K for the interfered radiance inevitably, no longer exists.” This statement is ambiguous.
5. line 25~26, “the adopted internal BB with the higher emissivity will produce the better NL correction performance in practice.” Nonlinear response is a characteristic of the non-ideal IR sounder, independent of the emissivity of the blackbody. The authors need to provide clear verification evidence to explain why the use of high emissivity blackbodies will lead to better NLC performance.
6. line 44~45, “It was partially validated by both domestic and international users that the spectral and radiometric accuracies of the measured spectra from FY-4A/GIIRS V3 algorithm for L1 data show a well behaved performance for both LWIR and MWIR bands” The authors need to be honest and admit that GIIRS-A is not good due to spectral contamination, spectral calibration, and radiometric calibration. the cited paper only presents the result of a short period of time and does not represent long-term performance.
7. line 46~47, “in order to increase the radiometric accuracy further, a new NL correction method which is aimed to carry out the NL processing of GIIRS is proposed in this article” The authors claimed in the article that they are committed to improve the radiation calibration accuracy of GIIRS, but in the end they do not give the actual application of nonlinear correction in GIIRS-A or GIIRS-B, just some pre-launch test results of GIIRS-B.
8. line 52~54, “for the LWIR and MWIR, the detectors have larger NL contributions to be corrected against those of SWIR which are negligible small without correction (Qi et al., 2020; Zavyalov et al., 2011).” According to the cited paper, the authors here consider the GIIRS mid-wave band to be CrIS or HIRAS mid-wave band, but referring to the parameters in Table 1, the infrared semiconductor material of 3 to 6 μm does not show a high nonlinearity, and in fact the GIIRS mid-wave band is more similar to the short-wave band of CrIS. I have learned from Qi and Lee in the CMA that GIIRS's mid-wave should be short-middle wave band (SMWIR), as defined by GIFTS 20 years ago. Lee has acknowledged that GIIRS mid-wave does not express a strong nonlinear characteristic, which is determined by the properties of semiconductor material. The nonlinearity of mid-wave claimed by the authors requires some definite evidences. And in the results section of this paper, the author does not show any results of nonlinear correction in mid-wave band.
9. line 60~61, “By looking for nonzero intensity in low frequency regions where the detector response is known to be zero, the final NL coefficient can be obtained (Chase, 1984).” misquotation! D. B. Chase's quote is that "The most reliable and straightforward method of evaluating detector nonlinearity is to look for nonzero intensity in a single beam spectrum in low frequency regions where the detector response is known to be zero." Thus, look for nonzero intensity in a spectrum is just a straightforward method to detect the presence or absence of nonlinearity, rather than to obtain nonlinear coefficients.
10. line 63, “HIRAS (Qi et al., 2020; Wu et al., 2020),” misquotation! I have discussed with Qi and Wu in many meetings, such as GSICS、ITSC, that CMA HIRAS does not adopt the nonlinear correction method of UW-SSEC, because HIRAS nonlinear response is different with CrIS, and the authors need to know exactly how your CMA colleagues are doing.
11. line 64~65, The authors seem do not understand the nonlinear correction method of CrIS. CrIS definitely uses the UW-SSEC method, which is not a new method either in TVAC test or in orbit calibration. The corrected coefficients in orbit are only a little tuning on the basis of the pre-launch coefficients. In fact, CrIS detector has a well response linearity (>99.8%) and the post-launch fine tuning is to adapt the spacecraft environment change, rather than re-derived a set of new coefficients.
12. line 71~72, “it is in need to determine and correct the NL response during calibration, particularly for the quadratic contribution of NL.” And in line 82~83, “The NL principle of GIIRS is essentially the same as that of the traditional broad band sensors, except that the band (LWIR and MWIR) of GIIRS is much wider.” If the authors understand Chase's analysis, they should know that the infrared imagers and the infrared sounders have different nonlinear characteristics.

1. line 75~78, The author needs to discuss how the instrument temperature field affects the detector nonlinearity. It is unreasonable to confuse the nonlinearity of microwave instruments and infrared sounders, since they utilize different detectors and have different response nonlinearities.
2. line 86, “spectral response function (SRF)” The authors need to know that the spectral response function (SRF) or ISRF is the response of the instrument to a beam of monochromatic light. The term has been defined by D. Siméoni et. al. for IR-FTS like IASI in 1990s. Eq.(5) is correct to use SRF, in an ideal or well spectrally calibrated FTS without apodization, SRF should be a sine cardinal function, rather than the sounder responsivity in Figure 6. And in line 289~290, “SRF of a sensor (i.e. GIIRS) generally refers to the ratio of the received radiation relative to the incident radiation at each wavenumber.” This is not a definition of the spectral response function of equation (5), but a definition of the spectral responsivity of the instrument. Spectral response function and spectral responsivity have very different meanings.
3. line 90~91, “which provide a new and more accurate way for in-orbit NL correction for both infrared and microwave sensors in theory.” The author should give some examples of the application of nonlinear coefficients in microwave sounders. I think discussing microwave nonlinear correction in this article deviates from the topic of the paper.
4. Table 2 is dispensable.
5. line 103~104, “which means the alternating current (AC) component of target radiance is retained.” In FTS, AC component generally refers to the interferogram without non-interference term, that is DC term, so I is an optical interferogram rather than a radiation spectrum, but the authors have considered the equation (1) is based on the radiance of the infrared imager, so this is wrong. And the ignoring of a0 is too arbitrary.
6. line 110~111, “In the step of NL coefficient extraction, after convolving BB radiance with sensor’s SRF, the theoretical interfered radiance (namely interferogram) received by GIIRS can be obtained.” The convolution of the blackbody spectrum with SRF is still a spectrum, not an interferogram.
7. line 113~114, “during laboratory calibration, NL coefficients ( 𝑎2) can be calculated by fitting the DN with the radiance at different temperatures (180K, …, 320K) by least square method.” DN is interferogram, while radiance is spectrum. Without Fourier transform, the interferogram cannot be fitted with radiance.
8. line 116~119, this description is ambiguous.
9. In Figure 2, the BB radiance has been modulated as an interferogram in temporal space, rather than a spectrum, and therefore cannot be convolved with SRF in frequency space. The signal received by the detector is interferogram rather than radiance.
10. Section 2.2.2 Subsample location alignment, the author’s so-called "ZPD detection method" is not a new approach, which is just the "zero padding" commonly used in Fourier spectrum analysis. The "zero padding" method for spaceborne IR-FTS calibration has been introduced by Bob Knuteson et. al. in the 20th IIPS conference in 2004. In GIFTS spectral calibration, Bob et. al. utilizes zero padding in spectral space combined "double FFT" described in (Han, 2018) to get the real maximum optical path difference (MPD), not ZPD, of the off-axis interferogram, so the frequency shift in off-axis spectrum could be corrected, and the spectral sample is approximately equal to the reciprocal of the 2*MPD. Bob had realized the zero padding method is time-consuming in data processing, so an equivalent convolution method proposed by J. Genest and P. Tremblay was replaced. The convolution method is high-efficiency, and has been used spectral calibration of ABB Bomem's interferometers, like Aura/TES, ACE-FTS, IASI, CrIS. CMA HIRAS maybe use the same method as CrIS described by Qi. Therefore, I recommend that authors learn some history of the spaceborne FTS and make respect for the work that has been done.
11. line 179~183, this section has little to do with the topic of this paper. Table 3 also does not give some useful information to readers.
12. line 186~188 and Eq. (10), In theory, the interferogram value at ZPD characterize the integrated energy of blackbody over the spectral response range. But real FTS has some modulation degree less than unit of ideal FTS, so the value at ZPD is not necessarily correlated with nonlinearity. As far as the interferogram signal is concerned, the nonlinearity occurs at each OPD position of the interferogram, not only at ZPD, which is why the nonlinearity of FTS is different from that of the imager. In Eq(10), the rationality of using second-order polynomials to fit ideal radiation needs to be discussed, otherwise it will be too arbitrary.
13. line 194~198, The authors need to explain why the off-axis angle changes with the direction of the moving mirror. That's a weird statement. According to the FTS optical path layout, the off-axis angle is constant in instruments like IASI and CrIS. If the alignment of the moving mirror and the fixed mirror change, it means that the modulation degree of the instrument also changed, and the model of equation (10) is not valid. Description in line 196~198 is not correct, off-axis correction is to correct the shifted spectrum and more important the ISRF. The spectral frequency shift is originated from the off-axis spectrum using the spectral abscissa calculated by the sample interval of the on-axis interferogram. If we get the real OPD of the off-axis interferogram, then we can get the true abscissa without any frequency shift, but with different spectral scales or spectral sample intervals.

1. Figure 3, In the flow chart, the updated coefficient a1^0 is the average of the original two coefficients a_1⁰=(a₁⁰+a₁¹)/2. That is so weird. The author needs to explain the rationality of this step.
2. Section 2.4, it is not necessary for the author to derive the UWM-SSEC method in Sec. 2.4 again. And in fact, CrIS nonlinear correction is not done on the DN values.
3. line 353~355, “Similarly, compared with detectors near the central positions of FOV, the NL parameters (𝜇) of the marginal ones are apparently underestimated by around 50% against those of central ones, which is also mainly induced by their bigger linearity coefficients” Generally speaking, the light intensity near the FTS optical axis is stronger than that at the edge of the field of view, which is common sense. The authors mistake it for a large linear coefficient, so the subsequent nonlinear correction results are not reliable.
4. line 355~356, “due to the relative lower optical efficiency at the locations near the marginal areas of FOV,” The lower intensity at the edge of the field of view is due to off-axis effects rather than low optical efficiency.
5. line 357~358, “It implies that the radiometric responsivities of the marginal detectors are generally lower, which can further lead to the smaller NL parameters (𝜇) even for the same detectors.” the detector responsivity does not decrease with its distribution location.
6. In Table 4, If the nonlinearity is corrected well enough, the coefficients can be applied to different observation scenes and do not vary with the energy of the observation targets, because nonlinearity is an inherent property of a non-ideal FTS. As can be seen from the table 4, both linear and nonlinear coefficients are variable, so it can be inferred that this new method is invalid and these coefficients have no practical values in atmospheric radiance calibration. What is strange is that the nonlinear coefficients obtained by the author using the UWM-SSEC method are also variable, which is completely different from the actual application of CrIS, so I think the author does not understand the UWM-SSEC method.
7. line 420~421, “Such results imply that the derived 𝑏2 values from the classical method are inaccurate.” This conclusion is absurd. Maybe the authors do not understand the UWM-SSEC method.
8. line 424~426, “From the perspective of NL correction, the NL characteristics of GIIRS are underestimated by the classical method, …” According to the height of the geostationary satellite and the spatial resolution of GIIRS pixels, it can be estimated that the pixel size of the GIIRS detector is not too large, about 100 μm, which is much smaller than CrIS pixel with a diameter of about 1 mm. Therefore, even though the performance of Chinese infrared detectors may not be comparable with that of CrIS, the nonlinear response of the GIIRS long-wave infrared HgCdTe detector should not be greater than CrIS. I think the UWM-SSEC method can easily correct the nonlinear bias of GIIRS, but the authors don't seem to really understand this method.
9. Figure 10 is worthless because people are more concerned with the spectral distribution of the radiometric calibration deviation of the infrared sounder than with the integrated energy.
10. Figure 11. From Figure 11 it can be confidently confirmed that the radiometric calibration failed, let alone the non-linear correction. According to pre-launch radiometric calibration tests such as IASI and CrIS, the BT deviation of the blackbody calibrated spectra should not have significant spectral characteristics, and its mean value should be a straight line trend along the spectral abscissa. In Figure 11, The BT deviation still remains the characteristics of the instrument's spectral responsivity. It means that the calibration does not eliminate the instrument effects, thereby defeating the purpose of radiometric calibration.
11. line 443~445. As for in-orbit radiometric calibration, people prefer to see the calibrated spectra and the calibrated deviation of the real atmospheric radiance, rather than the onboard blackbody radiance. Actually, the onboard blackbody should serve as the reference for atmospheric radiation calibration.