*4.2. Comparison of HIRAS-II with MERSI-LL*

The observed biases and standard deviations were counted based on the 12,395 pairs of samples matched by HIRAS-II and MERSI from 15–22 March 2022. The distribution of the brightness temperature differences (HIRAS-II minus MERSI-LL) with the HIRAS-II observed scene temperature for channel 4–7 are shown in the left subplot of Figure 6 with the vertical coordinates representing the brightness temperature differences and the horizontal coordinates representing the observed scene temperature. The color distinguishes the scene uniformity, and the dashed line gives the mean of the biases. The probability density distributions of the brightness temperature differences are given in the right subplot with the horizontal coordinate as the sample probability density. Channel 4 of MERSI-LL is a water vapor absorption band with a central wavelength of 7.22 μm (peak height of the weighting function 400 hPa), and channel 5–7 are window channels with a central wavelength of 8.55 μm, 10.8 μm, and 12.0 μm, respectively. The dynamic range of the channel 4 target brightness temperature is between 220 and 280 K, and the HIRAS-II measurement is slightly higher than the MERSI-LL observations (the mean bias is 0.6643 K) with a standard deviation of 0.2229 K. The dynamic range of channel 5 is slightly larger at approximately 220–300 K, and the observed brightness temperatures of HIRAS-II and MERSI are close, with a mean bias of 0.0023 K and a standard deviation of 0.3135 K. The dynamic range of channel and 7 target brightness temperature are between 210 and 310 K, and the biases of channel 6 and 7 show a U-shaped change with the increase in the scene temperature, and the biases are smallest (close to 0 K) when the scene temperature is between 250 K and 280 K. Channel 4 has smaller brightness temperature differences at lower scene temperatures (i.e., high latitudes) and relatively larger brightness temperature differences at higher scene temperatures (i.e., low latitudes), especially when the bias increases to 1.2 K near the equator. Although the channel 5 bias takes values of approximately 0 K, the bias dispersion increases as the HIRAS-II observed scene temperature increases. Both channel 6 and 7 have relatively larger brightness temperature differences at lower scene temperatures and higher scene temperatures, and the maximum value is close to 1.75 K. From the right subplot, it can be seen that the probability density distributions of the brightness temperature bias for channels 4–7 all conform to the normal distribution.

It is noteworthy that the brightness temperature differences of the water vapor channel 4 in Figure 6 are obviously positively correlated with the target scene temperature, and the window channels 6 and 7 also have an obvious scene temperature-dependence, while window channel 5 shows no scene temperature-dependent bias. At the same time, AHI water vapor channels 9 and 10—whose spectral positions are close to MERSI-LL channel 4—also do not find bias scene-dependent characteristics. Since HIRAS-II and MERSI-LL are mounted on the same platform, the scene uniformity is the only factor that introduces matching uncertainty into the intercomparison. Figure 7 shows the scatter distribution of MERSI-LL channel 4 (a), channel 5 (b), channel 6 (c), and channel 7 (d) brightness temperature differences (HIRAS-II minus MERSI-LL) with scene uniformity. A larger value of the horizontal coordinate in Figure 7 indicates worse scene uniformity, and the solid line indicates the linear fitting result. The brightness temperature differences of channel 5–7 are uniformly distributed with the scene uniformity and do not have linear variation characteristics (in Figure 7b). However, the brightness temperature differences of channel 4 show an obvious linear trend with the scene uniformity, and the biases gradually decrease as the scene uniformity worsens (in Figure 7a). Combined with the scatter color of channel 4 in Figure 6, the scene uniformity is relatively poor (yellow) in the high latitudes with a low brightness temperature, and the scene uniformity is good in the low latitudes with a high brightness temperature. This is because the underlying surface in the field of view varies greatly in the polar region when the instrument is scanning with the same spatial resolution and swath, especially the Arctic has greater underlying surface variability due to the presence of different surface types (e.g., land, snow, ocean, glacier, etc.) with higher variability in absolute temperature. Theoretically, the bias is smaller when scene uniformity is better. However, Figure 6 shows that the scene uniformity gradually improves with the increasing scene temperature, while the bias increases instead. This indicates that the scene uniformity is not the cause of the scene temperature-dependent bias.

**Figure 6.** (left) Scatterplot of the HIRAS-II–MERSI-LL BT bias versus the scene temperature and (right) the histogram of the BT differences. The dashed line indicates the mean value. The color indicates the scene homogeneity.

**Figure 7.** Scatterplot of brightness temperature biases between HIRAS-II and MERSI-LL varying with scene homogeneity of (**a**) channel 4, (**b**) channel 5, (**c**) channel 6, and (**d**) channel 7 (the solid line shows the linear fitting result).

The main factors that may cause spaceborne radiation imager calibration errors mainly include blackbody emissivity and spectral response function instrument nonlinearity. MERSI-LL channel 4 is located in the wing area of the water vapor absorption band, and a very small drift in the spectral response function can also lead to a temperaturedependent bias in the scene. However, to date, there have been no specific references about the design of the black bodies, the calibration system, and so on of these two instruments onboard FY-3E. These matters require further study in the future.

The day-to-day variations in the mean biases and standard deviations are counted based on the HIRAS-II–MERSI-LL matched samples. The daily mean biases of channel 4 range from 0.64 to 0.68 K, and the standard deviations are all approximately 0.2 K. The daily mean biases of channel 5 range from −0.02 to 0.02 K, and the standard deviations are approximately 0.3 K. The daily mean biases of channel 6 range from 0.62 K to 0.64 K, and the standard deviations are approximately 0.35 K. The daily mean biases of channel 7 range from 0.48 K to 0.51 K, and the standard deviations are approximately 0.3 K. The biases of the two instruments vary minimally and almost constantly over a period of time, indicating that the performance of the HIRAS-II instrument is stable.

#### **5. Conclusions**

To assess HIRAS-II's on-orbit observation quality, the geometrically, temporally, and spatially matched scene homogeneous HIRAS-II hyperspectral observations were convolved to the longwave infrared channels corresponding to the Himawari-8/AHI and FY-3E/MERSI-LL from 15 March to 21 April 2022, and their brightness temperature deviation characteristics were statistically calculated in this paper. The matching samples of HIRAS-II and AHI are concentrated near the equator, and the spectral matching channels are longwave infrared channel 8 to channel 16 onboard the same polar orbiting satellite platform FY-3E. The matching samples of HIRAS-II and MERSI-LL are evenly distributed all over the world with spectral matching channels 4 to channel 7. The following conclusions can be made based on this analysis:

1. The HIRAS-II on-orbit observed brightness temperatures are slightly warmer than the AHI observations, with a small positive bias in all the matched channels. The brightness temperature scatters of both observations are distributed near the *y* = *x* line with a correlation coefficient higher than 0.98 in all channels. The biases of water vapor channels 8–10 and ozone absorption channel 12 are relatively large, with a maximum of 0.65 K (channel 9 in the water vapor wing), and the biases of the window channels are relatively small, with a minimum of 0.22 K (channel 14). The standard deviations for all channels are small (0.22–0.31 K) and there is little difference between the channels.


As a final note, we just found the phenomenon of bias distribution, which is not yet fully explained due to lack of relevant references. Therefore, we will use NWP data, double-difference method to further evaluate the accuracy of HIRAS-II in future studies.

**Author Contributions:** Conceptualization, L.G. and H.C.; methodology, L.G.; software, H.C.; validation, H.C.; formal analysis, L.G.; investigation, H.C.; resources, L.G.; data curation, H.C.; writing original draft preparation, H.C.; writing—review and editing, H.C.; visualization, H.C.; supervision, L.G.; project administration, L.G.; funding acquisition, L.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China under grant no. 41975028.

**Data Availability Statement:** The HIRAS-II and MERSI-LL Level 1 data can be obtained at the Chinese Feng Yun satellite remote sensing data service network (http://data.nsmc.org.cn accessed on 11 April 2022). Himawari-8/AHI radiation data obtained from the Japan Earth Observation Data Center (https://www.eorc.jaxa.jp/ptree/index.html accessed on 11 April 2022).

**Acknowledgments:** The authors would like to thank the editor and reviewers for their helpful comments on the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
