**3. Observation Data Matching and Evaluation Method**

Four major steps are involved in an intercomparison of the FY-3E/HIRAS-II infrared hyperspectral observations with the Himawari-8/AHI radiance observations of the corresponding longwave infrared channel, including (1) spectral convolution, (2) observation geometry and temporal matching, (3) spatial matching, and (4) uniformity checking. The matching process is shown in Figure 1. The following will be a step-by-step detailed introduction.

**Figure 1.** Intercomparison flow chart of HIRAS-II, AHI, and MERSI-LL.

#### *3.1. Spectral Convolution*

The most fundamental problem in the intercomparison between the spaceborne imager and sounder observation is radiance spectral matching. The two types of instruments with different spectral resolutions cannot be directly compared. To be compared with the imager instrument observations, the hyperspectral radiance must be convolved to match the spectral response function (SRF) of the broadband imager [14,15]. The computational formula to achieve spectral convolution is

$$\mathcal{L} = \frac{\int\_{\mathbf{v}\_1}^{\mathbf{v}\_2} \mathcal{R}(\mathbf{v}) \mathcal{S}(\mathbf{v}) d\mathbf{v}}{\int\_{\mathbf{v}\_1}^{\mathbf{v}\_2} \mathcal{S}(\mathbf{v}) d\mathbf{v}} \tag{1}$$

where ν is the wavenumber, L is the radiance calculated by convolution, R(ν) is the hyperspectral radiance at the corresponding wavenumber and S(ν) is the spectral response function of the imager. The simulated HIRAS-II brightness temperature spectrum using fast radiative transfer mode RTTOV under American standard atmospheric conditions, as well as the AHI and MERSI-LL spectral response functions (SRF), are given in Figure 2. The bottom horizontal coordinate is the wavelength, the upper horizontal coordinate is the wavenumber, the left vertical coordinate is the simulated brightness temperature of HIRAS-II, and the right vertical coordinate is the spectral response function. The solid line in the figure is the spectral response function of the matched AHI channels 8–16, and the dashed line denotes the spectral response function of MERSI channels 4–7.

#### *3.2. Observation Geometry and Temporal Matching*

The most important step in the intercomparison between the imager and the sounder observation is to find the consistent (same) FOV [16]. The polar-orbiting satellite FY-3E passes the geostationary satellite Himawari's nadir 140.7 E at approximately 0830 or 2030 UTC daily, the observation time difference remained within 10 min. Since the measurements of the cross-track scanning instruments are sensitive to the scan angle (satellite zenith angle), the scan angle of both instruments in the matched field of view is specified to be less than 5◦ to ensure that HIRAS-II and AHI observe the same scene. To

minimize the difference in observation geometry and ensure that both instruments have similar observation geometry paths, the scan angle is further constrained [7,17]

$$\left|\frac{\cos\theta\_1}{\cos\theta\_2} - 1\right| < 0.002\tag{2}$$

where θ<sup>1</sup> and θ<sup>2</sup> are the scan angles of the geostationary and polar-orbiting satellites, respectively.

**Figure 2.** Simulated HIRAS-II brightness temperature spectra from RTTOV overlaid the spectral response functions of AHI (solid line) and MERSI-LL (dashed line), channel numbers for AHI are shown near the top of the graph and channel numbers for MERSI−LL are near the bottom.

#### *3.3. Spatial Matching and Uniformity Check*

The spatial field of view collocation of the FY-3E/HIRAS-II and Himawari-8/AHI in the infrared channel is shown in Figure 3, where the grid is the AHI pixel, the large circle is a HIRAS-II field of regard (FOR) centered on the field of view (FOV) to be matched (target) and the small circle is the HIRAS-II FOV within its FOR. The spatial resolution of the HIRAS-II FOV (14 km at the nadir) is coarser than that of the AHI infrared channel (2 km). Approximately 7 × 7 AHI pixels (small squares in Figure 3) fall in a HIRAS-II FOV (the small circle in Figure 3). The average of all these AHI pixel measurements is taken as the imager's measurement in the matching FOV [18]. This requires that the observation target be relatively homogeneous. Since there are many AHI pixels collocated in the HIRAS-II FOV, some of which are clear sky and some are cloudy, at the same time the underlying surface of the field of view is not homogeneous, it is necessary to check the uniformity of each HIRAS-II FOV, which is carried out by using the ratio of the standard deviation of the matched AHI radiations to its mean value

$$\text{Std}\_{\text{fov}} / \text{Mean}\_{\text{fov}} < \text{ } 0.01 \tag{3}$$

where Stdfov denotes the standard deviation of the observed radiance from all the matched AHI pixels within each HIRAS-II FOV, and Meanfov is the mean radiance of all these AHI pixels. The threshold value is set to 0.01. Only uniform scenes are selected for intercomparison to reduce the uncertainty introduced by the field of view averaging.

Furthermore, a constraint of background environmental uniformity of the HIRAS-II FOV is needed to compensate for the minor error of the spatial collocation, as well as to reduce the uncertainty due to different azimuths. The 3 × 3 HIRAS-II FOV (the large circle in Figure 3) centered on the HIRAS-II FOV to be matched is considered the background environment area.

$$\text{Std}\_{\text{env}} / \text{Mean}\_{\text{env}} < \text{ } 0.05 \tag{4}$$

where Stdenv denotes the standard deviation of all the matched AHI pixels' radiance within the background area, and Meanenv denotes the mean radiance of these matched AHI pixels.

**Figure 3.** Spatial matching of HIRAS-II and AHI. The small square represents the AHI pixel, the small circle is the HIRAS-II FOV, and the large circle is the HIRAS-II FOR.

#### *3.4. Statistical Calculation*

For each collocated HIRAS-II—AHI FOV, the brightness temperature difference (BT diff = BTHIRAS − BTAHI) and the standard deviation of the brightness temperature difference (Std = - ∑n <sup>i</sup>=1(BT diffi − BT diffmean) 2 /(n − 1)) are counted (n is the number of samples).

A total of 458 pairs of samples are obtained after collocating the HIRAS-II observations with the AHIs from 15 March to 21 April 2022 based on the above matching steps.

### *3.5. Matching with MERSI-LL on the Same Platform*

When the HIRAS-II observations are compared with those from the AHI nadir on the geostationary satellite, the matched fields of view are concentrated near the tropical equator, and the dynamic range of the observed brightness temperature is narrow. The HIRAS-II observations will be compared with measurements from one imager that is carried on a polar-orbiting platform to evaluate its observation accuracy on a global scale. However, FY-3E is the first early morning polar-orbiting satellite with a significant observation time difference (even more than 8 h) from the established mid-morning or afternoon orbit satellites. Therefore, the MERSI-LL imager on the same FY-3E platform is chosen to perform the HIRAS-II calibration in this paper, and the MERSI-LL channels 4–7 are spectral matched. Since HIRAS-II and MERSI-LL are on the same polar-orbiting satellite platform and are almost observed simultaneously, the matching process of the two instruments is relatively simple. Only the nadir HIRAS-II FOV is matched to ensure the same observation scene. The spectral matching, spatial matching, and uniformity checking steps are the same as those for AHI. Finally, a total of 12,395 pairs of HIRAS-II and MERSI-LL observation samples were matched over 8 days from 15 to 22 March 2022.

### **4. Results and Discussion**

### *4.1. Comparison of HIRAS-II with AHI*

There are nine Himawari-8/AHI channels (channels 8 to 16) that are spectral matched with FY-3E/HIRAS-II in the longwave infrared band. The scatter plots of the convolved HIRAS-II observed brightness temperature with AHI measurements in channel 8 to 16 are given sequentially in Figure 4. The horizontal coordinate is the HIRAS-II observed brightness temperature, the vertical axis is the AHI observation, the dashed line is the *y* = *x* line, and the solid line is the linear fitting result. Because the matched samples are concentrated near the nadir of the geostationary satellite, the dynamic range of the observed brightness temperature for each channel is narrow, and the value gradually decreases as the peak height of the weighting functions of atmospheric absorption channels increases. The observations of the two instruments are very close, with correlation coefficients higher

than 0.98, and the fitting lines almost coincide with the *y* = *x* line in all the channels. The statistical bias and standard deviation for the HIRAS-II—AHI matching samples from 15 March to 21 April 2022 are listed in Table 2. Figure 4 and Table 2 show that all the channels have a slightly positive bias; namely, that the HIRAS-II convolved observations are slightly warmer than AHI with a maximum bias of 0.65 K (channel 9 in the water vapor wing), and the minimum is 0.22 K (window channel 14). The standard deviation of all the channel biases ranges from 0.22 to 0.31 K with small values and little difference between the channels. Water vapor absorption channels 8–10 and ozone absorption channel 12 have relatively larger biases and small standard deviations, while the biases of the window channels (such as channels 14 and 15) are relatively small, and the standard deviations are slightly large. In addition, the closer the peak height of the weighting function is to the surface, the larger the standard deviation is. This is because the value range of the observed brightness temperature of the window channels is relatively larger than that of the absorption channels, so the dispersion is larger in the window channel.

**Figure 4.** Scatterplot of the convolved HIRAS-II brightness temperature and the AHI brightness temperature for channels 8–16. The dashed line is *y* = *x*, and the solid line is the linear fitting result.

The ideal condition for the realization of the cross-calibration using the simultaneous nadir overpass (SNO) method is that the two instruments observe the same target at the same time through the same atmospheric path. However, the matching condition is appropriately approximated in the actual application to obtain enough samples, and the introduction of the matching threshold may bring uncertainty to the calibration evaluation. For the HIRAS-II and AHI cross-calibration, the observation inconsistency may be partly due to the random errors caused by the differences in observation geometry, scene

uniformity, and observation time. To analyze the possible uncertainties caused by the colocation approximation factors, water vapor channel 8 with the highest peak height of the weighting function is taken as an example. The distribution of the brightness temperature differences of HIRAS-II and AHI with various matching factors: (a) observation geometry, (b) scene uniformity, (c) azimuthal difference, and (d) observation time difference are shown in Figure 5. The larger the value of the horizontal coordinate in Figure 5a denotes the larger the difference in the observation geometric viewpoint. A larger value of the *x*-axis in Figure 5b indicates worse uniformity within the field of view. The larger *x* value of Figure 5c corresponds to the larger difference in the observation azimuth of the two instruments. The solid line shows the linear fit pattern of the brightness temperature differences with the approximation factors. The brightness temperature differences are randomly and uniformly distributed with these factors and do not increase with the decrease in various matching degrees. There is no obvious linear variation characteristic with these matching factors, indicating that the influence of various matching factor differences within their threshold on observation bias can be neglected and that these reasonable matching thresholds bring little uncertainty to the bias assessment. Figure 5e shows the distribution of the brightness temperature differences with the HIRAS-II observed brightness temperature. These is also no significant scene temperature-dependent bias. The results of the remaining channels are similar and omitted. After excluding the random errors caused by the matching factors mentioned above, it can be concluded that the HIRAS-II—AHI brightness temperature differences mainly represent the systematic observation bias of the two instruments.

**Table 2.** Statistics of brightness temperature bias between HIRAS-II and AHI.


**Figure 5.** Brightness temperature biases between HIRAS-II and AHI of channel 8 varying with (**a**) observation geometry factor, (**b**) scene homogeneity factor, (**c**) azimuth angle factor, (**d**) observation time differences, and (**e**) HIRAS-II observations (the solid line shows the linear fitting result).
