Estimation of IFOV Inter-Channel Deviation for Microwave Radiation Imager Onboard FY-3G Satellite

Abstract

The Microwave Radiation Imager (MWRI) onboard the FengYun satellite plays a crucial role in global change monitoring and numerical weather prediction. Estimating and correcting geolocation errors are important to retrieving accurate geophysical variables. However, the instantaneous field of view (IFOV) inter-channel deviation, which is mainly caused by the structure mounting error and measurement error of feedhorns, is less studied. In this present study, we constructed a general theoretical model to automatically estimate the IFOV inter-channel deviations suitable for conical-scanning instruments. The model can automatically detect the along-track and across-track vectors that pass through the land–sea boundary points and are perpendicular to the actual coastlines. Regarding the midpoints of the vectors as the brightness temperature (Tb) inflection points, the IFOV inter-channel deviation is the pixel offset or distance of the maximum gradients of the Tb near the inflection points for each channel relative to the 89-GHz V-pol channel. We tested the model’s operational performance using the FY-3G/MWRI-Rainfall Mission (MWRI-RM) observations. Considering that parameter uploading adjusted the IFOV inter-channel deviations, the model’s validity was verified by comparing the adjustments calculated by the model with the theoretical changes caused by parameter uploading. The result shows that the differences between them for all window channels are less than 100 m, indicating the model’s effectiveness in evaluating the IFOV inter-channel deviation for the MWRI-RM. Furthermore, the estimated on-orbit IFOV inter-channel deviations for the MWRI-RM show that all channel deviations are less than 1 km, meeting the instrument’s design requirement of 2 km. We believe this study will provide a foundation for IFOV inter-channel registration of passive microwave payloads and spatial matching of multiple payloads.

1. Introduction

The Microwave Radiation Imager (MWRI) onboard the FengYun satellite plays an essential role in observing geophysical parameters, such as soil moisture [1], snow depth [2], sea surface temperature [3], sea ice [4] and ocean wind speed [5]. Since the first MWRI onboard the FY-3A satellite began operations in 2008, there are more than 15 years of MWRI observations available [6,7]. In April 2023, the first precipitation measurement satellite (FY-3G), equipped with the Microwave Radiation Imager-Rainfall Mission (MWRI-RM) payload, was successfully launched [8]. Currently, three MWRI payloads are in orbit and in good working order. Achieving accurate spatial matching between MWRIs on different platforms is a fundamental issue for radiation transfer.

Precise geolocation is a prerequisite for spatial matching between multiple platforms and payloads [9,10] and directly impacts the accuracy of the retrieved geophysical parameters [11,12]. The geolocation error estimate and correction for spaceborne instruments have been extensively studied [13]. Several typical methods are commonly used to estimate geolocation errors, including the coastline inflection method [14], the node differential method [15], and the image registration method [16]. The coastline inflection method calculates the distance between the observed coastline and the actual coastline based on abrupt changes in brightness temperature (Tb) near the coastline under clear-sky conditions [14]. The position of the observed coastline is determined by the inflection point, where four continuous observations cross the actual coastline. This method is widely used in estimating the geolocation errors of microwave payloads, such as the microwave imager [17], scatterometer [18] and polarimeter [19]. The node differential method is used to minimize the differences between ascending and descending swaths by adjusting the geolocation model parameters. Wiebe et al. [15] implemented this method to improve the geolocation accuracy of AMSR-E by optimizing the viewing angles, resulting in a residual geolocation error of 5% of the footprint size for 89 GHz channels. The image matching method employs a global network of ground control points to determine the payload geolocation errors [16], which is particularly effective for imaging payloads such as the Moderate Resolution Imaging Spectral radiometer (MODIS) [20], the Advanced Very High-Resolution Radiometer (AVHRR) [21], the Visible Infrared Imaging Radiometer Suite (VIIRS) [22] and the Medium Resolution Spectral Imager (MERSI) [23]. The estimated geolocation errors can be partially corrected by updating models of the satellite’s attitude (pitch, roll, and yaw) in the payload geolocation software [17,20].

Aside from the payload geolocation error, the instantaneous field of view (IFOV) geolocation error also depends on the IFOV inter-channel deviation. In contrast to the extensive research on payload geolocation errors, the assessment of IFOV inter-channel deviations has received little attention. It should be noted that the payload geolocation error estimate is based on a specific channel of the instrument. IFOV inter-channel deviation refers to the deviation of other channels’ IFOV relative to the specific channel’s IFOV. Due to instrument design, different feedhorns are used to receive signals at different frequencies. Structure mounting errors and measurement errors of feedhorns could cause IFOV inter-channel deviations, which can only be evaluated and corrected with on-orbit observations. In this way, exploring effective methods for accurately estimating the IFOV inter-channel deviations is necessary and imperative.

However, there is limited public research on IFOV inter-channel deviations available for conical-scanning passive microwave payloads and even fewer studies on automatic estimation algorithms. In view that the radiometer’s Tb inflection point appears near the coastline, IFOV inter-channel deviations can be determined by the distances of the coastlines observed by various channels under clear-sky conditions. As spaceborne MWRI performs mechanical conical scanning, the scanning direction is not always perpendicular to the flight direction. Thus, it is necessary to identify the Tb inflection points for along-/cross-track IFOV inter-channel deviations, respectively.

Here, we proposed an automatic estimation model for IFOV inter-channel deviations and verified the model performance on the FY-3G MWRI-RM. The on-orbit IFOV inter-channel deviations of the MWRI-RM were estimated simultaneously. In the following Section 2, the remote sensing and auxiliary data, as well as the MWRI-RM observation geometry, are described. Section 3 introduces the proposed automatic estimation model for IFOV inter-channel deviations in detail. The two main modules, namely the Coastline Inflection Point Automatic Identification module and the Automatic Estimation module, are presented in Section 3.1 and Section 3.2, respectively. In Section 4, the performance of the automatic estimation model is demonstrated, and Section 5 provides the conclusions and discussion.

2. Data and Materials

2.1. Basic Data

This study primarily uses the FY-3G MWRI-RM Level-1 dataset and high-precision coastline data for the IFOV inter-channel deviation estimation. The MWRI-RM Level-1 dataset is stored in single orbit format. It includes the Tb, geographic latitude and longitude, land–sea mask, and product quality code [24]. Since the observed Tb may be contaminated by radio frequency interference, we used the quality code to remove the affected Tb. The matched latitude and longitude coordinates are the center position of the 89 GHz V-pol channel’s IFOV. Although the MWRI-RM beam footprint covers one FOV area, the observed Tb is considered to come from the center point of the FOV. The spatial resolution of the Tb is 12.24 km × 2.23 km. As this study relies on the coastline inflection point method to estimate the IFOV inter-channel deviations, only 10 window channels out of the 26 MWRI-RM channels can be evaluated. These include the 10.65 V, 10.65 H, 18.7 V, 18.7 H, 23.8 V, 23.8 H, 36.5 V, 36.5 H, 89 V, and 89 H channel. The L1 orbit data from May 2023 to February 2024 are used in this study.

Additionally, high-precision coastline data were used as auxiliary data to extract the inflection points for the IFOV inter-channel deviation estimation. This dataset was created by Rich Pawlowicz and obtained from https://www.ngdc.noaa.gov/mgg/shorelines/data/gshhs/ (accessed on 20 July 2023). The spatial resolution of this dataset is 0.25°, with an average coastline vector length of 45 km and a standard deviation of 15 km. The original dataset is stored in the form of polygon vertices, and in our study, consecutive points are connected to represent the actual coastline vectors.

2.2. MWRI-RM Instrument Geometry

The MWRI-RM is a conical-scanning microwave radiometer, with its observation geometry shown in Figure 1. The window channels of the MWRI-RM are dual polarized (V and H only) at five frequencies using four feedhorns, where the 18.7 GHz and 23.8 GHz channels share one feedhorn, and the other frequencies each have one. The main antenna and feedhorns are rotating components, completing one rotation every 1.7 s relative to the satellite. The IFOVs of 10.65, 18.7, 23.8, 36.5, and 89 GHz are 21 × 35, 14 × 23, 13 × 21, 9 × 15, and 5 × 8 km, respectively.

The FY-3G satellite’s orbital inclination is set at 50°, and the altitude is 407 km, with the orbit period of about 93 min. For the MWRI-RM, two consecutive scanning lines are 12.24 km apart. The nadir angle of the conical scan is 48.7 degrees. Its ground observation area covers a 128° range centered on the flight direction, with 492 sampling points in the observation area, each sampled at an average interval of 1.24 × 10⁻³ s. The distance between the centers of two consecutive pixels in the cross-track direction is 2.23 km.

3. Automatic Estimation Model for IFOV Inter-Channel Deviation

The IFOV inter-channel deviation refers to the distance between the IFOVs of different channels. Ideal earth FOVs for all channels are concentric ellipses, as shown in Figure 2a, while the actual FOVs show a mismatch between different channels (Figure 2b). It is obvious that the IFOV inter-channel deviation is the combination of along-track and cross-track deviations. In other words, the IFOV inter-channel deviation can be decomposed into along-track and cross-track components, with the overall IFOV inter-channel deviation being the vector sum of these along-track and cross-track deviations. On account of the abrupt change in Tb near the land–sea boundary, the IFOV inter-channel deviation can be determined by the distance of the Tb inflection points between the channels. In the instrument design, the feedhorn for the 89 GHz is positioned at the main antenna’s focus. The IFOV inter-channel deviation is the pixel offset or distance of maximum Tb gradients for each channel relative to the 89 GHz V-pol channel.

As mentioned above, to estimate the IFOV inter-channel deviations, an automatic estimation model would include two sub-models, namely the along-track IFOV inter-channel deviation sub-model and the cross-track IFOV inter-channel deviation sub-model. Both the along-track and cross-track sub-models are composed of two modules: one is primarily used for identifying qualified coastline inflection points, called the Coastline Inflection Point Automatic Identification (CIPAI) module; the other is used for calculating the deviations, called the Automatic Estimation module.

3.1. Coastline Inflection Point Automatic Identification (CIPAI) Module

Identifying coastline inflection points serves as the foundation for the entire model. Theoretically, when the along-/cross-track vectors passing through the inflection point are perpendicular to the coastline, the Tb gradient is the greatest at the land–sea boundary, which is conducive to accurately identifying the position of the maximum Tb gradient. On the condition that the Tb near the inflection point is interfered with by clouds/rain, it may introduce errors in the subsequent IFOV deviation estimate. Accordingly, determining whether a point qualifies as an inflection point involves two primary constraints. The first constraint is the geometric condition, which aims to identify points where the along-/cross-track vectors intersect the high-precision coastline at a perpendicular angle. The second constraint is data quality control, ensuring that the Tbs near the inflection points are free from radio frequency interference and are not affected by clouds or rain.

To detect geometrically qualified points, this module first recognized the land–sea boundary points. And then, it identified the along-track or cross-track vector that passes through the boundary points and intersects perpendicularly with the actual coastline. The midpoints of the vectors were marked as geometrically qualified points. The processing flow is shown in Figure 3. Only the geometrically qualified points were processed further.

• Land–sea Boundary Points Recognition: Using the land–sea mask from the MWRI L1 dataset, we can identify the land–sea boundary [13]. For adjacent coastlines, such as the coastlines near the Malacca Strait, it is challenging to determine the Tb inflection points. Therefore, we selected the dispersed boundary points. Specifically, for the along-track sub-model, only land–sea boundary points that are more than 40 scan lines apart were selected as the boundary points. For the cross-track sub-model, when only one land–sea boundary intersects with a scan line, the intersection point is retained as a boundary point. As is shown in Figure 4, the detected boundary points may not be overlapped with the actual coastline. In subsequent analyses, redundancy processing is used to reduce errors.
• Intersection Determination: The along-track and cross-track vectors are defined as follows. The direction of the along-track vector is the satellite’s flight direction. The along-track vector is represented by the vector that connects the consecutive five points in the along-track direction and passes through one boundary point. While, the direction of the cross-track vector refers to the tangent direction of the scan line for conical-scanning instruments. The cross-track vector is approximated by the vector that connects the consecutive 11 points in the cross-track direction and passes through 1 boundary point. In addition, the coastline vectors are derived from the high-precision coastline data. Figure 4 provides a schematic illustrating the relationship between boundary points, along-/cross-track vectors, and coastline vectors.

Suppose the coastline vector is represented as $\overrightarrow{C}$ (with endpoints [$C_{x1}$, $C_{y1}$] and [$C_{x2}$, $C_{y2}$]), the along-track/cross-track vectors are represented as $\overrightarrow{T}$ (with endpoints [$T_{x1}$, $T_{y1}$] and [$T_{x2}$, $T_{y2}$]). The two vectors are considered non-intersecting if any of the conditions in Equation (1) are met; otherwise, they are considered intersecting.

$$\begin{gathered} \max (C_{x1}, C_{x2}) < \min (T_{x1}, T_{x2}\left) \\ \max (T_{x1}, T_{x2}) < \min (C_{x1}, C_{x2}\right) \\ \max (C_{y1}, C_{y2}) < \min (T_{y1}, T_{y2}\left) \\ \max (T_{y1}, T_{y2}) < \min (C_{y1}, C_{y2}\right) \end{gathered}$$

(1)

Due to the potential geolocation errors and the possible inaccuracy of the land–sea mask in the L1 dataset, we examined the intersection of multiple vectors near the boundary points with the high-precision coastline vectors. Specifically, for the along-track sub-model, if the 10th scan position on the 120th scan line is marked as a land–sea boundary point, the buffer region is the area between the 116th and 124th lines. The module determined whether the vectors connecting the 10th scan position on the 116th to 120th, 117 to 121st, …, and 120th to 124th lines intersect with the nearby coastline vectors. For the cross-track sub-model, if the 60th scan position on the 120th scan line is marked as a land–sea boundary point, the buffer region is the scan position from the 50th to the 70th on that scan line. The module examined the intersection between the coastline vector and the vectors connecting the 50th and 60th, 51st and 61st, …, 60th, and 70th scan positions on that scan line.

• Perpendicularity Identification: Assuming the along-track/cross-track vectors intersect with the coastline vector, the next step is to determine whether the intersection angle is perpendicular. The intersection angle can be calculated as follows:

$$cos\theta ={\displaystyle \frac{\overrightarrow{a}·\overrightarrow{b}}{\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|}}={\displaystyle \frac{x_a·x_b+y_a·y_b}{\sqrt{x_a^2+y_a^2}·\sqrt{x_b^2+y_b^2}}}$$

(2)

$$\theta =\arccos \left(cos\theta \right)$$

(3)

where $x_a=C_{x2}-C_{x1}, y_a=C_{y2}-C_{y1}, x_b=T_{x2}-T_{x1}, y_b=T_{y2}-T_{y1}$, $\theta$ is the angle between the vectors. When one along-track (cross-track) vector is perpendicular to the coastline vector, the midpoint of the along-track (cross-track) vector is considered a sample point that meets the geometric conditions. Due to the randomness of the intersection positions between the coastline and the FOVs, a sufficiently large sample size can effectively reduce random errors. To expand the sample size, as long as the intersection angle is within the range of 89–91°, the cross-track or along-track vector is considered perpendicular to the coastline. As shown in Figure 4, the arrows represent the along-track/cross-track vectors perpendicular to high-resolution coastline. Each swath of MWRI-RM may yield multiple sample points that meet the geometric conditions.

Figure 4. Schematic of qualified boundary points and coastline inflection points for along-track (a) and cross-track (b) deviation estimations. The demonstrated observations are part of the descending swath of MWRI-RM at UTC 202308280048 (Figure 4a) and part of the ascending swath of MWRI-RM at UTC 202308261403 (Figure 4b). Thin black ellipses represent MWRI-RM FOVs, and the blue line denotes the coastline. Color shadings denote Tb for channel 89 GHz V-pol. Black circles and dots indicate selected boundary points and coastline inflection points, respectively. Arrows indicate the along-track vectors in (a) and cross-track vectors in (b). For clarity, Figure 4a displays one point out of every 4 in the scanning direction.

Figure 4. Schematic of qualified boundary points and coastline inflection points for along-track (a) and cross-track (b) deviation estimations. The demonstrated observations are part of the descending swath of MWRI-RM at UTC 202308280048 (Figure 4a) and part of the ascending swath of MWRI-RM at UTC 202308261403 (Figure 4b). Thin black ellipses represent MWRI-RM FOVs, and the blue line denotes the coastline. Color shadings denote Tb for channel 89 GHz V-pol. Black circles and dots indicate selected boundary points and coastline inflection points, respectively. Arrows indicate the along-track vectors in (a) and cross-track vectors in (b). For clarity, Figure 4a displays one point out of every 4 in the scanning direction.

As mentioned, in addition to meeting the geometric conditions, the coastline inflection points should also satisfy the quality control conditions. To achieve this, geometrically qualified sample points were used to select the sample sections. To reduce the estimation errors, the Tbs in the sample section should not be affected by other factors, such as radio frequency interference or clouds/rain (Figure 3). Specifically, in the cross-track/along-track directions, 40 points centered on each boundary point were taken as a sample section. Only sample sections free from radio frequency interference were retained. Next, sample sections in which Tbs are affected by clouds/rain should be excluded. Generally, the gradient of the Tbs is large at the coastline inflection points and in the vicinity of clouds/rain (Figure 5). Large gradients, apart from the inflection points, may cause inaccurate detection of the land–sea boundary by the Tb gradient. On the condition that the gradient of the normalized Tbs in the along-track (cross-track) sample section is greater than 0.5 (0.2), respectively, the corresponding sample section and coastline infection point were removed. It is evident that the gradient changes are relatively smooth for the retained sample section (Figure 5). The retained sample sections and corresponding coastline inflection points were processed in the next module.

3.2. Automatic Estimation Module

The primary objective of this module is to calculate the along-track and cross-track IFOV inter-channel deviations. In the previous CIPAI module, we obtained the sample sections and the corresponding coastline inflection points for the along-track sub-model and cross-track sub-model, respectively. The section of each of the N inflection points forms the deviation calculation matrix $M_{N\times 40}$. We calculated the Tb gradients of $M_{N\times 40}$ before estimating the deviation. To achieve subpixel accuracy, the gradient matrix needs to be interpolated. A commonly used and highly accurate cubic spline interpolation method was employed. Next, the position of the maximum Tb gradient for each channel in each section was examined, and the pixel offset relative to the 89 V channel was obtained. The average pixel offsets of all inflection points for each channel are the IFOV inter-channel deviations. The offset distance can be calculated by multiplying the step distance in the cross-track (2.23 km) or along-track (12.24 km) direction by the offset pixels.

4. Estimation of IFOV Inter-Channel Deviations

4.1. Along-Track Deviation Case Analysis

To test the performance of the along-track IFOV deviation sub-model, we selected the descending swath of the MWRI-RM at 00:48 UTC on 28 August 2023 as the test data. At the time, the MWRI-RM passed over the northeastern part of Africa, visually near the coastline of the Horn of Africa, which looks perpendicular to the along-track direction. We inferred that there would be inflection points suitable for deviation estimation.

Using the land–sea mask from the MWRI-RM Level-1 data, 9991 points were identified and located on the land–sea boundaries. Then, we identified six coastline segments perpendicular to the along-track vectors, selecting 72 sample points that met the geometric conditions (Figure 6a). Next, based on the data quality control conditions, 35 coastline inflection points and their corresponding sample sections (Figure 6b) were selected for deviation estimation. Before calculating the IFOV inter-channel deviation, to achieve subpixel accuracy, we applied spline interpolation to the gradient matrix of the Tb sections. For each inflection point, we examined the positions of the maximum Tb gradients for the 10 window channels and calculated the deviations of the other nine channels relative to the 89 V channel. Finally, the average channel deviations of the 35 inflection points were used as the final calculated deviations.

The deviations of all nine channels display approximately normal distributions, as shown in Figure 7. The calculated IFOV deviations in the along-track direction range from about −0.5 to 0.5 pixels. The average deviation of the 10.65 GHz channel is the largest, at 1 km, while the deviations of the higher frequency channels are all below 0.5 km. Additionally, the results show that the standard deviation (STD) of IFOV inter-channel deviations of lower frequency channels are larger compared to that of the higher frequency channels (Figure 7). This may be related to the larger IFOV and larger uncertainty of lower frequency channels. It is worth noting that in this experiment, the IFOV was treated as a point, whereas the actual IFOV has a considerable spatial extent. For example, the 10.65 GHz channel corresponds to an elliptical FOV of 21 km × 35 km. This spatial extent can cause the true position of the coastline-cutting FOV to be uncertain, potentially introducing errors in the result based on the small sample data. To reduce such random errors, subsequent experiments would use long-term observations to evaluate the on-orbit IFOV inter-channel deviations of the instrument.

4.2. Cross-Track Deviation Case Analysis

In this section, we examined the effectiveness of the cross-track IFOV deviation estimation sub-model by using another track of observations. Specifically, we selected the ascending swath of the MWRI-RM at 14:03 UTC on 26 August 2023. At this time, the MWRI-RM passed over the northeastern part of Africa, visually near the coastline of the Horn of Africa, which seems perpendicular to the cross-track direction. Therefore, we hypothesized that there would be inflection points suitable for deviation estimation.

Similarly, by the land–sea mask from the MWRI-RM Level-1 data, the sub-model identified 652 grid points as land–sea boundary points and 183 sample points that met the geometric conditions. Based on the data quality control conditions, 22 coastline inflection points and the corresponding sample sections were identified for deviation calculation (Figure 8a). After spline interpolation to the gradient matrix of the Tb sections, we obtained the deviations of the maximum Tb gradient position relative to the 89 V channel. Finally, the average channel deviations of the 22 inflection points were used as the final calculated deviations.

Similar to the probability density distribution of the along-track deviations, the cross-track deviations also present approximately normal distributions (Figure 8b). IFOV deviations in the cross-track direction vary from about −2.5 to 2.0 pixels, as shown in Figure 8b. The 10.65 GHz channel has the largest deviation, approximately 1 km, while the deviations of the higher frequency channels are all below 0.2 km. It is obvious that the STD of the deviations of lower frequency channels is also larger than that of the higher frequency channels. Additionally, the number of inflection points selected from the single-track data for evaluation is relatively small; in subsequent research, we used longer time series observations to evaluate the on-orbit cross-track IFOV inter-channel deviations.

4.3. Estimation of On-Orbit IFOV Inter-Channel Deviation

To evaluate the on-orbit IFOV inter-channel deviations of the FY-3G MWRI-RM, we used the long-term observations from September 2023 to February 2024. The evaluation was conducted by separately calculating the cross-track deviations, along-track deviations, and comprehensive IFOV inter-channel deviations.

For the cross-track deviations, our model first detected inflection points that met the geometric conditions and quality control requirements. A total of 4880 inflection points were detected (

Table 1. Number of sample points for estimating on-orbit IFOV inter-channel deviation.

	Cross-Track Dev. Estimate		Along-Track dev. Estimate
	No. of Geometrically Qualified Points	No. of Inflection Points	No. of Geometrically Qualified Points	No. of Inflection Points
Sep. (2023)	3593	838	12,520	5285
Oct. (2023)	3627	889	12,490	4945
Nov. (2023)	3429	883	12,171	4876
Dec. (2023)	3753	854	12,498	4925
Jan. (2024)	3306	718	10,939	4375
Feb. (2024)	3189	698	10,446	4214
Total	20,897	4880	71,064	28,620

), and the spatial distribution is shown in Figure 9a. The inflection points are evenly distributed along the coastlines of all major plates except for Europe. We calculated the long-term IFOV inter-channel deviations and compared them to the monthly means. The results show that the deviations of all channels display an approximately normal distribution (Figure 10), indicating the effectivity of our model in identifying inflection points—most of the deviations were spread within 4 km. The average deviations of the on-orbit IFOV for all channels are well below 1 km, with the largest being 0.75 km for the 10 V channel (

Table 2. On-orbit IFOV inter-channel deviations relative to 89 GHz V-pol channel for FY-3G/MWRI-RM.

Channel	Cross-Track Dev.				Along-Track Dev.				Comprehensive Dev.
	Mean (Pixel)	STD (Pixel)	Mean (km)	STD (km)	Mean (Pixel)	STD (Pixel)	Mean (km)	STD (km)	Mean (km)
10.65 V	−0.33	0.80	−0.75	1.78	0.01	0.22	0.07	2.70	1.78
10.65 H	−0.28	0.70	−0.62	1.57	0.00	0.21	−0.04	2.61	1.57
18.7 V	−0.04	0.61	−0.08	1.35	−0.02	0.16	−0.26	1.96	1.38
18.7 H	0.02	0.49	0.05	1.09	−0.03	0.16	−0.36	1.97	1.15
23.8 V	0.00	0.57	−0.01	1.27	−0.01	0.14	−0.17	1.69	1.28
23.8 H	0.00	0.48	0.00	1.07	−0.02	0.14	−0.28	1.74	1.10
36.5 V	−0.04	0.27	−0.10	0.60	0.00	0.10	0.03	1.27	0.60
36.5 H	−0.09	0.24	−0.21	0.53	0.00	0.10	−0.03	1.28	0.53
89 H	0.00	0.14	0.00	0.31	0.00	0.05	−0.02	0.64	0.31

). The results demonstrate that the lower frequency channels (10 GHz) have a larger STD, and the STD of 89 GHz is small (Figure 10 and Table 2). This may be due to the larger antenna beam width of the lower frequency channels, resulting in a broader ground footprint and a larger uncertainty. There is no significant difference between the monthly calculation results and the long-term results at the 0.05 level by the Student’s t-test and joint hypotheses test.

For along-track channel deviations, the number of inflection points used for estimation each month was more than 4000 (Table 1). As shown in Figure 9b, the inflection points are primarily distributed along the coastlines of North and South America and Africa. Using long-term observations, the IFOV inter-channel deviations were calculated. As shown in Figure 10, the vast majority of deviations for each channel are smaller than 3 km. The mean deviations for each channel from a low frequency to high frequency are 0.07 km, −0.04 km, −0.26 km, −0.36 km, −0.17 km, −0.28 km, 0.03 km, −0.03 km, and −0.02 km, respectively, as shown in Table 2. It is evident that the lower frequency channels have larger STDs compared to the higher frequency channels. That is in accordance with the hardware design that the lower frequency channels correspond to a broader ground footprint and a larger uncertainty. Moreover, we found that the STD of along-track deviations is slightly larger than that of the cross-track deviations (Figure 10), which may be related to the larger size in the along-track direction. The ratio of the STD of along-track deviations and cross-track deviations is about 1.5 (Table 2), which corresponds with the ratio of the long axis and the short axis of the elliptical FOV.

The comprehensive channel deviations, which are the vector sum of the cross-track and along-track channel deviations, are shown in the last column of Table 2. It can be observed that the 10 GHz channels have the largest deviation, with the vertical and horizontal polarization channel deviations being 0.75 km and 0.62 km, respectively. The 18 GHz channels follow, with vertical and horizontal polarization channel deviations of 0.28 km and 0.36 km, respectively. The 23 GHz channel deviations are 0.17 km and 0.28 km, the 36 GHz channel deviations are 0.10 km and 0.21 km, and the 89 H channel deviation is the smallest at 0.02 km. The IFOV deviations of all channels relative to the 89 V channel are less than 1 km, meeting the design requirements.

4.4. Model Validation

To examine the model’s effectiveness, we intended to adopt an indirect method to verify the model’s accuracy. In view that telemetry parameter uploading can adjust the on-orbit IFOV inter-channel deviations by revising the sampling time sequence, the theoretical deviation changes caused by parameter uploading can be obtained. Moreover, we employed our model to calculate the adjustments before and after parameter uploading. Assuming that the two sets of changes are similar, it would demonstrate the model’s effectiveness in evaluating the channel deviations.

On 22 August 2023, we uploaded the parameters by telemetry to adjust the IFOV inter-channel deviations. The theoretical changes in the inter-channel deviations caused by parameter uploading are shown in the second column of

Table 3. Changes in IFOV inter-channel deviations after parameter uploading.

Channel	Pre-Upload Cross-Track Dev.		Changes in Cross-Track Dev. (km)	Theoretical Upload Effect (km)
	Mean (km)	STD (km)
10.65 V	4.63	0.75	−5.38	−5.45
10.65 H	4.43	0.70	−5.05	−5.16
18.7 V	3.09	0.59	−3.17	−3.16
18.7 H	2.90	0.48	−2.85	−2.87
23.8 V	1.96	0.54	−1.97	−2.01
23.8 H	2.02	0.48	−2.02	−2.08
36.5 V	1.23	0.28	−1.33	−1.36
36.5 H	1.15	0.23	−1.35	−1.36
89 H	−0.02	0.14	0.02	0.00

. We selected the observations from May to July 2023 as the pre-upload measurement to evaluate the pre-upload IFOV inter-channel deviation. The mean and STD of the pre-upload cross-track deviations are shown in Table 3. The post-upload deviations from September 2023 to February 2024 have been demonstrated in Section 4.3 (Table 2). By subtracting the pre-upload deviations from the post-upload deviations, we obtained the changes in the cross-track IFOV inter-channel deviations before and after parameter uploading (Table 3).

Comparing the model-calculated deviation adjustments with the theoretical changes caused by parameter uploading, the result shows that the differences of almost all channels are within 100 m. It indicates that the model has high reliability and accuracy in practical applications, effectively evaluating the on-orbit IFOV inter-channel deviations of conical-scanning microwave radiometers. It could play an essential role in improving the quality and accuracy of observation data to meet the needs of scientific research and applications.

Comparing the model-calculated deviation adjustments with the theoretical changes caused by parameter uploading, the results show that the differences of almost all channels are within 100 m. It indicates that the model has high reliability and accuracy in practical applications, effectively evaluating the on-orbit IFOV inter-channel deviations of conical-scanning microwave radiometers. It could play an essential role in improving the quality and accuracy of observation data to meet the needs of scientific research and applications.

5. Conclusions and Discussion

This study presents a novel automatic estimation model for IFOV inter-channel deviations for conical-scanning payloads. The model includes both along-track and cross-track sub-models, each comprising a Coastline Inflection Point Automatic Identification module and an Automatic Estimation module. The performance of this Automatic Estimation model was tested using the FY-3G MWRI-RM. The main conclusions are as follows:

(1)

By establishing the Automatic Identification module, it can automatically detect the Tb inflection points where the along-/cross-track vectors are perpendicular to the actual coastlines. Compared to manually selecting the inflection points, the Automatic Identification module can identify a larger number of objective samples in a broader region for an IFOV inter-channel deviation estimation.

(2)

Through the evaluation of on-orbit IFOV inter-channel deviations using over 6 months of L1 observations, spanning from September 2023 to February 2024, the result shows that the IFOV deviations of all channels are well below 1 km, meeting the instrument design requirements of 2 km. Furthermore, the IFOV deviations in low-frequency channels are larger compared to the high-frequency channels, with the deviations ranging from 0.7 km (10 GHz) to 0.02 km (89 GHz).

(3)

By comparing the adjustments calculated by our model with the theoretical changes caused by parameter uploading, the model’s effectiveness was validated. The results show that the difference is less than 100 m, indicating that the model has a high calculation accuracy and is suitable for estimating IFOV inter-channel deviations of the MWRI-RM.

The automatic estimation model for IFOV inter-channel deviations can estimate the deviations and monitor the changes in on-orbit conical-scanning passive microwave payloads, facilitating high-quality quantitative applications of MWRI-RM data. Future research can further enhance the precision of the automatic estimation model through the following strategies: (1) using higher quality and more accurate datasets, such as those containing geographic positions, land–sea masks, and coastline information; and (2) applying additional constraints for selecting qualified inflection points, such as land cover types, terrain features, and other relevant factors. Furthermore, the MWRI IFOV inter-channel deviations estimated in this paper are global averages. IFOV inter-channel deviations may exhibit regional differences due to instrument angle variations, which will be explored in the future.