Effects of Solar Intrusion on the Calibration of the Metop-C Advanced Microwave Sounding Unit-A2 Channels

Abstract

This study presents our first discovery about two abnormal problems in the blackbody calibration target associated with the antenna unit A2 in the Metop-C AMSU-A instrument. The problems include the anomalous patterns in both blackbody kinetic temperature $\left(T_w\right)$ and radiative temperature (measured in warm count or $C_w$), and the time lag between orbital cycles of $T_w$ and $C_w$. This study further determines solar intrusion as the root cause of the anomalous pattern problem. According to our analysis, solar illumination is constantly observed during each orbit near the satellite terminator, causing anomalous changes in $C_w$ and $T_w$, characterized by sudden and abnormal increases typically for more than 16 min. The resultant maximum antenna temperature errors due to abnormal increases in $C_w$ are approximately in the range from 0.15 K to 0.25 K, while the maximum errors due to the abnormal increase in $T_w$ are in the range from 0.04 K to 0.07 K, varying with orbit, season, and channel. The time shift feature is characterized with a changeable time lag with the season in the $T_w$ orbital cycle in comparison with the $C_w$ cycle. The longest time lag up to about 18 min occurs in summer through early fall, while the time lag can be decreased down to about 9 min in winter through early spring. Hence, this study underscores the imperative need for future research to rectify radiance errors and reconstruct a more accurate long-term Metop-C AMSU-A radiance data set for channels 1 and 2, crucial for climate studies.

1. Introduction

The Advanced Microwave Sounding Unit-A (AMSU-A) Instrument is a microwave radiometer consisting of 15 channels from 23.8 to 89 GHz, and its major specifications are shown in

Table 1. AMSU-A Instrument specifications [1,2,3].

Ch.	Center Frequency (MHz)	Conversion Bandwidth (MHz)	Temperature Sensitivity NEDT (K)
1	23,800	270	0.3
2	31,400	180	0.3
3	50,300	180	0.4
4	52,800	400	0.25
5	53,596 ± 115	170	0.25
6	54,400	400	0.25
7	54,940	400	0.25
8	55,500	330	0.25
9	fo = 57,290.344	330	0.25
10	fo ± 217	78	0.4
11	fo ± 322.2 ± 48	36	0.4
12	fo ± 322.2 ± 22	16	0.6
13	fo ± 322.2 ± 10	8	0.8
14	fo ± 322.2 ± 4.5	3	1.2
15	89,000	1500	0.5

[1,2,3]. Specifically, it has three antenna systems, A1-1, A1-2, and A2. The A1-1 system contains channels 6–7 and 9–15; A1-2 contains channels 3–5 and 8; A2 contains channels 1 and 2 [1,2,3]. The AMSU-A instrument is/was an operational payload onboard the National Oceanic and Atmospheric Administration (NOAA)-15 through NOAA-19 and Meteorological Operational satellite (Metop)-A through Metop-C. It is noted that the NOAA-16, NOAA-17, and Metop-A satellites were decommissioned on 9 June 2014, 10 April 2013, and 15 November 2021, respectively. The AMSU-A channel 15 onboard the Metop-B were disabled on 18 January 2017. In the past decades, intensive pre- and post-launch calibration/validation activities have been successfully applied to the AMSU-A instruments to derive high quality Earth scene antenna Temperature Data Record (TDR) and Sensor Data Record (SDR) data from Raw Data Record (RDR) (e.g., [4,5,6,7,8,9,10,11,12,13,14]). The AMSU-A data have contributed significantly to improvements in weather forecasts by Numerical Weather Prediction (NWP) Systems (e.g., [15,16,17,18]), retrievals of environmental products [19,20,21], and monitoring of climate changes [22,23,24]. As the last unit in the series, the AMSU-A instrument onboard the Metop-C satellite not only ensures the continuation of those applications but also enables a longer AMSU-A data record.

In spite of wide applications of the AMSU-A TDR data, new improvements in the quality of AMSU-A data are valuable to further enrich the value of the data in various applications. Especially, the absolute radiometric calibration accuracy of the instrument data becomes more important for climate analysis due to its long data record. In addition, the calibration accuracy must be traceable to the National Institute of Standards and Technology (NIST) via secondary temperature standards. As a result, it is a continuous effort to monitor and detect new anomalies that may degrade the quality of the data. For example, the performance of AMSU-A TDR data quality in available channels are routinely monitored in the NOAA STAR Integrated Calibration and Validation System (ICVS) (https://www.star.nesdis.noaa.gov/icvs/index.php, accessed on 6 June 2012). A few key parameters about the quality of the AMSU-A TDR data are monitored in the ICVS website in a near-real-time mode, e.g., channel noise equivalent differential temperature (NEDT), gain, space view (cold) count, blackbody target (warm) count, kinetic or bulk temperature of the blackbody target, instrument shelf temperature, etc. In addition, the radiative transfer model simulation to the Earth scene brightness temperature is used to identify anomalous features in brightness temperatures at sounding channels.

In our monitoring process, it is first found that certain anomalous patterns always remain in the blackbody calibration target associated with kinetic temperature ($T_w$) and warm count ($C_w$) for AMSU-A channels 1 and 2 onboard Metop satellites. Those anomalous patterns are associated with sudden and unexpected increases for a few minutes during each orbit in both the kinetic temperature and the radiative temperature of the blackbody target (expressed as a warm count in the measurement) (see the analysis in Section 3 below). In addition, a time lag is observed in the orbital variation of the kinetic temperature in comparison with that of the radiative temperature (see the analysis in Section 3 below). According to our analysis, similar anomalous features also partially exist on the afternoon satellites NOAA-18 and NOAA-19 (the results are not shown in this study). To the authors’ best knowledge, those discoveries are the first report for onboard AMSU-A instruments. The blackbody target anomalous problems were also not captured in the pre-launch analysis for all AMSU-A instruments. In practice, any error sources on the blackbody target can introduce uncertainties in the calibration and produce erroneous radiance or antenna temperatures because the blackbody target is used to determine Earth scene radiance or antenna temperatures [4,7,12]. Moreover, the window channels 1 and 2 for the AMSU-A provide unique information to the other 12 temperature sounding channels from 3 through 14 by correcting for the surface emissivity, atmospheric liquid cloud water, and total precipitable water, thus playing a critical role in various applications of AMSU-A data. Therefore, it is desirable to analyze those anomalous features that happen in the blackbody calibration target in channels 1 and 2.

This study will present our first findings on detected anomalous features in the blackbody calibration target associated with $T_w$ and $C_w$ in channels 1 and 2 by using the Metop-C AMSU-A as a demonstration due to its significance in the AMSU-A data record. Moreover, solar intrusion will be determined as the root cause to the anomalous pattern problem based on a few established facts in this study. The solar intrusion in the AMSU-A instrument is investigated as the first report among pre-launch and post-launch calibration and validation activities. In this regard, however, the solar intrusion is not new to other satellite instruments. For instance, both instruments, Advanced Microwave Scanning Radiometer and WindSat, exhibited significant solar intrusion into the hot calibration load, leading to erroneous values for the hot load temperature [25,26,27]. Additionally, a solar intrusion effect was reported as early as 1998 for the Advanced Very High Resolution Radiometer (AVHRR) instrument flown on the NOAA polar orbiting satellites, causing an anomalous pattern in the blackbody warm count [28,29]. The AVHRR instrument suffered from solar contaminations when exposed to sunlight at spacecraft sunrise, related to a large scan angle within observations [28,29]. The AMSU-A instrument has similar large scan angles to the AVHRR, and the abnormal pattern problem in $T_w$ and $C_w$ does occur with large solar zenith angles. These facts motivate our identification of solar intrusion as the primary cause of the AMSU-A anomalous pattern issue observed in the AMSU-A. In addition to the anomalous pattern problem, this study will also examine the time lag phenomenon in the orbital variation of $T_w$ in comparison with that of $C_w$, making the initial discovery. Its root cause is expected to be investigated in future studies after we have a good understanding of it.

This paper is organized as follows. The next section describes the calibration equation and operational processing for the AMSU-A TDR data. Section 3 investigates anomalous features in the blackbody calibration target for Metop-C AMSU-A in channels 1 and 2, while Section 4 addresses implications of the largest anomalous changes in both $C_w$ and $T_w$ for calibration accuracy of antenna temperatures. Section 5 investigates the root cause to the anomalous pattern problems in $C_w$ and $T_w$. The final section summarizes and concludes our novel findings about the anomalous features and root cause. The discoveries of this study are anticipated to offer valuable insights into anomalous characteristics, affected regions, a root cause, and their impacts on radiance calibration accuracy. While this study focuses on Metop-C AMSU-A, the analysis method can be applicable for AMSU-A instruments on the NOAA-18, NOAA-19, Metop-A, and Metop-B, where solar intrusion is partially observed.

2. Calibration Equation and Operational Processing

In the AMSU-A calibration process [12], as given for other microwave radiometers such as the Advanced Technology Microwave Sounder (ATMS) [30], two calibration measurements, i.e., the cold space and the warm load, are used together with a non-linear radiometric calibration equation to determine Earth scene radiance $R_s$ per scan, viewing angle, and channel, as shown below.

In the radiance domain [5,12,30,31],

$$R_s=R_c+{(R}_W-R_C)\frac{\left(C_s-C_c\right)}{\left(C_w-C_c\right)}+Q,$$

(1)

where

$$Q=\mu {{(R}_W-R_C)}^2\frac{\left(C_S-C_w\right)\left(C_S-C_c\right)}{{(C_w-C_c)}^2},$$

(2)

$$G=\frac{\left(C_w-C_c\right)}{\left(R_W-R_C\right)}.$$

(3)

Indices of the channel frequency and beam position (satellite scan viewing angle) are omitted in the variables of the equations throughout this study for brevity. In the above equations, $R_S$ represents the Earth scene radiance of individual channels; $C_S$ is the radiometric count from the Earth scene target; $G$ is the channel calibration gain; $C_w$ and $C_c$ denote the blackbody and space count, respectively. In addition, $R_W$ and $R_C$ denote the radiance corresponding to $T_W$ and $T_c$, respectively, where $T_W$ denotes the platinum resistance thermometer (PRT) temperature of the warm load converted from measured radiometric counts, and its calculation and calibration are given in [5]. The conversion coefficients from counts to PRT temperatures such as $T_W$ are included in TDR data. $T_c$ is cosmic temperature after certain correction [12], and $Q$ is the nonlinearity of instrument square-law detector that is a function of nonlinearity parameter μ. Variables, i.e., $R_C, R_W,$ and $R_S,$ in the above equations are performed in radiance with the unit of mW/(m²·sr·cm⁻¹).

Table 2. Variables in the equations and explanations.

Symbol	Quantity
$R_S$	$\mathrm{Earth} \mathrm{scene} \mathrm{radiance}, \frac{mW}{m^2·sr·{cm}^{-1}}$
$T_A$	$\mathrm{Antenna} \mathrm{temperature} \mathrm{in} \mathrm{Kelvin}, \mathrm{which} \mathrm{is} \mathrm{converted} \mathrm{from} R_S$ by using the inverse of Planck function
$T_W$	Kinetic or bulk temperature of the blackbody target (warm load), also named as warm load PRT temperature
$T_c$	Cosmic temperature after certain corrections [12]
$R_W$	$\mathrm{Radiance} \mathrm{corresponding} \mathrm{to} T_W$ using Planck function
$R_C$	$\mathrm{Radiance} \mathrm{corresponding} \mathrm{to} T_c$ using Planck function
$C_w$	Warm load radiometric count (warm count), corresponding to the radiative temperature of the blackbody target
$C_c$	Cold space radiometric count (cold count)
$C_S$	Earth scene radiometric count (scene count)
Q	Nonlinearity of instrument square-law detector in radiance domain
$Q_T$	Nonlinearity in temperature domain
μ	Nonlinearity parameter μ in radiance domain
${\mu }_T$	Nonlinearity parameter μ in temperature domain
$G$	Calibration channel gain in the domain of radiance
$G_T$	Calibration channel gain in the domain of temperature

provides a summary about physical explanations of major variables in the equations in this study.

The calibration equation in the radiance domain can be converted to the antenna temperature $T_A$ domain. $T_A$ has the same format as that in (1) to (3) except for a conversion of each parameter from radiance to brightness temperature by using the Planck function instead of Rayleigh–Jeans approximation [32]. The nonlinearity $Q$ in (2) needs to be replaced by a new variable $Q_T$ that is computed using the same expression as $Q$ in (2) except in the temperature domain.

In the operational processing of AMSU-A data in channels 1 and 2, hereinafter named as AMSU-A2 channels since they are associated with the antenna unit A2, six PRT sensors are distributed at the base of the in-flight warm calibration target to determine its kinetic or bulk temperature, $T_w$, which is often referred to as PRT temperature due to the use of the PRT sensors [31,33]. It is actually the average of six PRT sensors for the AMSU-A2 channels unless new descriptions are given. According to our analysis, the uncertainty of $T_w$ per PRT sensor is in an order of 0.05 K. This estimate is referred to the ICVS web-based monitoring tool: https://www.star.nesdis.noaa.gov/icvs/status_MetOPC_AMSUA.php, accessed on 5 April 2019. Based on the measurement error analysis with small sampling size, the uncertainty of the averaged trends after satellite merging is expressed as $\pm \frac{∆}{2\sqrt{K}}$ [34,35]. In this study, Δ (≈0.05 K/PRT sensor) denotes the maximum relative error for one PRT sensor from another PRT sensor used in the AMSU-A2 unit, and K (=6) the number of PRT sensors used for the AMSU-A2 unit. As a result, the averaged uncertainty of the $T_w$ is about 0.01 K.

The warm count $C_w$ in (1) is a weighted average by using originally measured $C_W$ data within seven neighboring scans to reduce fluctuations of the original $C_W$ along the scan due to instrument noise [5,33]. For each scan, the weighted-average warm (cold) count, i.e., ${\overline{C}}_x,$ is obtained by convolving $C_x$ (where x = w or c) over $(2N+1)$ neighboring scan lines using certain weighting values, as shown below.

$${\overline{C}}_x\left(t_j\right)=\frac{\sum _{i=-N}^N{W}_i{C}_x\left(t_i\right)}{\sum _{i=-N}^N{W}_i}.$$

(4)

Here, $t_j$ denotes the time of the current scan line; $t_i$ represents the time of the scan lines just before or after the current scan line; $N$ is the number of scans used in the weighing process before or after the current scan line; $w_i$ represents a set of triangular weights relative to the calculated scan at $t_j$. For example, when $N=3,$ there are a total of seven scan lines in (4), $w_i$ takes the values of 1, 2, 3, 4, 3, 2, and 1 for the seven scan lines with $i=1,2,3,4,3,2, \mathrm{a}\mathrm{n}\mathrm{d} 1,$ respectively. In the operational processing, $C_x\left(t_i\right)$ in (4) is the average of two measurements, namely $C_x^{1st}\left(t_i\right)$ and $C_x^{2nd}\left(t_i\right)$, from different viewing points per scan, i.e., ${C_x\left(t_i\right)=[C}_x^{1st}\left(t_i\right)+C_x^{2nd}\left(t_i\right)]/2$.

The calibration equation in (1) assumes that there are no extraneous radiations other than radiation from the calibration target. This assumption works well for pre-launch or post-launch AMSU-A instruments for most of the AMSU-A channels. As an example, Figure 1 shows time series of two kinetic temperatures that are associated with the antenna unit A1-1 and A1-2, and the warm counts at the two channels corresponding to the A1-1 and A1-2, by using approximately two orbits of operational AMSU-A TDR data on 28 May 2021. Both $T_W$ and ${\overline{C}}_{w7}$ exhibit an expected orbital cycle from orbital minimum (peak) to an orbital peak (minimum) due to changes in the instrument temperature during ascending and descending observations. Here, ${\overline{C}}_{w7}$ represents the weighting average of seven neighboring scan lines using (4). Additionally, the variations of $T_W$ and ${\overline{C}}_{w7}$ generally align with the averaged trend of the data, either decreasing from $p_{max}$ to $p_{min}$ or increasing from $p_{min}$ to $p_{max}$, as depicted by the conceptual linear fitting lines in the figure. As anticipated, certain fluctuations persist within orbital variations due to instrument noise, causing a few outliers that exceed largely the normal trend at random positions. For example, despite the application of the seven-neighboring average in (4), ${\overline{C}}_{w7}$ still frequently exhibits large fluctuations during orbital observations. The fluctuations do not follow a stable pattern, and they do not occur at a consistent position from one orbit to another orbit. In addition, $T_W$ typically displays a small fluctuation within ±0.01 K for a couple of minutes before it jumps or drops to a higher or lower level of the value, which is consistent with the calculation of the averaged $T_w$ uncertainty by using $\pm \frac{∆}{2\sqrt{K}}$. Overall, the observed features are expected, without anomalous patterns.

3. Anomalous Features in AMSU-A2 Blackbody Calibration Target

In reality, the relationship between the calibration targets and the required radiance in (1) could be disrupted if one of the following problematic situations occurs: one situation is that the radiometer receives an extraneous radiation, such as a solar intrusion from sources other than the blackbody, during the blackbody view; another situation is that a discrepancy exists in either phase (time) or magnitude between the orbital variations of $T_W$ and $C_w$. Unfortunately, both problems occur for the AMSU-A instrument associated with channels 1 and 2, as described below.

3.1. Anomalous Features

Figure 2a,b show the time series of $T_W$ and ${\overline{C}}_{w7}$ for the operational data during 14 orbits on 28 May 2021 for Metop-C AMSU-A channels 1 and 2, respectively. An abnormal pattern with sudden jumps persistently remains in each orbit of $T_W$ and ${\overline{C}}_{w7}$ in comparison with an averaged normal variation trend in the absence of the abnormal pattern problem. A thorough discussion will be provided alongside a detailed time series zoom-in depicted in Figure 3 below. The affected area locates at a similar position during each orbit in a day for the two channels. In addition, the orbital variation of $T_W$ delays for certain time in comparison with that of $C_W$.

To better understand these anomalous features, Figure 3a focuses on two orbits of the data in channel 1 that were used in Figure 2. In addition, the latitude and solar zenith angle (SZA) are added as Figure 3b. Several specific positions in the time series of the data, e.g., starting, peak, and ending positions of the anomalous pattern regions in both ${\overline{C}}_{w7}$ and $T_w$, are marked in the first orbit to highlight the regions in the presence of the anomalies. Two important features are observed based on the figure, as described below.

Firstly, both ${\overline{C}}_{w7}$ or $T_W$ exhibit abnormal patterns with unexpected sudden increases in comparison with an averaged normal variation trend for more than 16 min during each orbit of the observations, which are entirely different the instrument noise-caused fluctuations in Figure 1 above. A detailed explanation about this is provided below.

For a conceptual demonstration, two pairs of points $(p_1$ and $p_3)$ and ($p_1^{\prime }$ and $p_3^{\prime })$ in Figure 3a indicate the approximate starting and ending positions of noticeable abnormal patterns during the first orbit for ${\overline{C}}_{w7}$ and $T_w$, respectively. The resultant variations in both ${\overline{C}}_{w7}$ and $T_W$ during the marked areas significantly deviate from the averaged trend of the data in the absence of the anomalies. Recall that in the absence of the anomaly, $T_w$ associated with antenna unit A1-1 and A1-2 can exhibit an orbital cycle with a relatively smooth trend from a minimum (or maximum) to a maximum (or minimum) (see Figure 1a,b above), where there was no abnormal problem. Therefore, for a conceptual demonstration, a linear dot-dash line in red is added in Figure 3a, from $p_0$ (${\overline{C}}_{w7max}$) to $p_3,$ approximately representing the averaged normal trend of ${\overline{C}}_{w7}$ in the absence of the anomaly along the decreasing direction during the first orbit of the observations. Similarly, a pink nonlinear dot-dash curve from $p_1^{\prime }$ to $p_4^{\prime }$ roughly represents the averaged normal trend of $T_W$ in the decreasing direction. Other methods can also be used to fit the normal trend of the data, all indicating the occurrence of the abnormal pattern. More importantly, these abnormal patterns are wholly distinct from the aforementioned noise-caused fluctuations: the anomaly pattern lasts for an extended period (more than 16 min, as seen on the scale in the figure) and constantly persists over similar locations during each of 14 orbits in a day (see Figure 2 above). Additionally, as shown in Figure 3b, the SZAs associated with the abnormal patterns are over 100°, indicating a possible impact of solar intrusion on the AMSU-A blackbody target associated with the antenna unit A2 (see the analysis in Section 5 for details). These conclusions are also applicable for channel 2.

As analyzed above, the abnormal patterns in both ${\overline{C}}_{w7}$ and $T_w$ have been observed in comparison with corresponding averaged-normal variation trend in the absence of the degraded data. However, accurately determining the starting and ending positions is challenging due to remaining fluctuations in the data. This study does not attempt to develop a physical model due to lack of sufficient information. Instead, we present an empirical method to estimate the starting and ending positions of the anomaly to capture main abnormal features. $T_W$ exhibits better stability over time (scan) than ${\overline{C}}_{w7}$, where the fluctuation in $T_W$ usually is less than 0.01 K. Consequently, we will primarily use the anomalous features of $T_W$ to estimate the starting and ending positions, while those of ${\overline{C}}_{w7}$ will be used to confirm the analysis conclusion.

Using the first orbit of the data as a demonstration, $p_1^{\prime }$ in Figure 3a is used to represent the starting time of the $T_W$ anomaly pattern. It is defined as the local minimum position between $p_0^{\prime }$ (a peak of $T_w$ in the first orbit of observations in the absence of the abnormal occurrence) and $p_2^{\prime }$ (a local maximum due to the anomaly occurrence). In the absence of the anomaly, $T_w$ associated with antenna unit A2 should exhibit an orbital cycle with a relatively smooth trend from a minimum (or maximum) to a maximum (or minimum), similar to that in the antenna units A1-1 and A1-2 [see Figure 1a,b above], where there was no abnormal problem. It is interesting to note that the position $p_1^{\prime }$ is in proximity to the satellite terminator about 8 min prior to the spacecraft sunset (see Section 5 for details), with approximately one minute of uncertainty. $p_1^{\prime }$ is also only about a couple of minutes (see Δ${\tau }_0$ in Figure 3a) after the local minimum position of ${\overline{C}}_{w7}$ (see $p_1$ in the figure) when the ${\overline{C}}_{w7}$ anomaly problem starts. Those two facts further confirm the reasonability of the estimated starting position for the $T_W$ anomaly pattern. Regarding the time-shift of about 2 min between the positions of $p_1$ and $p_1^{\prime }$, marked with Δ${\tau }_0$ in the figure, it approximately denotes the time lag of the $T_w$ anomaly behind the ${\overline{C}}_{w7}$ anomaly. This time lag is thought to be related to the overall time lag in the orbital cycle of $T_W$ and that of ${\overline{C}}_{w7}$, which will be addressed soon.

For the ending position of the anomalous pattern, we only make a conservative estimate in the following analysis. According to our analysis in Section 4 below, an additional radiation resulting from solar intrusion is responsible for the occurrence of the anomaly pattern. The resulting $T_W$ anomaly in the blackbody kinetic temperature should experience the following variations: in the first half-cycle, the $T_W$ anomaly should gradually increase from zero (the solar intrusion just starts) to a peak (the solar intrusion just ends); in the second half-cycle, the $T_W$ anomaly should gradually decrease from the peak to zero due to a cooling process. In this study, this cycle is approximately assumed to be symmetric. With this approximation, the time length of two half-cycles is the same.

Using the first orbit of the data in Figure 3a as an example, the resultant anomalous increase in $T_W$ varies from a minimum (~zero) at $p_1^{\prime }$ to a peak (~0.07 K) at $p_2^{\prime },$ corresponding to the starting and stopping time of the solar intrusion, with a time length ${\tau }_{12}^{\prime }$. Subsequently, the anomalous variation of $T_W$ gradually decreases from the peak at $p_2^{\prime }$ to zero anomaly at $p_3^{\prime }$, corresponding to a time ${\tau }_{23}^{\prime }$. With the above symmetric approximation, ${\tau }_{12}^{\prime }\approx {\tau }_{23}^{\prime }$. Hence, $p_3^{\prime }$ can be estimated using this approximation, representing the ending position of the $T_W$ anomaly pattern. However, it should be emphasized that the symmetric assumption mostly underestimates the time length of the $T_W$ anomalous pattern. In view of Figure 3a, the variational pattern of $T_w$ after $p_3^{\prime }$ is still not smooth for at least a few minutes. This implies that these $T_w$ values might still be affected by the solar intrusion effect, although the anomaly is weak. As a result, the impact of the anomaly would be increased if the accurate ending position of the anomaly is a position after $p_3^{\prime }$ such as $p_3^{″}$ or $p_3^{‴}.$ Therefore, the current method only provides a very conservative estimate about the anomaly length and magnitude.

With the estimated $T_W$ anomaly length, furthermore, we can derive the approximate ending position of the ${\overline{C}}_{w7}$ anomaly with an additional approximation: the time length of the ${\overline{C}}_{w7}$ anomaly is supposed to be the same as that of the $T_w$ anomaly. For Figure 3a, the $p_3$ is defined as the ending position of the ${\overline{C}}_{w7}$ anomaly pattern, where the time length (${\tau }_{13})$ from $p_1$ to $p_3$ equals to that of the $T_W$ anomaly pattern (${\tau }_{12}^{\prime }+{\tau }_{23}^{\prime }),$ i.e., ${\tau }_{13}\approx {\tau }_{12}^{\prime }+{\tau }_{23}^{\prime }$. It is interesting to notice that $p_3$ is also nearby a local minimum point in ${\overline{C}}_{w7}$ before ${\overline{C}}_{w7}$ returns to a normal pattern. Therefore, this coincidence of the results using two different methods indicates the basic reasonability of the approximations.

Secondly, after gaining a good understanding of the anomalous patterns, we can analyze another important abnormal feature from Figure 3a: a time lag persists constantly throughout the entire time series of $T_W$ and ${\overline{C}}_{w7}$ during the first two orbits. This feature actually exists in each of the orbits in Figure 2 above. This time lag indicates the blackbody kinetic (bulk) temperature, $T_W,$ always responds more slowly than the blackbody radiative temperature measured in warm count.

Currently, we are unable to calculate accurately the lag length using the features in the figure due to fluctuations in both $T_W$ and ${\overline{C}}_{w7}$, although the time lag feature is visually observed in the figure. Instead, we only make an approximate estimation by computing the time difference between the peaking or minimum positions in the orbital ${\overline{C}}_{w7} \mathrm{a}\mathrm{n}\mathrm{d}{ T}_W$ in the absence of the anomaly patterns.

For instance, two points, $p_0$ and $p_0^{\prime }$, are added in Figure 3a to symbolize the positions where ${\overline{C}}_{w7}$ and $T_w$ reach to the maximum without the anomaly pattern, respectively. Certainly, the instrument noise causes instability of the maximum position, especially for ${\overline{C}}_{w7}$. For $T_w,$ the values around $p_0^{\prime }$ can be nearly constant for a few hundreds of seconds. Hence, $p_0^{\prime }$ is defined as the middle point within this nearly constant peaking range, representing the maximum position in $T_w$ during the first orbit of the observations without considering the anomaly-caused peaking position.

A similar calculation is made for ${\overline{C}}_{w7}$ to locate $p_0,$ which denotes the middle position in the peaking area to reduce the impact of fluctuations. As a result, the time difference between $p_0$ and $p_0^{\prime }$ is about 18 min, marked as Δ${\tau }_1$ in Figure 3a. This estimation is further confirmed by using the time difference between $p_4$ and $p_4^{\prime }$, which correspond to the averaged (middle point) minimum positions in ${\overline{C}}_{w7}$ and $T_w$ in the first orbit. Additionally, the time lag between the two anomalous patterns, seen as Δ${\tau }_0$ in the figure, should be related to this overall time lag. However, this time lag (a couple of minutes) is much shorter than the overall time lag between the orbital variations of ${\overline{C}}_{w7}$ and $T_w$. Similar features exist for channel 2 and other orbits. However, it is still not clear what causes the differences in the time lags between the orbital cycles and the anomalies in ${\overline{C}}_{w7}$ and $T_w$, which defers to further study.

3.2. More Discussions

The above analysis has addressed two important problematic features that occurred in ${\overline{C}}_{w7}$ and $T_w$ by using one day of the Metop-C AMSU-A data in channels 1 and 2. A further discussion is still necessary to better characterize the anomalous problems. For instance, do warm counts in individual measurements, i.e., $C_x^{1st}\left(t_i\right)$ and $C_x^{2nd}\left(t_i\right),$ have similar abnormal features? Is the abnormal problem caused by the instrument noise (fluctuations)? Is it possible to use a polynomial function to fit abnormal patterns in ${\overline{C}}_{w7}$ and $T_w$ to facilitate a more objective analysis of the issues in future studies? Do the observed abnormal features constantly persist during each of the orbits? Below are discussions for those questions.

Firstly, ${\overline{C}}_{w7}$ in the above figures represents an average of measurements at two different viewing directions. To identify any irregular characteristics in individual measurements, we also utilize (4) for two separate measurements (namely, $C_x^{1st}\left(t_i\right)$ and $C_x^{2nd}\left(t_i\right))$ to compute the average across seven scans of the data, i.e., ${\overline{C}}_x^{1st}\left(t_j\right)$ and ${\overline{C}}_x^{2nd}\left(t_j\right)$. Furthermore, we conduct an analysis of time series data for both ${\overline{C}}_{w7}^{1st}$ and ${\overline{C}}_{w7}^{2nd}$ using (2) for each of the individual measurements. Both ${\overline{C}}_{w7}^{1st}$ and ${\overline{C}}_{w7}^{2nd}$ exhibit anomalous characteristics similar to ${\overline{C}}_{w7}$ (the figure is omitted). This suggests that the warm counts at two different viewing directions also perform anomalously. Hereinafter, we will utilize the averaged of these two individual measurements in accordance with our operational processing.

Secondly, it is necessary to understand whether the anomalous patterns and time lag are caused by the instrument noise-caused fluctuations. The noise-caused fluctuations in the time series of ${\overline{C}}_{w7}$ and $T_w$ can be largely smoothed through averaging more neighboring scans. Hence, a sensitivity analysis is conducted by applying an average to more neighboring scans of the data on 28 May 2021. The sensitivity analysis consists of seven types of averaged data: N = 3, 4, 5, 6, 7, 10, and 20, in (4), which correspond to 7, 9, 11, 13, 15, 21, and 41 neighboring scans, respectively. As a result of this design, seven distinct sets of averaged data are obtained for the warm count and kinetic temperature: ${\overline{C}}_{w7}, {\overline{C}}_{w9}, {\overline{C}}_{w11}, {\overline{C}}_{w13}, {\overline{C}}_{w15}, {\overline{C}}_{w21}, {\overline{C}}_{w41}$ and ${\overline{T}}_{w7}, {\overline{T}}_{w9}, {\overline{T}}_{w11}, {\overline{T}}_{w13}, {\overline{T}}_{w15}, {\overline{T}}_{w21}, {\overline{T}}_{w41}.$ Both ${\overline{C}}_{w7}$ and ${\overline{T}}_{w7}$ are included for comparison since they represent data from the same orbit length.

As a demonstration, Figure 4a,b show the time series of warm count and kinetic temperature during the first orbit period through averaging 11 and 21 neighboring scans, i.e., ${\overline{C}}_{w11}, {\overline{C}}_{w21},$ and ${\overline{T}}_{w11}, {\overline{T}}_{w21}.$ The noise-caused fluctuations in warm count are smoothed with slightly reduced values of both maximum and minimum during an orbit of observations through averaging more neighboring scans. However, the anomalous features of the pattern are not changed in warm count and kinetic temperature. A similar time lag with about 18 min is also observed in the kinetic temperature orbital cycle behind the warm count cycle, based on the results by using more neighboring scans. Regarding the time lag between the anomalies, the kinetic temperature anomaly occurs for about 2 min behind the warm count anomaly by using 11 and 21 neighboring scans, which is also similar to that by using 7 neighboring scans in the average. In general, the abnormal pattern problem persists in the blackbody calibration target across all types of averaged data sets. The time lag magnitudes also show consistency across different averaging methods. Thus, these findings suggest that the observed abnormal features are not a result of fluctuations. Increasing the number of neighboring scans averaged can indeed enhance the identification of these abnormal issues.

Thirdly, more data sets are analyzed to understand whether those anomalous features constantly exist in each of the orbit AMSU-A data sets in channels 1 and 2. Figure 5 further presents the time series of $T_W$ and $C_W$ in channel 1 for four randomly selected days, denoting one day in each of the four seasons, i.e., 18 December 2019, 18 March 2020, 18 July 2020, and 18 September 2020. Hereinafter,${\overline{C}}_{w7}$ is replaced by $C_W$ to simplify our descriptions. Only one orbit of the data per day are plotted since the rest of the orbits have similar anomalous features for the same day. The features of channel 2 are similar to those of channel 1 (the figure is omitted).

In view of the results in Figure 5, it is clearly found that the phenomena of the anomalous pattern and time lag constantly persist in both $T_W$ and $C_W$ for the four days. Certainly, the magnitude of the maximum anomaly pattern is slightly variable with the season. For instance, the maximum $∆T_{Wmax}$ ($T_W$ anomaly) is about 0.1 K, 0.07 K, 0.08 K, and 0.09 K for the four days, respectively. For the $C_W$ anomaly, its maximum magnitude is changed primarily from three to five counts, obviously affected by noise-caused fluctuations. The differences in magnitude should be related to changeable solar intrusion with the season and to the fluctuations. Regarding the anomaly pattern length, it is typically more than 16 min, even based on a conservative estimate as mentioned above. More data sets are analyzed in Section 3.2 below, leading to a similar conclusion.

To estimate the time lag of the orbital cycle of $T_W$ behind that of $C_W$, we still use the two methods as mentioned above: the time difference between the normal maximum or the minimum positions in $T_W$ and $C_W$ in the absence of the anomaly. Approximate scales about the time difference are added in each of the figures. Generally, the resultant results are comparable using the two methods with an exception in Figure 5b. The time lag seems changeable with the season, with a long time around 18 min in summer and early fall (seen 18 July and 18 September 2020) and a short time down to about 9 min in winter and early spring (seen 18 March 2020). However, this conclusion is to be further validated since uncertainties remain in the current analysis. Moreover, we observe the time lag between the $T_W$ and $C_W$ anomalies for the data among the four different days, which is in a couple of minutes, further confirming the authenticity of the identified abnormal patterns and the time lag in the blackbody calibration target in channels 1 and 2 associated with the antenna unit A2.

Lastly, it is crucial to explore the feasibility of describing the abnormal patterns in both $T_W$ and $C_w$ using an appropriate polynomial function. Such an analysis will prove beneficial for our future studies, aiding in the development of an objective anomaly-correction algorithm for those issues. In this instance, we utilize data solely from the anomalous pattern occurring during the first orbit of 28 May 2021, to provide a demonstration of the viability of this concept. Figure 6a,b compare observed and fitted values about $T_W$ and $C_w$ in the data. We tested several degrees of polynomial functions to fit the variations of $T_W$ and $C_w$ with time. For the anomaly-contaminated $T_W$, the fourth degree of polynomial function can provide the best fitting to the detected anomalous variation with an R-squared value up to 0.97. Other lower degrees of polynomial functions still can produce an R-squared value above 0.9 (see Figure 6a). However, for the anomaly-contaminated $C_W$, a higher degree of polynomial function can not obviously improve the fitting performance due to noise-caused high fluctuations in $C_W$ (e.g., see Figure 3 above). A further smoothing for $C_W$ should be first needed to reduce the impact of fluctuations on the fitting performance of the anomaly-contaminated data. Additional analyses are also needed in the future to develop a robust polynomial fitting algorithm about abnormal patterns in both $T_W$ and $C_w$ by covering different seasons of the anomaly-contaminated data.

In summary, two anomalous features in the blackbody calibration target in channels 1 and 2, namely abnormal pattern and time lag, have been found to persist consistently during each orbit. The anomalous pattern can last for more than 16 min during each orbit, with the blackbody kinetic temperature anomaly occurring a couple of minutes after the warm count anomaly. There is a good potential to describe the anomalous patterns associated with the blackbody kinetic temperature and warm count in a polynomial function, although certain errors remain in fitting. Furthermore, the orbital variation of the blackbody kinetic temperature delays for a few minutes in comparison with that of the blackbody warm count. This indicates that the blackbody kinetic temperature responds more slowly to changes of the environmental temperature than the blackbody radiative temperature (warm count). However, uncertainties remain with our analysis, emphasizing the need for the development of a precise physical model about the anomaly and time lag problems through future studies.

4. Implication for Calibration Radiometric Accuracy

It is important to understand the possible impacts of the anomalous problems on the accuracy of AMSU-A TDR data. Currently, there are uncertainties in determining the anomalous increases (i.e., $∆C_w$ and $∆T_w$) by using the above approximate method. Hence, this study only investigates the possibly largest implications of the problems during each orbit for the calibration accuracy of antenna temperatures in channels 1 and 2. According to our analysis, the anomalous pattern problem can have a larger impact on the calibration accuracy of the antenna temperature, so more assessments will be given to it here, while a simple assessment will be conducted for the time lag problem.

Generally, the impact assessment can be conducted using the two-point calibration equation in (1). For demonstration purposes, the chart in Figure 7 illustrates the calibration process in the absence/presence of the anomalous error $∆T_W.$ The nonlinearity effect is neglected in the chart because the contribution of the nonlinearity $Q$ in (2) is usually less than one Kelvin (as reported in [33] for Metop-C AMSU-A). Moreover, the blackbody temperature operates within a relatively small dynamic range from orbit to orbit, and as a result, the nonlinearity effect at the blackbody temperature with a small variation is insignificant. In view of Figure 7, with a positive anomaly in $T_w$, point $W$ shifts to point $W^{\prime }$, and the radiance $R_s$ increases to $R_s^{\prime }$ due to a reduced slope $C{W}^{\prime }$ (i.e., the channel gain). Similarly, with a positive anomaly in $C_w$, the radiance $R_s$ decreases due to an increased slope. Through the combined effect of two anomalies in $T_w$ and $C_w$, the accuracy of radiance can be degraded.

Mathematically, in the radiance domain, we can derive the error in Earth scene radiance in the presence of $∆C_w$ and $∆R_w$ by applying a derivative to (1) with respect to both $R_w$ and $C_w$ without the nonlinearity item $Q.$ Then, approximately, we derive the following expression from it to estimate radiance errors in terms of errors in both $R_w$ and $C_w.$

$${∆R}_S\approx \frac{C_S-C_C}{C_w-C_C}(∆R_w-\frac{1}{G}∆C_w).$$

(5)

For end-users, the output corresponding to $R_S$ is usually presented in temperature unit instead of radiance. To convert between radiance and temperature, the inverse of the Planck function is utilized. On the other hand, $R_w$ is obtained from $T_w$ via the Planck function [12]. Therefore, the antenna temperature error ${∆T}_A$ is discussed below instead of the radiance error, although the conversion from radiance to temperature is used in this analysis. Thus, (5) is re-written as follows:

$${∆T}_A=-\frac{C_S-C_C}{C_w-C_C}\frac{1}{G_T}∆C_w+\frac{C_S-C_C}{C_w-C_C}∆T_w,$$

(6)

where $G_T$ is the gain expressed in the domain of temperature to distinguish it from $G$ that is expressed in in the domain of radiance (see (3) above). Additionally, the antenna temperature is denoted by using $T_A$ instead of $T_s$ since $T_s$ is widely assumed to represent the surface temperature in various applications.

Firstly, for the anomalous pattern problem, which causes sudden and lasting increases in both $C_w$ and $T_w$, i.e., $∆C_w$ and $∆T_w$, theoretically, we can assume that

$$∆C_w=C_w^{OBS}-C_w^{fit},$$

(7)

$$∆T_w=T_w^{OBS}-T_w^{fit},$$

(8)

where the superscript ‘OBS’ and ‘fit’ represent the measurement and fitted values, respectively, for each of $T_w$ and $C_w$ during the anomalous period.

$C_w^{fit}$ and $T_w^{fit}$ represent the anomaly-free warm count and kinetic temperature of the blackbody target, respectively, during the solar contamination. However, we do not have the truth about the anomaly-free warm count and kinetic temperature of the blackbody target during each orbit. To understand the possibly largest impact of the anomalies during each orbit, we make an approximate estimate about them by using linear fitting with the assumption that $∆T_w=0.0$ and $∆C_w=0.0$ at the two edge points of the abnormal patterns.

By using Figure 4a as an example, two pairs of points ($p_1$, $p_2$) and ($p_1^{\prime }$, $p_2^{\prime })$ represent two edge points for the $C_w$ and $T_w$ anomalous patterns in the first orbit of the data on 28 May 2021. It is conservatively estimated that the maximum abnormal increase in $C_w$ (denoted as $∆C_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$ in the figure) is about four counts, while that in $T_w$ (denoted as $∆T_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$) is about 0.07 K, as discussed in Section 3 above. According to (6), for the data in channel 1 in Figure 4a, the resultant maximum radiance error due to $∆C_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$, which is denoted as ${∆T}_{Amax}^{{∆C}_w},$ is approximately 0.16 K, and the radiance error due to $∆T_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$, which is denoted as ${∆T}_{Amax}^{{∆T}_w},$ is about 0.05 K. Similar radiance errors exist in channel 2. Notice that the overall maximum radiance error (${{∆T}_A}_{max})$ due to the anomaly pattern issue is a combined impact of $∆C_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$ and $∆T_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$ through (6), where each of them has a different sign, as described in (6). As estimated above, the radiance error due to $∆C_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$ is much larger than that due to $∆T_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$, so the overall radiance errors are dominated by $∆C_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$.

Certainly, the magnitudes of both $∆C_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$ and $∆T_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$ within the anomalous pattern can change slightly with an updated ending position of the anomaly or a different fitting method. For instance, $∆T_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$ could be on the order of 0.1 K, which is bigger than our current estimate, if the anomaly ended at the point $p_3^{″}$ instead of $p_3^{\prime }$, which might be more reasonable (see Figure 4a). Hence, this study only provides conservative estimates for the largest anomalous increases within the two anomalous patterns. Due to the important impact of the anomalous pattern problem, a similar assessment is applied to 25 days of the data sets spanning 2 years. Figure 8a,b provide the daily-averaged largest radiance errors (absolute value) at the two channels for ${∆T}_{Amax}^{{∆C}_w},{∆T}_{Amax}^{{∆T}_w}$ and ${{∆T}_A}_{max},$ respectively. Generally, the daily averaged radiance errors from each of the anomalies primarily distribute in a range from 0.04 K to 0.07 K for ${{|∆T}_A^{{∆T}_w}|}_{max}$ and in the range from 0.15 K to 0.25 K for ${{|∆T}_A^{{∆C}_w}|}_{max}$. The combined radiance errors, ${{∆T}_A}_{max},$ vary in the range from 0.14 K to 0.24 K, depending on orbit, season, and channel.

Table 3. Averaged maximum antenna temperature errors due to various error sources and the corresponding standard deviations for channels 1 and 2, derived from the entire test data sets used in Figure 8.

Channel Index	${\mathit{T}}_{\mathit{A}}$ Error $\mathbf{Due} \mathbf{to} {∆\mathit{C}}_{\mathit{w}\mathit{m}\mathit{a}\mathit{x},\mathbf{S}\mathbf{o}\mathbf{l}\mathbf{a}\mathbf{r}}$ (K)		${\mathit{T}}_{\mathit{A}}$ Error $\mathbf{Due} \mathbf{to} {∆\mathit{T}}_{\mathit{w}\mathit{m}\mathit{a}\mathit{x},\mathbf{S}\mathbf{o}\mathbf{l}\mathbf{a}\mathbf{r}}$ (K)		${\mathit{T}}_{\mathit{A}}$ Error $\mathbf{Due} \mathbf{to} \mathbf{Both} {∆\mathit{C}}_{\mathit{w}\mathit{m}\mathit{a}\mathit{x},\mathbf{S}\mathbf{o}\mathbf{l}\mathbf{a}\mathbf{r}}$$\mathbf{and} {∆\mathit{T}}_{\mathit{w}\mathit{m}\mathit{a}\mathit{x},\mathbf{S}\mathbf{o}\mathbf{l}\mathbf{a}\mathbf{r}}$ (K)
	$\overline{{|∆\mathit{T}}_{\mathit{A}\mathit{m}\mathit{a}\mathit{x}}^{{∆\mathit{C}}_{\mathit{w}}}|}$	${\mathit{\sigma }}_1$	$\overline{{|∆\mathit{T}}_{\mathit{A}\mathit{m}\mathit{a}\mathit{x}}^{{∆\mathit{T}}_{\mathit{w}}}|}$	${\mathit{\sigma }}_2$	$\overline{{|∆\mathit{T}}_{\mathit{A}\mathit{m}\mathit{a}\mathit{x}}|}$	${\mathit{\sigma }}_3$
1	0.22	0.09	0.05	0.01	0.16	0.05
2	0.19	0.06	0.05	0.01	0.17	0.05

Notes: (1). $\overline{{|∆T}_{Amax}^{{∆C}_w}|}$, $\overline{{|∆T}_{Amax}^{{∆T}_w}|}$, and $\overline{{|∆T}_{Amax}|}$ denote the average of all daily-averaged maximum antenna temperature errors with regard to the largest anomalies in $C_w$, $T_w$ and both of them, respectively. (2). ${\sigma }_1$, ${\sigma }_2$, and ${\sigma }_3$ represent the standard deviations from $\overline{{|∆T}_{Amax}^{{∆C}_w}|}$, $\overline{{|∆T}_{Amax}^{{∆T}_w}|}$, and $\overline{{|∆T}_{Amax}|}$ separately. (3). The explanations of ${∆C}_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$ and ${∆T}_{wmax,\mathrm{S}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}}$ are referred to Figure 4 above.

presents the averaged maximum antenna temperature errors due to various error sources and the corresponding standard deviations for channels 1 and 2, which are derived from the entire test data sets used in Figure 8. Evidently, despite seasonal fluctuations, the warm count error source, $\overline{{|∆T}_{Amax}^{{∆C}_w}|},$ is the predominant factor contributing to radiance errors, surpassing the influence of the blackbody kinetic temperature error source.

Secondly, for the time lag problem in the $T_w$ orbital cycle in comparison to the $C_w$ cycle, a simple impact assessment is performed here. The error in $C_w$ is reasonably assumed to be zero since the time lag is defined against the orbital cycle of $C_w$. So, the impact on the calibration accuracy of $T_A$ is determined by the error in $T_w$ due to the time lag, i.e., ${∆T}_A=\frac{C_S-C_C}{C_w-C_C}∆T_w$. Generally, the $T_w$ varies by a small variation (~0.4 K) during each orbit, and the maximum error in $T_w$ (denoted as $∆T_{wmax, Lag}$ in the figure) due to the time lag is only in the order of 0.1 K. A conceptual demonstration is added in Figure 4a, which uses 11 neighboring scans for the average, since Figure 3a has been crowded with multiple notes or lines. The resulting maximum error in $T_A$ per orbit is in the order of 0.08 K, changing with the magnitudes of $C_S,C_C$, and $C_w$. Certainly, for most of the data during the orbit, the resulting $T_A$ error should be much smaller than this. In addition, the errors during most of the orbit might fall within the range of the instrument’s noise level. This might partly explain why the radiance errors resulting from this entire time lag were not identified in previous calibration studies of AMSU-A instruments.

It is important to mention that the magnitudes of the radiance errors are computed without taking into account instrument noise. In practice, the AMUS-A instrument always exhibits a certain level of noise in its measurements [10,11,14], which is quantified by NEDT. Traditionally, the onboard AMSU-A NEDT has been determined simply based on the standard deviation of warm counts per orbit [5]. Other methods are also applicable by further including noise contribution from other calibration parameters, which can result in small differences in magnitude [10,14,36,37]. The estimated NEDT values for channels 1 and 2 are approximately 0.18 K, referring to the ICVS web-based monitoring system in https://www.star.nesdis.noaa.gov/icvs/status_MetOPC_AMSUA.php, accessed on 5 April 2019. Therefore, this NEDT introduces an additional uncertainty up to 0.18 K to the above-estimated radiance errors.

Therefore, the calibration accuracy of the AMSU-A antenna temperature in channels 1 and 2 can be affected by the anomalous pattern problem and the overall time lag in the $T_w$ orbital cycle in comparison to the $C_w$ orbital cycle. Particularly, the warm count anomaly can lead to the largest radiance errors approximately from 0.14 K to 0.24 K. This estimate can be affected by instrument noise. Therefore, it is necessary to investigate the root cause to the warm count anomaly along with the kinetic temperature anomaly in the following section. The root cause to the overall time lag of the $T_w$ orbital cycle is deferred to future studies when it is well understood.

5. Root Cause Analysis of the Anomalous Pattern Problem

Previous studies on AMSU-A calibration parameters have typically focused on short-term and long-term stabilities, as seen in references [9,12,13], while the long-term trends of those parameters for all 15 AMSU-A channels are routinely monitored in the NOAA ICVS web site (https://www.star.nesdis.noaa.gov/icvs/index.php, accessed on 6 June 2012). The abnormal patterns in $T_w$ and $C_w$ were not addressed in previous studies. Although there is no known reference for the AMSU-A, a solar anomalous effect was reported as early as 1998 for the AVHRR instrument flown in the NOAA polar orbiting satellites. The AVHRR instrument suffered from solar contaminations when exposed to sunlight at spacecraft sunrise, which was related to a large scan angle within the AVHRR observations. The AMSU-A instrument also has a large scan angle, which increases the technical risk of solar intrusion to the AMSU-A2 blackbody calibration target. Moreover, other established facts below support the existence of solar intrusion, as described below.

Firstly, the fact that solar intrusion is the root cause of the AMSU-A2 calibration anomaly is supported by the orbital simulation for Metop-C AMSU-A observations through consistent occurrence time and solar angle position. The orbital simulation was performed using the physics-based and industry standard software package Satellite Toolkit (STK) version 11.5. STK has many modules and uses several physical models, and the model used in this study was the Simplified General Propagation model (SGP4). SGP4 was initially published along with sample code in 1988 and further refined over time [38] for accurately predicting the position of a satellite at any given time with the TLE (Two-Line Elements) provided by NORAD (North American Aerospace Defense Command). Specifically, it can calculate the solar angles at the spacecraft and AMSU-A instrument at the exact time of the selected orbit using the “Two-Line-Elements” (TLEs), with the industry standard STK or Satellite Toolkit. The calculated information also includes the time of the satellite sunrise and sunset based on the solar angles at the spacecraft. The SGP4 prediction accuracy is around 1 km on the Earth with the most up-to-date TLEs which are released daily (available from https://www.celestrak.com, accessed on 1 January 1986) [39]. Therefore, the orbital simulation can provide a very realistic scenario of the satellite position in relation to the Earth, Sun, and instrument on the Metop-C satellite.

Figure 9a is the orbit simulation for the first orbit of the AMSU-A observations on 28 May 2021. According to the orbit simulation results, two satellite terminator times, i.e., the time of satellite sunset and sunrise, happen in 1:09 UTC and 1:41 UTC, respectively, for the selected orbit, which is also added in the figure. Note that the abovementioned abnormal pattern in $C_w$ during the same orbit happens approximately from 1:02 UTC to 1:19 UTC with uncertainty of about 1 min, with the peak at a time close to the sunset time, seen in Figure 4 above. In other words, the solar contamination impact takes place when the spacecraft is in proximity to the satellite terminator roughly 7–8 min prior to spacecraft sunset. Regarding an additional more than 8 min of anomalous pattern, it is a cooling process from the abnormally increased peak to zero that is associated with the thermal conductivity characteristics of the blackbody target. However, further study is needed to quantify this cooling process. Therefore, the starting and peaking positions of the anomalous pattern are consistent with the satellite position relative to the Sun in the orbit simulation. This consistency shows that solar intrusion can be the root cause of the AMSU-A2 calibration anomaly.

Secondly, the specific structure of the AMSU-A instrument confirms the feasibility of the solar intrusion. Within the AMSU-A instrument, the warm load targets were designed to be surrounded by a metal shroud to prevent stray radiation from external sources [34,40]. In fact, the above-mentioned anomalous features were not observed in pre-launch in the Metop-C AMSU-A instrument. This fact implies that the design of AMSU-A is mostly reasonable. However, it should be challenging to capture solar intrusion issue since the ground experiments for AMSU-A instruments were made under limited circumstances. It is possible that the on-orbit warm load shroud could not be perfectly mated in all directions with the shroud surrounding the rotating reflector antenna. Especially, AMSU-A instrument has a large scan angle of 96.66°, as shown in Figure 9b about the AMSU-A scan geometry. This large scan angle likely offers an easy entrance to sunlight under certain large SZA circumstances.

Thirdly, the solar intrusion to the blackbody target is confirmed by a similar feature in instrument temperature ($T_{Shelf}$) associated with the AMSU-A2 channels. Figure 10 displays the time series of the AMSU-A2 $T_{Shelf}$, where $T_w$ is included for comparison. According to the analysis of the $T_w$ anomaly, the solar radiance contamination remains primarily from the point $p_1^{\prime }$ to the point $p_3^{\prime }$ with a peak around the point $p_2^{\prime }.$ Obviously, during this period, the $T_{Shelf}$ also exhibits a relatively rapid increase (a positive anomaly), which further confirms the presence of extraneous radiance rather than a warm load calibration source.

Furthermore, solar intrusion happens on each orbit of AMSU-A observations in channels 1 and 2, which is confirmed by the analysis in the previous section. A follow-up question is whether solar intrusion at each orbit always occurs under circumstances with large SZAs. The position of solar contamination is theoretically a function of many factors, including instrument alignment within the satellite, orbit, season, and time, as described for the AVHRR solar contamination [28]. However, we lack this information from either pre-launch or flight measurements to establish a solid physical model for this analysis. While this study did not yield precise values for the starting and ending positions of the anomalies including corresponding SZA due to lack of sufficient information, we have determined approximate estimates for these parameters based on observable and abnormal increases in both $T_w$ and $C_w$ (see the analysis in Section 3.1 above). The analysis has been further applied to 25 days of the Metop-C AMSU-A data sets spanning 2 years in channels 1 and 2 used in Figure 8 (Section 4 above). Through the analysis, the SZA values with the starting and ending positions of the anomalies in $T_w$ can be obtained from the AMSU-A TDR data. As shown in Figure 11, the magnitudes of SZAs are typically larger than 95°. Additionally, both starting and ending SZAs display a stable semi-annual or annual pattern. For example, the daily-averaged starting SZA shows a maximum of 107° typically in February and September, and a minimum of 102° in May (June) and November (December). The daily-averaged ending SZA behaves in an annual pattern, reaching the peak of 149° typically in June and the lowest of 138° in February. Overall, all orbital anomaly events during two years are found to occur under large SZAs with a minimum of 95°.

Table 4. Averaged Solar Zenith Angle (SZA) values at the starting and ending positions of the detected anomaly in $T_w$ for all abnormal events depicted in Figure 11.

Starting SZA (°)		Ending SZA (°)
$\overline{{\mathit{\theta }}_{\mathit{s}\mathit{t}\mathit{a}\mathit{r}\mathit{t}}}$	${\mathit{\sigma }}_4$	$\overline{{\mathit{\theta }}_{\mathit{e}\mathit{n}\mathit{d}}}$	${\mathit{\sigma }}_5$
104.35	1.53	144.12	0.67

Notes: (1). $\overline{{\theta }_{start}}$ and $\overline{{\theta }_{end}}$ represents the averaged starting and ending SZAs, respectively, in the presence of the anomalous patterns in $T_w$ across the whole data sets. (2). ${\sigma }_4$ and ${\sigma }_5$ denote the averaged uncertainty of all daily-averaged $\mathrm{S}\mathrm{Z}\mathrm{A}\mathrm{s}$ from $\overline{{\theta }_{start}}$ and $\overline{{\theta }_{end}}$, respectively.

presents the averaged SZA values at the starting and ending positions of the detected anomalies in $T_w$ for the entire anomalous events depicted in Figure 11. So, the averaged affected regions by solar intrusion cover the variation of about 40° in SZA, with an averaged uncertainty less than 2°.

Therefore, the above facts demonstrate that solar illumination is accountable for the anomalies in both the radiative temperature ($C_w$) and kinetic temperature ($T_w$) observed in the AMSU-A blackbody target associated with the antenna unit A2. This assertion is supported through the Metop-C AMSU-A orbit simulation, the AMSU-A sensor structure design, the AMSU-A2 instrument shelf temperature ($T_{Shelf}$) anomaly, the specific occurrence circumstances with large SZAs, and similar SZA regions during each of the orbits in a day.

6. Summary and Conclusions

This study presents the first discovery of both the solar intrusion-caused anomalous pattern and the time lag problems on the Metop-C AMSU-A data in channels 1 and 2 associated with the antenna unit A2. The anomalous pattern is characterized by abnormal increases in both $C_w$ and $T_w,$ typically lasting for more than 16 min during each orbit of satellite observations. The peaking anomalous increase during each orbit varies approximately from three to five counts for $C_w$ and from 0.06 to 0.1 K for $T_w$, depending upon orbit, season, and channel. By analyzing 25 days of the data spanning 2 years from 18 December 2019 through 18 December 2021, the resultant maximum antenna temperature errors due to abnormal increases in $C_w$ are characteristically in the range from 0.15 K to 0.25 K, which dominated the radiance error during the abnormal pattern period, since the maximum errors due to the abnormal increase in $T_w$ are in the range approximately from 0.04 K to 0.07 K. The combined largest radiance errors vary approximately from 0.14 K to 0.24 K, depending upon orbit, season, and channel. Regarding the time lag problem, the orbital variation of $T_w$ has a delay typically of more than 9 min in comparison with that of $C_w$, which can cause an antenna temperature error up to 0.1 K. Hence, this study underscores the imperative need in future study to rectify radiance errors to reconstruct a more accurate long-term Metop-C AMSU-A radiance data set in channels 1 and 2, especially for climate studies.

Furthermore, this study further investigates the solar intrusion on the blackbody calibration target in channels 1 and 2, which is the root cause of the abnormal patterns in $C_w$ and $T_w$. Solar illumination is constantly observed during each orbit near the satellite terminator, and its impact occurs in close proximity to the satellite terminator a few minutes before spacecraft sunset, and this influence can persist for a few additional minutes after spacecraft sunrise. Solar contamination results in a blackbody calibration problem for channels 1 and 2 within each orbit, manifesting as abrupt increases in kinetic temperature and radiative temperature (warm count) of the AMSU-A2 blackbody calibration target. Solar intrusions typically occur under circumstances with solar zenith angles above 95°. Moreover, solar intrusion leads to abrupt increases in AMSU-A2 shelf temperature.

While this study has undertaken an initial assessment of the anomalous pattern problem, including the feasibility of fitting these anomalous patterns using polynomial functions, and has identified the root cause (solar contamination) and resultant radiance calibration errors, it is essential to acknowledge that several uncertainties persist in the analysis. For example, the determination of the occurrence of each anomaly event in either $C_w$ or $T_w$ relies on an approximation. This approximation assumes the $T_w$ anomaly effect during each orbit is symmetric, where the duration from the onset of the anomaly to its peak is equivalent to the duration from the peak to the conclusion of the anomaly. The results have shown that the $T_w$ for a few scan lines after the derived termination of the anomaly is still not smooth. This suggests that the current approximations used in this study might underestimate the impact of the anomaly. Additionally, the $C_w$ and $T_w$ anomalies are estimated in this study based on a linear fitting approximation for the anomaly-free $C_w$ and $T_w$. These approximations might under/overestimate slightly magnitudes of ${∆C}_w$ and ${∆T}_w$ including their peak values. Finally, we have not investigated the root cause to the time lag problem.

Overall, the discoveries in this study necessitate further research to reconstruct Metop-C AMSU-A2 TDR data by mitigating the radiance errors due to the solar intrusion effect and the time lag problem. The outcomes of this study hold significance for the analysis of solar contamination in the AMSU-A2 unit aboard the NOAA-18, NOAA-19, Metop-A, and Metop-B, where solar intrusion is partially present.